{-# 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.Algebra.Construct.NaturalChoice.MinOp 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.Sigma
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.Structures
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Function.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Base.Double
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Construct.NaturalChoice.MinOp._._≈_
d__'8776'__20 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__20 :: T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> ()
d__'8776'__20 = T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._._≲_
d__'8818'__22 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> ()
d__'8818'__22 :: T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> ()
d__'8818'__22 = T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Associative
d_Associative_100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Associative_100 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Associative_100 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Commutative
d_Commutative_104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Commutative_104 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Commutative_104 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Congruent₁
d_Congruent'8321'_106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny) -> ()
d_Congruent'8321'_106 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny)
-> ()
d_Congruent'8321'_106 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Congruent₂
d_Congruent'8322'_108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Congruent'8322'_108 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Congruent'8322'_108 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Idempotent
d_Idempotent_112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Idempotent_112 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Idempotent_112 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Identity
d_Identity_116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Identity_116 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Identity_116 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.LeftIdentity
d_LeftIdentity_130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftIdentity_130 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_LeftIdentity_130 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.LeftZero
d_LeftZero_134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftZero_134 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_LeftZero_134 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.RightIdentity
d_RightIdentity_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightIdentity_142 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_RightIdentity_142 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.RightZero
d_RightZero_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightZero_146 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_RightZero_146 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Selective
d_Selective_148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Selective_148 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Selective_148 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Zero
d_Zero_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Zero_150 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Zero_150 = ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.IsBand
d_IsBand_156 :: p -> p -> p -> p -> p -> p -> ()
d_IsBand_156 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsCommutativeSemigroup
d_IsCommutativeSemigroup_170 :: p -> p -> p -> p -> p -> p -> ()
d_IsCommutativeSemigroup_170 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsMagma
d_IsMagma_184 :: p -> p -> p -> p -> p -> p -> ()
d_IsMagma_184 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsMonoid
d_IsMonoid_186 :: p -> p -> p -> p -> p -> p -> p -> ()
d_IsMonoid_186 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsSelectiveMagma
d_IsSelectiveMagma_192 :: p -> p -> p -> p -> p -> p -> ()
d_IsSelectiveMagma_192 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsSemigroup
d_IsSemigroup_194 :: p -> p -> p -> p -> p -> p -> ()
d_IsSemigroup_194 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsSemilattice
d_IsSemilattice_196 :: p -> p -> p -> p -> p -> p -> ()
d_IsSemilattice_196 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp.x⊓y≤x
d_x'8851'y'8804'x_1626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8804'x_1626 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8804'x_1626 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_1626 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
du_x'8851'y'8804'x_1626 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_1626 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_1626 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3
  = let v4 :: t
v4
          = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
              (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
              AgdaAny
v2 AgdaAny
v3 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v4 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v5
           -> let v6 :: T_IsTotalPreorder_118
v6
                    = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v6))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v2
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                            T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)))
                   (let v7 :: T_IsTotalPreorder_118
v7
                          = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                              (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsPreorder_70 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v7))
                         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v5
           -> let v6 :: T_IsTotalPreorder_118
v6
                    = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v6))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v3
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                            T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.x⊓y≤y
d_x'8851'y'8804'y_1652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8804'y_1652 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8804'y_1652 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_1652 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
du_x'8851'y'8804'y_1652 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_1652 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_1652 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3
  = let v4 :: t
v4
          = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
              (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
              AgdaAny
v2 AgdaAny
v3 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v4 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v5
           -> let v6 :: T_IsTotalPreorder_118
v6
                    = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v6))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v2
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                            T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v5
           -> let v6 :: T_IsTotalPreorder_118
v6
                    = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v6))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v3
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                            T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)))
                   (let v7 :: T_IsTotalPreorder_118
v7
                          = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                              (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsPreorder_70 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v7))
                         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))))
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-comm
d_'8851''45'comm_1674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'comm_1674 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'comm_1674 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
du_'8851''45'comm_1674 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3
  = let v4 :: t
v4
          = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
              (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
              AgdaAny
v2 AgdaAny
v3 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v4 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v5
           -> let v6 :: t
v6
                    = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                   (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                      ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                         T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6)))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   AgdaAny
v2
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v3 AgdaAny
v2)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                      T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v3 AgdaAny
v2)
                         AgdaAny
v2
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                            T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v2 AgdaAny
v5))))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v5
           -> let v6 :: t
v6
                    = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                   (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                      ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                         T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6)))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   AgdaAny
v3
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v3 AgdaAny
v2)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                      T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v3 AgdaAny
v2)
                         AgdaAny
v3
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                            T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v2 AgdaAny
v5))))
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-congˡ
d_'8851''45'cong'737'_1700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'cong'737'_1700 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'cong'737'_1700 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'cong'737'_1700 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'cong'737'_1700 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = let v6 :: t
v6
          = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
              (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
              AgdaAny
v2 AgdaAny
v3 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v6 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v7
           -> (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
                ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                      ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                         (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v4)
                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                      ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v2 AgdaAny
v4)
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v2 AgdaAny
v4)
                      ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v4))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                         T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v4
                         (let v8 :: T_IsTotalPreorder_118
v8
                                = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                    (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                               ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v8))
                               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7)))))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                      T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v7
           -> (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
                ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                      ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                         (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v4)
                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                      ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v2 AgdaAny
v4)
                      ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                         T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v4)
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v4)
                         ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                               ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                  (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                               AgdaAny
v2 AgdaAny
v4))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                            T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v4
                            (let v8 :: T_IsTotalPreorder_118
v8
                                   = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                       (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                             AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                                  ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                     (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v8))
                                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7)))))
                      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                      T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7))
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-congʳ
d_'8851''45'cong'691'_1738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'cong'691'_1738 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'cong'691'_1738 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_1738 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'cong'691'_1738 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'cong'691'_1738 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_1738 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
      ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            AgdaAny
v3 AgdaAny
v2)
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            AgdaAny
v2 AgdaAny
v3)
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            AgdaAny
v4 AgdaAny
v2)
         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
               ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                  (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2 AgdaAny
v3)
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2 AgdaAny
v4)
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v4 AgdaAny
v2)
            ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
               ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                  ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                     (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2 AgdaAny
v4)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v4 AgdaAny
v2)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v4 AgdaAny
v2)
               ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                  ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                     ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v4 AgdaAny
v2))
               ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
            ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))
         ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-cong
d_'8851''45'cong_1748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'cong_1748 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'cong_1748 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong_1748 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8851''45'cong_1748 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'cong_1748 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong_1748 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = let v8 :: t
v8
          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8)))
         (((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2)
            (\ AgdaAny
v9 AgdaAny
v10 -> AgdaAny
v9) AgdaAny
v4 AgdaAny
v5)
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
            (\ AgdaAny
v9 AgdaAny
v10 -> AgdaAny
v10)
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2)
            AgdaAny
v4 AgdaAny
v5)
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
            (\ AgdaAny
v9 AgdaAny
v10 -> AgdaAny
v10)
            (\ AgdaAny
v9 ->
               (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                 AgdaAny
v9 AgdaAny
v5)
            AgdaAny
v2 AgdaAny
v3)
         ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7))
         ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_1738 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-assoc
d_'8851''45'assoc_1762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'assoc_1762 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'assoc_1762 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_1762 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_'8851''45'assoc_1762 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_1762 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_1762 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = let v5 :: t
v5
          = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
              (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
              AgdaAny
v2 AgdaAny
v3 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v6 :: t
v6
             = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
                 (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                    (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
                 AgdaAny
v3 AgdaAny
v4 in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v5 of
            MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v7
              -> case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v6 of
                   MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v8
                     -> (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
                          ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                             T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                             ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                   (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                             ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
                                AgdaAny
v4)
                             ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                                AgdaAny
v2 AgdaAny
v4)
                             ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                                AgdaAny
v2
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                             ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                                ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                   ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                      (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v4)
                                (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                      T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                                ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                   T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                      ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                         (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                      T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                      T_MinOperator_84
v1 AgdaAny
v2
                                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                         T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                                      ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                         T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
                                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                         T_MinOperator_84
v1 AgdaAny
v2
                                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                            T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                         T_MinOperator_84
v1 AgdaAny
v2
                                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                            T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                                      ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                            T_MinOperator_84
v1 AgdaAny
v2
                                            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                               T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4)))
                                      ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                         T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                            T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4)
                                         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                                            T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4 AgdaAny
v8)))
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                                      T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7))
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v4
                                   ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                                      (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
                                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                                      AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v7 AgdaAny
v8)))
                             ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_1738 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
                                (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7)))
                   MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v8
                     -> (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
                          ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                             T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                             ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                   (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                             ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
                                AgdaAny
v4)
                             ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                                AgdaAny
v2 AgdaAny
v4)
                             ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                                AgdaAny
v2
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                             ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                                ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                   ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                      (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v4)
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                      T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                      T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4))
                                ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                      ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                         (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                      T_MinOperator_84
v1 AgdaAny
v2
                                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                         T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4)))
                                ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                   T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                      T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4)
                                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                                      T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4 AgdaAny
v8)))
                             ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_1738 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
                                (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                                   T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7)))
                   T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
            MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v7
              -> (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                      ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v4)
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v3 AgdaAny
v4)
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v2
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v3 AgdaAny
v4))
                      ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                         T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v3 AgdaAny
v4)
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2
                            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                               AgdaAny
v3 AgdaAny
v4))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2
                            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                               AgdaAny
v3 AgdaAny
v4))
                         ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                               ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                  (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                               AgdaAny
v2
                               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                  T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                            T_MinOperator_84
v1 AgdaAny
v2
                            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                               AgdaAny
v3 AgdaAny
v4)
                            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                               (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                                  ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
                                     T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                                     (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
                                  T_MinOperator_84
v1 AgdaAny
v3 AgdaAny
v4)
                               AgdaAny
v3 AgdaAny
v2
                               ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_1626 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
                               AgdaAny
v7)))
                      ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                         T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_1738 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v2 AgdaAny
v3)
                         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                            T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7)))
            T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-idem
d_'8851''45'idem_1802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny
d_'8851''45'idem_1802 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
d_'8851''45'idem_1802 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5
  = T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny
du_'8851''45'idem_1802 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5
du_'8851''45'idem_1802 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny
du_'8851''45'idem_1802 :: T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny
du_'8851''45'idem_1802 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2
  = (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
      T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v2
      (let v3 :: T_IsTotalPreorder_118
v3
             = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v3))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-sel
d_'8851''45'sel_1806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_1806 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> T__'8846'__30
d_'8851''45'sel_1806 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> T__'8846'__30
du_'8851''45'sel_1806 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6
du_'8851''45'sel_1806 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_'8851''45'sel_1806 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> T__'8846'__30
du_'8851''45'sel_1806 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> T__'8846'__30 -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T__'8846'__30 -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.du_map_84
      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
         T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
         T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3)
      ((T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
         (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
            (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
         AgdaAny
v2 AgdaAny
v3)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-identityˡ
d_'8851''45'identity'737'_1814 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'737'_1814 :: T_MinOperator_84
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'737'_1814 T_MinOperator_84
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
      T_MinOperator_84
v0 AgdaAny
v1 AgdaAny
v3 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-identityʳ
d_'8851''45'identity'691'_1820 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'691'_1820 :: T_MinOperator_84
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'691'_1820 T_MinOperator_84
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
      T_MinOperator_84
v0 AgdaAny
v3 AgdaAny
v1 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-identity
d_'8851''45'identity_1826 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'identity_1826 :: T_MinOperator_84 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_Σ_14
d_'8851''45'identity_1826 T_MinOperator_84
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 ->
            (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
              T_MinOperator_84
v0 AgdaAny
v1 AgdaAny
v3 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)))
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 ->
            (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
              T_MinOperator_84
v0 AgdaAny
v3 AgdaAny
v1 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-zeroˡ
d_'8851''45'zero'737'_1832 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'737'_1832 :: T_MinOperator_84
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'737'_1832 T_MinOperator_84
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
      T_MinOperator_84
v0 AgdaAny
v1 AgdaAny
v3 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-zeroʳ
d_'8851''45'zero'691'_1838 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'691'_1838 :: T_MinOperator_84
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'691'_1838 T_MinOperator_84
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
      T_MinOperator_84
v0 AgdaAny
v3 AgdaAny
v1 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-zero
d_'8851''45'zero_1844 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'zero_1844 :: T_MinOperator_84 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_Σ_14
d_'8851''45'zero_1844 T_MinOperator_84
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 ->
            (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
              T_MinOperator_84
v0 AgdaAny
v1 AgdaAny
v3 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)))
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 ->
            (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
              T_MinOperator_84
v0 AgdaAny
v3 AgdaAny
v1 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isMagma
d_'8851''45'isMagma_1848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
d_'8851''45'isMagma_1848 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_IsMagma_86
d_'8851''45'isMagma_1848 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86
du_'8851''45'isMagma_1848 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'isMagma_1848 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_86
du_'8851''45'isMagma_1848 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86
du_'8851''45'isMagma_1848 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_86)
-> AgdaAny -> AgdaAny -> T_IsMagma_86
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_86
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_553
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0))))
      ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong_1748 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isSemigroup
d_'8851''45'isSemigroup_1850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
d_'8851''45'isSemigroup_1850 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_IsSemigroup_194
d_'8851''45'isSemigroup_1850 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
du_'8851''45'isSemigroup_1850 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'isSemigroup_1850 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_194
du_'8851''45'isSemigroup_1850 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
du_'8851''45'isSemigroup_1850 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = (T_IsMagma_86
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_194
forall a b. a -> b
coe
      T_IsMagma_86
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_194
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_4001
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86
du_'8851''45'isMagma_1848 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_1762 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isBand
d_'8851''45'isBand_1852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_230
d_'8851''45'isBand_1852 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_IsBand_230
d_'8851''45'isBand_1852 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230
du_'8851''45'isBand_1852 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'isBand_1852 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_230
du_'8851''45'isBand_1852 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230
du_'8851''45'isBand_1852 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = (T_IsSemigroup_194 -> (AgdaAny -> AgdaAny) -> T_IsBand_230)
-> AgdaAny -> AgdaAny -> T_IsBand_230
forall a b. a -> b
coe
      T_IsSemigroup_194 -> (AgdaAny -> AgdaAny) -> T_IsBand_230
MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_4787
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
du_'8851''45'isSemigroup_1850 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny
du_'8851''45'idem_1802 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_1854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
d_'8851''45'isCommutativeSemigroup_1854 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_IsCommutativeSemigroup_270
d_'8851''45'isCommutativeSemigroup_1854 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204
-> T_MinOperator_84 -> T_IsCommutativeSemigroup_270
du_'8851''45'isCommutativeSemigroup_1854 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'isCommutativeSemigroup_1854 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_270
du_'8851''45'isCommutativeSemigroup_1854 :: T_TotalPreorder_204
-> T_MinOperator_84 -> T_IsCommutativeSemigroup_270
du_'8851''45'isCommutativeSemigroup_1854 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = (T_IsSemigroup_194
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_270
forall a b. a -> b
coe
      T_IsSemigroup_194
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_270
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_5673
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
du_'8851''45'isSemigroup_1850 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isSemilattice
d_'8851''45'isSemilattice_1856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
d_'8851''45'isSemilattice_1856 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_IsSemilattice_312
d_'8851''45'isSemilattice_1856 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312
du_'8851''45'isSemilattice_1856 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'isSemilattice_1856 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemilattice_312
du_'8851''45'isSemilattice_1856 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312
du_'8851''45'isSemilattice_1856 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = (T_IsBand_230
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemilattice_312)
-> AgdaAny -> AgdaAny -> T_IsSemilattice_312
forall a b. a -> b
coe
      T_IsBand_230
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemilattice_312
MAlonzo.Code.Algebra.Structures.C_IsSemilattice'46'constructor_6687
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230
du_'8851''45'isBand_1852 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_1858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158
d_'8851''45'isSelectiveMagma_1858 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_IsSelectiveMagma_158
d_'8851''45'isSelectiveMagma_1858 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158
du_'8851''45'isSelectiveMagma_1858 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'isSelectiveMagma_1858 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_158
du_'8851''45'isSelectiveMagma_1858 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158
du_'8851''45'isSelectiveMagma_1858 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = (T_IsMagma_86
 -> (AgdaAny -> AgdaAny -> T__'8846'__30) -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny -> T_IsSelectiveMagma_158
forall a b. a -> b
coe
      T_IsMagma_86
-> (AgdaAny -> AgdaAny -> T__'8846'__30) -> T_IsSelectiveMagma_158
MAlonzo.Code.Algebra.Structures.C_IsSelectiveMagma'46'constructor_3217
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86
du_'8851''45'isMagma_1848 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> T__'8846'__30
du_'8851''45'sel_1806 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isMonoid
d_'8851''45'isMonoid_1862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
d_'8851''45'isMonoid_1862 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_358
d_'8851''45'isMonoid_1862 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_358
du_'8851''45'isMonoid_1862 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
du_'8851''45'isMonoid_1862 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_358
du_'8851''45'isMonoid_1862 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_358
du_'8851''45'isMonoid_1862 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny -> AgdaAny
v3
  = (T_IsSemigroup_194 -> T_Σ_14 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny -> T_IsMonoid_358
forall a b. a -> b
coe
      T_IsSemigroup_194 -> T_Σ_14 -> T_IsMonoid_358
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_7687
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
du_'8851''45'isSemigroup_1850 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
         ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 ->
               (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v4 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3 AgdaAny
v4)))
         ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 ->
               (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                 T_MinOperator_84
v1 AgdaAny
v4 AgdaAny
v2 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3 AgdaAny
v4))))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-rawMagma
d_'8851''45'rawMagma_1866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_RawMagma_8
d_'8851''45'rawMagma_1866 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_RawMagma_8
d_'8851''45'rawMagma_1866 ~()
v0 ~()
v1 ~()
v2 ~T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_MinOperator_84 -> T_RawMagma_8
du_'8851''45'rawMagma_1866 T_MinOperator_84
v4
du_'8851''45'rawMagma_1866 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_RawMagma_8
du_'8851''45'rawMagma_1866 :: T_MinOperator_84 -> T_RawMagma_8
du_'8851''45'rawMagma_1866 T_MinOperator_84
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_8
MAlonzo.Code.Algebra.Bundles.C_RawMagma'46'constructor_79
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v0))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-magma
d_'8851''45'magma_1868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_36
d_'8851''45'magma_1868 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_Magma_36
d_'8851''45'magma_1868 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_Magma_36
du_'8851''45'magma_1868 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'magma_1868 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_36
du_'8851''45'magma_1868 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_Magma_36
du_'8851''45'magma_1868 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Magma_36
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_86 -> T_Magma_36
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_581
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsMagma_86
du_'8851''45'isMagma_1848 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-semigroup
d_'8851''45'semigroup_1870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
d_'8851''45'semigroup_1870 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_Semigroup_206
d_'8851''45'semigroup_1870 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semigroup_206
du_'8851''45'semigroup_1870 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'semigroup_1870 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_206
du_'8851''45'semigroup_1870 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semigroup_206
du_'8851''45'semigroup_1870 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_194 -> T_Semigroup_206)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Semigroup_206
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_194 -> T_Semigroup_206
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_3669
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemigroup_194
du_'8851''45'isSemigroup_1850 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-band
d_'8851''45'band_1872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_266
d_'8851''45'band_1872 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_Band_266
d_'8851''45'band_1872 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_Band_266
du_'8851''45'band_1872 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'band_1872 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_266
du_'8851''45'band_1872 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_Band_266
du_'8851''45'band_1872 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_230 -> T_Band_266)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Band_266
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_230 -> T_Band_266
MAlonzo.Code.Algebra.Bundles.C_Band'46'constructor_4745
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsBand_230
du_'8851''45'isBand_1852 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_1874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_332
d_'8851''45'commutativeSemigroup_1874 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_CommutativeSemigroup_332
d_'8851''45'commutativeSemigroup_1874 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204
-> T_MinOperator_84 -> T_CommutativeSemigroup_332
du_'8851''45'commutativeSemigroup_1874 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'commutativeSemigroup_1874 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_332
du_'8851''45'commutativeSemigroup_1874 :: T_TotalPreorder_204
-> T_MinOperator_84 -> T_CommutativeSemigroup_332
du_'8851''45'commutativeSemigroup_1874 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeSemigroup_332
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_270 -> T_CommutativeSemigroup_332
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_5887
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> T_IsCommutativeSemigroup_270)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> T_IsCommutativeSemigroup_270
du_'8851''45'isCommutativeSemigroup_1854 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-semilattice
d_'8851''45'semilattice_1876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Semilattice_402
d_'8851''45'semilattice_1876 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_Semilattice_402
d_'8851''45'semilattice_1876 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semilattice_402
du_'8851''45'semilattice_1876 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'semilattice_1876 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_Semilattice_402
du_'8851''45'semilattice_1876 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_Semilattice_402
du_'8851''45'semilattice_1876 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemilattice_312 -> T_Semilattice_402)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Semilattice_402
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemilattice_312 -> T_Semilattice_402
MAlonzo.Code.Algebra.Bundles.C_Semilattice'46'constructor_7205
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSemilattice_312
du_'8851''45'isSemilattice_1856 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-selectiveMagma
d_'8851''45'selectiveMagma_1878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_90
d_'8851''45'selectiveMagma_1878 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> T_SelectiveMagma_90
d_'8851''45'selectiveMagma_1878 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4
  = T_TotalPreorder_204 -> T_MinOperator_84 -> T_SelectiveMagma_90
du_'8851''45'selectiveMagma_1878 T_TotalPreorder_204
v3 T_MinOperator_84
v4
du_'8851''45'selectiveMagma_1878 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_90
du_'8851''45'selectiveMagma_1878 :: T_TotalPreorder_204 -> T_MinOperator_84 -> T_SelectiveMagma_90
du_'8851''45'selectiveMagma_1878 T_TotalPreorder_204
v0 T_MinOperator_84
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSelectiveMagma_158 -> T_SelectiveMagma_90)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_SelectiveMagma_90
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_158 -> T_SelectiveMagma_90
MAlonzo.Code.Algebra.Bundles.C_SelectiveMagma'46'constructor_1577
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v1))
      ((T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> T_IsSelectiveMagma_158
du_'8851''45'isSelectiveMagma_1858 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-monoid
d_'8851''45'monoid_1882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_506
d_'8851''45'monoid_1882 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_Monoid_506
d_'8851''45'monoid_1882 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_Monoid_506
du_'8851''45'monoid_1882 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
du_'8851''45'monoid_1882 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_506
du_'8851''45'monoid_1882 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_Monoid_506
du_'8851''45'monoid_1882 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny -> AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Monoid_506
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_358 -> T_Monoid_506
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_8851
      (T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100
         (T_MinOperator_84 -> T_MinOperator_84
forall a b. a -> b
coe T_MinOperator_84
v1))
      AgdaAny
v2
      ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsMonoid_358)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_358
du_'8851''45'isMonoid_1862 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3))
-- Algebra.Construct.NaturalChoice.MinOp.x⊓y≈x⇒x≤y
d_x'8851'y'8776'x'8658'x'8804'y_1890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8776'x'8658'x'8804'y_1890 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8776'x'8658'x'8804'y_1890 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_1890 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_x'8851'y'8776'x'8658'x'8804'y_1890 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_1890 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_1890 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = let v5 :: t
v5
          = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
              (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
              AgdaAny
v2 AgdaAny
v3 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v5 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v6
           -> (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
                (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                   ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
                      T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                      (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                AgdaAny
v2 AgdaAny
v3
                (let v7 :: t
v7
                       = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                           T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                 AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                      (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                         ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                            T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7)))
                      AgdaAny
v2
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v2 AgdaAny
v3)
                      AgdaAny
v3
                      (let v8 :: t
v8
                             = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                                 T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                       AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                            (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                               ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                                  T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8)))
                            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                               AgdaAny
v2 AgdaAny
v3)
                            AgdaAny
v2 AgdaAny
v4))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                         T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v6)))
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.x⊓y≈y⇒y≤x
d_x'8851'y'8776'y'8658'y'8804'x_1922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8776'y'8658'y'8804'x_1922 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8776'y'8658'y'8804'x_1922 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'y'8658'y'8804'x_1922 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_x'8851'y'8776'y'8658'y'8804'x_1922 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'y'8658'y'8804'x_1922 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'y'8658'y'8804'x_1922 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_1890 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
      ((T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
               ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                  (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v3 AgdaAny
v2)
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2 AgdaAny
v3)
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
            ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
               ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                  ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                     (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2 AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
               ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                  ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                     ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
            ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_1674 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Construct.NaturalChoice.MinOp.mono-≤-distrib-⊓
d_mono'45''8804''45'distrib'45''8851'_1936 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny
d_mono'45''8804''45'distrib'45''8851'_1936 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_mono'45''8804''45'distrib'45''8851'_1936 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                                           AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_mono'45''8804''45'distrib'45''8851'_1936 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_mono'45''8804''45'distrib'45''8851'_1936 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny
du_mono'45''8804''45'distrib'45''8851'_1936 :: T_TotalPreorder_204
-> T_MinOperator_84
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_mono'45''8804''45'distrib'45''8851'_1936 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = let v7 :: t
v7
          = (T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_118 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_128
              (T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0))
              AgdaAny
v5 AgdaAny
v6 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v7 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v8
           -> (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
                ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                      ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                         (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                   ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> AgdaAny
v2
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v5 AgdaAny
v6))
                   ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6))
                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                      ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                      ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5)
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6))
                      ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6)))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                         T_MinOperator_84
v1 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6) ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v8)))
                   ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v5 AgdaAny
v6)
                      AgdaAny
v5
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_106
                         T_MinOperator_84
v1 AgdaAny
v5 AgdaAny
v6 AgdaAny
v8)))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v8
           -> (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
                ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                      ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                         (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                   ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> AgdaAny
v2
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v5 AgdaAny
v6))
                   ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6))
                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                      ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                      ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6)
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6))
                      ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6)))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                         T_MinOperator_84
v1 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5) ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6) ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v6 AgdaAny
v5 AgdaAny
v8)))
                   ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v5 AgdaAny
v6)
                      AgdaAny
v6
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_112
                         T_MinOperator_84
v1 AgdaAny
v5 AgdaAny
v6 AgdaAny
v8)))
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.x≤y⇒x⊓z≤y
d_x'8804'y'8658'x'8851'z'8804'y_1982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8658'x'8851'z'8804'y_1982 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8658'x'8851'z'8804'y_1982 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'x'8851'z'8804'y_1982 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8658'x'8851'z'8804'y_1982 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8658'x'8851'z'8804'y_1982 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'x'8851'z'8804'y_1982 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
         AgdaAny
v2 AgdaAny
v4)
      AgdaAny
v2 AgdaAny
v3
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_1626 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
      AgdaAny
v5
-- Algebra.Construct.NaturalChoice.MinOp.x≤y⇒z⊓x≤y
d_x'8804'y'8658'z'8851'x'8804'y_1994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8658'z'8851'x'8804'y_1994 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8658'z'8851'x'8804'y_1994 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'z'8851'x'8804'y_1994 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8658'z'8851'x'8804'y_1994 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8658'z'8851'x'8804'y_1994 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'z'8851'x'8804'y_1994 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
         AgdaAny
v4 AgdaAny
v2)
      AgdaAny
v2 AgdaAny
v3
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_1652 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
      AgdaAny
v5
-- Algebra.Construct.NaturalChoice.MinOp.x≤y⊓z⇒x≤y
d_x'8804'y'8851'z'8658'x'8804'y_2006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'y_2006 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'y_2006 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'y_2006 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8851'z'8658'x'8804'y_2006 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'y_2006 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'y_2006 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
      AgdaAny
v2
      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
         AgdaAny
v3 AgdaAny
v4)
      AgdaAny
v3 AgdaAny
v5
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_1626 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
-- Algebra.Construct.NaturalChoice.MinOp.x≤y⊓z⇒x≤z
d_x'8804'y'8851'z'8658'x'8804'z_2020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'z_2020 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'z_2020 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'z_2020 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8851'z'8658'x'8804'z_2020 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'z_2020 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'z_2020 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
      AgdaAny
v2
      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
         AgdaAny
v3 AgdaAny
v4)
      AgdaAny
v4 AgdaAny
v5
      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_1652 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-mono-≤
d_'8851''45'mono'45''8804'_2028 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'mono'45''8804'_2028 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'mono'45''8804'_2028 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
                                AgdaAny
v10
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_2028 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8851''45'mono'45''8804'_2028 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'mono'45''8804'_2028 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_2028 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = let v8 :: t
v8
          = (T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> T__'8846'__30
du_'8851''45'sel_1806 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5) in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (case AgdaAny -> T__'8846'__30
forall a b. a -> b
coe AgdaAny
forall a. a
v8 of
         MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 AgdaAny
v9
           -> let v10 :: T_IsTotalPreorder_118
v10
                    = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v10))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v4)
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v3 AgdaAny
v5)
                   (let v11 :: t
v11
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v11)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v3 AgdaAny
v5)
                         AgdaAny
v3 AgdaAny
v9))
                   ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                      (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v2 AgdaAny
v4)
                      AgdaAny
v2 AgdaAny
v3
                      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_1626 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
                      AgdaAny
v6))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v9
           -> let v10 :: T_IsTotalPreorder_118
v10
                    = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                   T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                   ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v10))
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v2 AgdaAny
v4)
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)
                   ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                      AgdaAny
v3 AgdaAny
v5)
                   (let v11 :: t
v11
                          = (T_TotalPreorder_204 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_204 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_248 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                         (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                            ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
                               T_Preorder_132 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v11)))
                         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                            AgdaAny
v3 AgdaAny
v5)
                         AgdaAny
v5 AgdaAny
v9))
                   ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                      (T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                         ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> T_IsTotalPreorder_118
forall a b. a -> b
coe
                            T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                            (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                      ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                         AgdaAny
v2 AgdaAny
v4)
                      AgdaAny
v4 AgdaAny
v5
                      ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_1652 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))
                      AgdaAny
v7))
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-monoˡ-≤
d_'8851''45'mono'737''45''8804'_2078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'mono'737''45''8804'_2078 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'mono'737''45''8804'_2078 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'737''45''8804'_2078 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'mono'737''45''8804'_2078 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'mono'737''45''8804'_2078 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'737''45''8804'_2078 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_2028 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)
      (let v6 :: T_IsTotalPreorder_118
v6
             = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v6))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_2088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'mono'691''45''8804'_2088 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'mono'691''45''8804'_2088 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'691''45''8804'_2088 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'mono'691''45''8804'_2088 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'mono'691''45''8804'_2088 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'691''45''8804'_2088 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_2028 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
      (let v6 :: T_IsTotalPreorder_118
v6
             = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                 (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v6))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))
      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-glb
d_'8851''45'glb_2100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'glb_2100 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'glb_2100 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'glb_2100 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8851''45'glb_2100 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'glb_2100 :: T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'glb_2100 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = let v7 :: T_IsTotalPreorder_118
v7
          = T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
              (T_TotalPreorder_204 -> T_TotalPreorder_204
forall a b. a -> b
coe T_TotalPreorder_204
v0) in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126 (T_IsTotalPreorder_118 -> AgdaAny
forall a b. a -> b
coe T_IsTotalPreorder_118
v7))
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            AgdaAny
v3 AgdaAny
v4)
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            AgdaAny
v2 AgdaAny
v2)
         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny
du_'8851''45'idem_1802 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
         ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_2028 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-triangulate
d_'8851''45'triangulate_2114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'triangulate_2114 :: ()
-> ()
-> ()
-> T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'triangulate_2114 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'triangulate_2114 T_TotalPreorder_204
v3 T_MinOperator_84
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_'8851''45'triangulate_2114 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_204 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_84 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'triangulate_2114 :: T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'triangulate_2114 T_TotalPreorder_204
v0 T_MinOperator_84
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T__IsRelatedTo__56 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T__IsRelatedTo__56 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_begin'45'equality__124
      ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
         ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
            ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
               (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2 AgdaAny
v3)
            AgdaAny
v4)
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v3 AgdaAny
v3))
            AgdaAny
v4)
         ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2 AgdaAny
v3)
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v3 AgdaAny
v4))
         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
            ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
               ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                  (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v3 AgdaAny
v3))
               AgdaAny
v4)
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               AgdaAny
v2
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v3 AgdaAny
v3)
                  AgdaAny
v4))
            ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2 AgdaAny
v3)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v3 AgdaAny
v4))
            ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776'_156
               ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                  ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                     (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3 AgdaAny
v3)
                     AgdaAny
v4))
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v3
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3 AgdaAny
v4)))
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v2 AgdaAny
v3)
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v3 AgdaAny
v4))
               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__56
 -> AgdaAny
 -> T__IsRelatedTo__56)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__56
-> AgdaAny
-> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_step'45''8776''728'_176
                  ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                     ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                        (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v2
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3
                        ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                           AgdaAny
v3 AgdaAny
v4)))
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v2 AgdaAny
v3)
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3 AgdaAny
v4))
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v2 AgdaAny
v3)
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3 AgdaAny
v4))
                  ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__56
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du__'8718'_234
                     ((T_IsTotalPreorder_118 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsTotalPreorder_118 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_126
                        ((T_TotalPreorder_204 -> T_IsTotalPreorder_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_TotalPreorder_204 -> T_IsTotalPreorder_118
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_226
                           (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0)))
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                           AgdaAny
v2 AgdaAny
v3)
                        ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                           AgdaAny
v3 AgdaAny
v4)))
                  ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_1762 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3 AgdaAny
v4)))
               ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3 AgdaAny
v3)
                     AgdaAny
v4)
                  ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                     AgdaAny
v3
                     ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                        AgdaAny
v3 AgdaAny
v4))
                  ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_1762 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
            ((T_TotalPreorder_204
 -> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_204
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_1762 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v3 AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
         ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_1738 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
            (((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
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-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_302
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2)
               (\ AgdaAny
v5 AgdaAny
v6 -> AgdaAny
v5)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v3 AgdaAny
v3)
               AgdaAny
v3)
            (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__308
               (\ AgdaAny
v5 AgdaAny
v6 -> AgdaAny
v6)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v2)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v3 AgdaAny
v3)
               AgdaAny
v3)
            ((T_TotalPreorder_204
 -> T_MinOperator_84
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_204
-> T_MinOperator_84
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_1700 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
               ((T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_84 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__100 T_MinOperator_84
v1
                  AgdaAny
v3 AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) ((T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204 -> T_MinOperator_84 -> AgdaAny -> AgdaAny
du_'8851''45'idem_1802 (T_TotalPreorder_204 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_204
v0) (T_MinOperator_84 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_84
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))