{-# 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.Bundles.Raw
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.Reasoning.Syntax
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Construct.NaturalChoice.MinOp._._≈_
d__'8776'__22 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__22 :: T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> ()
d__'8776'__22 = T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._._≲_
d__'8818'__24 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> ()
d__'8818'__24 :: T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> ()
d__'8818'__24 = T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Associative
d_Associative_118 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Associative_118 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Associative_118 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Commutative
d_Commutative_122 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Commutative_122 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Commutative_122 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Congruent₁
d_Congruent'8321'_124 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny) -> ()
d_Congruent'8321'_124 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny)
-> ()
d_Congruent'8321'_124 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Congruent₂
d_Congruent'8322'_126 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Congruent'8322'_126 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Congruent'8322'_126 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Idempotent
d_Idempotent_132 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Idempotent_132 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Idempotent_132 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Identity
d_Identity_138 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Identity_138 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Identity_138 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.LeftIdentity
d_LeftIdentity_164 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftIdentity_164 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_LeftIdentity_164 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.LeftZero
d_LeftZero_172 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftZero_172 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_LeftZero_172 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.RightIdentity
d_RightIdentity_194 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightIdentity_194 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_RightIdentity_194 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.RightZero
d_RightZero_202 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightZero_202 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_RightZero_202 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Selective
d_Selective_204 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Selective_204 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Selective_204 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.Zero
d_Zero_222 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Zero_222 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Zero_222 = ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Construct.NaturalChoice.MinOp._.IsBand
d_IsBand_230 :: p -> p -> p -> p -> p -> p -> ()
d_IsBand_230 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsCommutativeSemigroup
d_IsCommutativeSemigroup_242 :: p -> p -> p -> p -> p -> p -> ()
d_IsCommutativeSemigroup_242 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsMagma
d_IsMagma_270 :: p -> p -> p -> p -> p -> p -> ()
d_IsMagma_270 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsMonoid
d_IsMonoid_276 :: p -> p -> p -> p -> p -> p -> p -> ()
d_IsMonoid_276 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsSelectiveMagma
d_IsSelectiveMagma_296 :: p -> p -> p -> p -> p -> p -> ()
d_IsSelectiveMagma_296 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsSemigroup
d_IsSemigroup_298 :: p -> p -> p -> p -> p -> p -> ()
d_IsSemigroup_298 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Construct.NaturalChoice.MinOp._.IsBand.idem
d_idem_412 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_412 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_412 T_IsBand_508
v0
  = (T_IsBand_508 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsBand.isSemigroup
d_isSemigroup_420 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_420 :: T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_420 T_IsBand_508
v0
  = (T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsCommutativeSemigroup.comm
d_comm_776 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 :: T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_776 T_IsCommutativeSemigroup_548
v0
  = (T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_558 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsCommutativeSemigroup.isSemigroup
d_isSemigroup_786 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_786 :: T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
d_isSemigroup_786 T_IsCommutativeSemigroup_548
v0
  = (T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsCommutativeSemigroup_548 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_556 (T_IsCommutativeSemigroup_548 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemigroup_548
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsMagma.isEquivalence
d_isEquivalence_1570 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1570 :: T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_1570 T_IsMagma_176
v0
  = (T_IsMagma_176 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsMagma.∙-cong
d_'8729''45'cong_1584 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1584 :: T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1584 T_IsMagma_176
v0
  = (T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186 (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsMonoid.identity
d_identity_1680 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1680 :: T_IsMonoid_686 -> T_Σ_14
d_identity_1680 T_IsMonoid_686
v0
  = (T_IsMonoid_686 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_686 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_698 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsMonoid.isSemigroup
d_isSemigroup_1692 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_1692 :: T_IsMonoid_686 -> T_IsSemigroup_472
d_isSemigroup_1692 T_IsMonoid_686
v0
  = (T_IsMonoid_686 -> T_IsSemigroup_472)
-> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsMonoid_686 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_696 (T_IsMonoid_686 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_686
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsSelectiveMagma.isMagma
d_isMagma_2400 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2400 :: T_IsSelectiveMagma_436 -> T_IsMagma_176
d_isMagma_2400 T_IsSelectiveMagma_436
v0
  = (T_IsSelectiveMagma_436 -> T_IsMagma_176)
-> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_444 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsSelectiveMagma.sel
d_sel_2408 ::
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_2408 :: T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_2408 T_IsSelectiveMagma_436
v0
  = (T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a b. a -> b
coe T_IsSelectiveMagma_436 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Algebra.Structures.d_sel_446 (T_IsSelectiveMagma_436 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_436
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsSemigroup.assoc
d_assoc_2424 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2424 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2424 T_IsSemigroup_472
v0
  = (T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_482 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)
-- Algebra.Construct.NaturalChoice.MinOp._.IsSemigroup.isMagma
d_isMagma_2428 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2428 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_2428 T_IsSemigroup_472
v0
  = (T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_472
v0)
-- Algebra.Construct.NaturalChoice.MinOp.x⊓y≤x
d_x'8851'y'8804'x_2808 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8804'x_2808 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8804'x_2808 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_2808 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
du_x'8851'y'8804'x_2808 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_2808 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_2808 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3
  = let v4 :: t
v4
          = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
              (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
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
           -> (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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                   ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                      T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                      (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                   AgdaAny
v2 AgdaAny
v3)
                AgdaAny
v2
                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                   T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v5
           -> let v6 :: t
v6
                    = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_'8818''45'resp'737''45''8776'_100
                   ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (let v8 :: t
v8
                             = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                                 T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v8))
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v2 AgdaAny
v3)
                            AgdaAny
v3
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                               T_MinOperator_98
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_2834 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8804'y_2834 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8804'y_2834 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_2834 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
du_x'8851'y'8804'y_2834 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_2834 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_2834 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3
  = let v4 :: t
v4
          = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
              (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
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_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_'8818''45'resp'737''45''8776'_100
                   ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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))
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v3)
                   (let v7 :: t
v7
                          = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (let v8 :: t
v8
                             = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                                 T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v8))
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v2 AgdaAny
v3)
                            AgdaAny
v2
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                               T_MinOperator_98
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
           -> (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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                   ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                      T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                      (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                   AgdaAny
v2 AgdaAny
v3)
                AgdaAny
v3
                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                   T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)
         T__'8846'__30
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-comm
d_'8851''45'comm_2856 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'comm_2856 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'comm_2856 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_2856 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
du_'8851''45'comm_2856 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_2856 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_2856 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3
  = let v4 :: t
v4
          = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
              (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
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_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                (let v7 :: t
v7
                       = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                           T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v7))
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v2 AgdaAny
v3)
                      AgdaAny
v2
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v3 AgdaAny
v2)
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)
                      (let v8 :: t
v8
                             = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                                 T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                       AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         (let v9 :: t
v9
                                = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                                    T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v9))
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v2)
                               AgdaAny
v2
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                  T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v2 AgdaAny
v5))))))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v5
           -> let v6 :: t
v6
                    = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                (let v7 :: t
v7
                       = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                           T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v7))
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v2 AgdaAny
v3)
                      AgdaAny
v3
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v3 AgdaAny
v2)
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v5)
                      (let v8 :: t
v8
                             = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                                 T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                       AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         (let v9 :: t
v9
                                = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                                    T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v9))
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v2)
                               AgdaAny
v3
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                  T_MinOperator_98
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'_2882 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'cong'737'_2882 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'cong'737'_2882 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'cong'737'_2882 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'cong'737'_2882 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = let v6 :: t
v6
          = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
              (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
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
           -> let v8 :: b
v8
                    = T_SubRelation_60 -> b
forall a b. a -> b
coe
                        T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v3)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v4)
                   (let v9 :: T_IsPreorder_70
v9
                          = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                              ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                 T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                            (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v9))
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v2
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                            AgdaAny
v2 AgdaAny
v4)
                         (let v10 :: T_IsPreorder_70
v10
                                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                  ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10)))
                               AgdaAny
v2
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                               (let v11 :: T_IsPreorder_70
v11
                                      = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                          ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                             T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                     ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11))
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)))
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4
                                  (let v11 :: t
v11
                                         = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                                             T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252
                                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_'8818''45'resp'691''45''8776'_106
                                        ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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))
                                        (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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                            T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7))))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v7
           -> let v8 :: b
v8
                    = T_SubRelation_60 -> b
forall a b. a -> b
coe
                        T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v3)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v4)
                   (let v9 :: T_IsPreorder_70
v9
                          = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                              ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                 T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                            (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v9))
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v3
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                            AgdaAny
v2 AgdaAny
v4)
                         (let v10 :: T_IsPreorder_70
v10
                                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                               AgdaAny
v3 AgdaAny
v4
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                               (let v11 :: T_IsPreorder_70
v11
                                      = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                          ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                             T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                     ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11))
                                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                        ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                           T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11)))
                                     AgdaAny
v4
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                                     (let v12 :: T_IsPreorder_70
v12
                                            = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                   T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                   (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                           (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                           ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                              T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                              (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v12))
                                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                              T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)))
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                        T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4
                                        (let v12 :: t
v12
                                               = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                                                   T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252
                                                   (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_'8818''45'resp'737''45''8776'_100
                                              ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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
v12))
                                              (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
v5))
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                            T_MinOperator_98
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'_2920 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'cong'691'_2920 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'cong'691'_2920 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_2920 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'cong'691'_2920 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'cong'691'_2920 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_2920 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = let v6 :: b
v6
          = T_SubRelation_60 -> b
forall a b. a -> b
coe
              T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6)
         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
            AgdaAny
v3 AgdaAny
v2)
         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
            AgdaAny
v4 AgdaAny
v2)
         (let v7 :: T_IsPreorder_70
v7
                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v7))
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                  ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v7)))
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                  AgdaAny
v3 AgdaAny
v2)
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                  AgdaAny
v2 AgdaAny
v3)
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                  AgdaAny
v4 AgdaAny
v2)
               (let v8 :: T_IsPreorder_70
v8
                      = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                          ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                             T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                     ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v8))
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v2 AgdaAny
v3)
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v2 AgdaAny
v4)
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v4 AgdaAny
v2)
                     (let v9 :: T_IsPreorder_70
v9
                            = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                   T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v9))
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              AgdaAny
v2 AgdaAny
v4)
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              AgdaAny
v4 AgdaAny
v2)
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              AgdaAny
v4 AgdaAny
v2)
                           (let v10 :: T_IsPreorder_70
v10
                                  = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                         T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                            AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                 ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1 AgdaAny
v4 AgdaAny
v2)))
                           ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_2856 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
                     ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                        T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_2856 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_2930 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'cong_2930 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'cong_2930 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong_2930 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8851''45'cong_2930 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'cong_2930 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong_2930 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = let v8 :: t
v8
          = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
              T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v9 :: t
v9
             = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v9))
            (((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'_292
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                  AgdaAny
v2)
               (\ AgdaAny
v10 AgdaAny
v11 -> AgdaAny
v10) 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'__298
               (\ AgdaAny
v10 AgdaAny
v11 -> AgdaAny
v11)
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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'__298
               (\ AgdaAny
v10 AgdaAny
v11 -> AgdaAny
v11)
               (\ AgdaAny
v10 ->
                  (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                    AgdaAny
v10 AgdaAny
v5)
               AgdaAny
v2 AgdaAny
v3)
            ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_2920 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_2944 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'assoc_2944 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'assoc_2944 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_2944 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_'8851''45'assoc_2944 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_2944 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_2944 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = let v5 :: t
v5
          = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
              (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
v0))
              AgdaAny
v2 AgdaAny
v3 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v6 :: t
v6
             = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
                 T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
                 (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                    (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
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
                     -> let v9 :: b
v9
                              = T_SubRelation_60 -> b
forall a b. a -> b
coe
                                  T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                        AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                             (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v9)
                             ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                   T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                AgdaAny
v4)
                             ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                AgdaAny
v2
                                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                   T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                             (let v10 :: T_IsPreorder_70
v10
                                    = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                        ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                           T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                           (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                      (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      T_MinOperator_98
v1
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                      AgdaAny
v4)
                                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      T_MinOperator_98
v1 AgdaAny
v2
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                   (let v11 :: T_IsPreorder_70
v11
                                          = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                              ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                 T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                            (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11))
                                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                            T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                                         AgdaAny
v2
                                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                            T_MinOperator_98
v1 AgdaAny
v2
                                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                               T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                         (let v12 :: T_IsPreorder_70
v12
                                                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v12))
                                               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                                  ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v12)))
                                               AgdaAny
v2
                                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                  T_MinOperator_98
v1 AgdaAny
v2
                                                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                     T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                               (let v13 :: T_IsPreorder_70
v13
                                                      = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                          ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                             T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                                     ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                        T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v13))
                                                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                                        ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                                           T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v13)))
                                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                        T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                        T_MinOperator_98
v1 AgdaAny
v2
                                                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                           T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                        T_MinOperator_98
v1 AgdaAny
v2
                                                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                           T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                                     (let v14 :: T_IsPreorder_70
v14
                                                            = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                                ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                                   T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                                   (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                        (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                           (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                                           ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                              T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                                              (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v14))
                                                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                              T_MinOperator_98
v1 AgdaAny
v2
                                                              ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                                 T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))))
                                                     ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                                        T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)
                                                        (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                           T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4)
                                                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                                                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                                           T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4 AgdaAny
v8))))
                                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7)))
                                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                            T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                  ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                     T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                     (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
                                               AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v7 AgdaAny
v8))))
                                   ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                      T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_2920 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v7)))))
                   MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v8
                     -> let v9 :: b
v9
                              = T_SubRelation_60 -> b
forall a b. a -> b
coe
                                  T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                        AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                             (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v9)
                             ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                   T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                AgdaAny
v4)
                             ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                AgdaAny
v2
                                ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                   T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                             (let v10 :: T_IsPreorder_70
v10
                                    = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                        ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                           T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                           (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                   ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                      (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      T_MinOperator_98
v1
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                      AgdaAny
v4)
                                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                      T_MinOperator_98
v1 AgdaAny
v2
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                   (let v11 :: T_IsPreorder_70
v11
                                          = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                              ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                 T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                            (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11))
                                         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                            ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                               T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                               (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11)))
                                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                            T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v4)
                                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                            T_MinOperator_98
v1 AgdaAny
v2
                                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                               T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                            T_MinOperator_98
v1 AgdaAny
v2
                                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                               T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                         (let v12 :: T_IsPreorder_70
v12
                                                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                            (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                               ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                  T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v12))
                                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                  T_MinOperator_98
v1 AgdaAny
v2
                                                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                                     T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))))
                                         ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                            T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                               T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4)
                                            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                               T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4 AgdaAny
v8))))
                                   ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                                      T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_2920 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                         T_MinOperator_98
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
              -> let v8 :: b
v8
                       = T_SubRelation_60 -> b
forall a b. a -> b
coe
                           T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                 AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v8)
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v4)
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v2
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                            AgdaAny
v3 AgdaAny
v4))
                      (let v9 :: T_IsPreorder_70
v9
                             = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                 ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                    T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                    (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                       AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                            ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                               (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v9))
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                               AgdaAny
v4)
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v3 AgdaAny
v4)
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v2
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                            (let v10 :: T_IsPreorder_70
v10
                                   = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                       ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                          T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                          (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                             AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                  ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                     ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                        T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10)))
                                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4)
                                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     T_MinOperator_98
v1 AgdaAny
v2
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     T_MinOperator_98
v1 AgdaAny
v2
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                  (let v11 :: T_IsPreorder_70
v11
                                         = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                             ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                                T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                                (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                        ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                           T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11))
                                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           T_MinOperator_98
v1 AgdaAny
v2
                                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                              T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))))
                                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                     T_MinOperator_98
v1 AgdaAny
v2
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                           ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                              T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                              (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
                                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                           T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4)
                                        AgdaAny
v3 AgdaAny
v2
                                        ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                           T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_2808 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                               T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_2920 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                  T_MinOperator_98
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_2984 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny
d_'8851''45'idem_2984 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
d_'8851''45'idem_2984 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5
  = T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny
du_'8851''45'idem_2984 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5
du_'8851''45'idem_2984 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny
du_'8851''45'idem_2984 :: T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny
du_'8851''45'idem_2984 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2
  = (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
      T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v2
      (let v3 :: t
v3
             = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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
v3))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-sel
d_'8851''45'sel_2988 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_'8851''45'sel_2988 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> T__'8846'__30
d_'8851''45'sel_2988 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> T__'8846'__30
du_'8851''45'sel_2988 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6
du_'8851''45'sel_2988 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_'8851''45'sel_2988 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> T__'8846'__30
du_'8851''45'sel_2988 T_TotalPreorder_222
v0 T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
         T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
      ((T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
         (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
            (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
v0))
         AgdaAny
v2 AgdaAny
v3)
-- Algebra.Construct.NaturalChoice.MinOp.⊓-identityˡ
d_'8851''45'identity'737'_2996 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'737'_2996 :: T_MinOperator_98
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'737'_2996 T_MinOperator_98
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
      T_MinOperator_98
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'_3002 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'691'_3002 :: T_MinOperator_98
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'identity'691'_3002 T_MinOperator_98
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
      T_MinOperator_98
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_3008 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'identity_3008 :: T_MinOperator_98 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_Σ_14
d_'8851''45'identity_3008 T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
              T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
              T_MinOperator_98
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'_3014 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'737'_3014 :: T_MinOperator_98
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'737'_3014 T_MinOperator_98
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
      T_MinOperator_98
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'_3020 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'691'_3020 :: T_MinOperator_98
-> AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8851''45'zero'691'_3020 T_MinOperator_98
v0 AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
      T_MinOperator_98
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_3026 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8851''45'zero_3026 :: T_MinOperator_98 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_Σ_14
d_'8851''45'zero_3026 T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
              T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
              T_MinOperator_98
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_3030 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_'8851''45'isMagma_3030 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_IsMagma_176
d_'8851''45'isMagma_3030 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
du_'8851''45'isMagma_3030 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'isMagma_3030 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
du_'8851''45'isMagma_3030 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
du_'8851''45'isMagma_3030 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = (T_IsEquivalence_26
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> T_IsMagma_176
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
      ((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_124 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
            ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
               (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0))))
      ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong_2930 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isSemigroup
d_'8851''45'isSemigroup_3032 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_'8851''45'isSemigroup_3032 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_IsSemigroup_472
d_'8851''45'isSemigroup_3032 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
du_'8851''45'isSemigroup_3032 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'isSemigroup_3032 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
du_'8851''45'isSemigroup_3032 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
du_'8851''45'isSemigroup_3032 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_472
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
du_'8851''45'isMagma_3030 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_2944 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isBand
d_'8851''45'isBand_3034 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
d_'8851''45'isBand_3034 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_IsBand_508
d_'8851''45'isBand_3034 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508
du_'8851''45'isBand_3034 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'isBand_3034 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508
du_'8851''45'isBand_3034 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508
du_'8851''45'isBand_3034 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = (T_IsSemigroup_472 -> (AgdaAny -> AgdaAny) -> T_IsBand_508)
-> AgdaAny -> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe
      T_IsSemigroup_472 -> (AgdaAny -> AgdaAny) -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_11205
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
du_'8851''45'isSemigroup_3032 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny
du_'8851''45'idem_2984 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isCommutativeSemigroup
d_'8851''45'isCommutativeSemigroup_3036 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_3036 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_IsCommutativeSemigroup_548
d_'8851''45'isCommutativeSemigroup_3036 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222
-> T_MinOperator_98 -> T_IsCommutativeSemigroup_548
du_'8851''45'isCommutativeSemigroup_3036 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'isCommutativeSemigroup_3036 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
du_'8851''45'isCommutativeSemigroup_3036 :: T_TotalPreorder_222
-> T_MinOperator_98 -> T_IsCommutativeSemigroup_548
du_'8851''45'isCommutativeSemigroup_3036 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = (T_IsSemigroup_472
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemigroup_548
forall a b. a -> b
coe
      T_IsSemigroup_472
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemigroup_548
MAlonzo.Code.Algebra.Structures.C_IsCommutativeSemigroup'46'constructor_12093
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
du_'8851''45'isSemigroup_3032 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_2856 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isSelectiveMagma
d_'8851''45'isSelectiveMagma_3038 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_3038 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_IsSelectiveMagma_436
d_'8851''45'isSelectiveMagma_3038 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436
du_'8851''45'isSelectiveMagma_3038 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'isSelectiveMagma_3038 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
du_'8851''45'isSelectiveMagma_3038 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436
du_'8851''45'isSelectiveMagma_3038 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = (T_IsMagma_176
 -> (AgdaAny -> AgdaAny -> T__'8846'__30) -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny -> T_IsSelectiveMagma_436
forall a b. a -> b
coe
      T_IsMagma_176
-> (AgdaAny -> AgdaAny -> T__'8846'__30) -> T_IsSelectiveMagma_436
MAlonzo.Code.Algebra.Structures.C_IsSelectiveMagma'46'constructor_9631
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
du_'8851''45'isMagma_3030 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> T__'8846'__30
du_'8851''45'sel_2988 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-isMonoid
d_'8851''45'isMonoid_3042 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
d_'8851''45'isMonoid_3042 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_686
d_'8851''45'isMonoid_3042 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_686
du_'8851''45'isMonoid_3042 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
du_'8851''45'isMonoid_3042 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
du_'8851''45'isMonoid_3042 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_686
du_'8851''45'isMonoid_3042 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny -> AgdaAny
v3
  = (T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny -> T_IsMonoid_686
forall a b. a -> b
coe
      T_IsSemigroup_472 -> T_Σ_14 -> T_IsMonoid_686
MAlonzo.Code.Algebra.Structures.C_IsMonoid'46'constructor_15873
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
du_'8851''45'isSemigroup_3032 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                 T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                 T_MinOperator_98
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_3046 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
d_'8851''45'rawMagma_3046 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_RawMagma_36
d_'8851''45'rawMagma_3046 ~()
v0 ~()
v1 ~()
v2 ~T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_MinOperator_98 -> T_RawMagma_36
du_'8851''45'rawMagma_3046 T_MinOperator_98
v4
du_'8851''45'rawMagma_3046 ::
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
du_'8851''45'rawMagma_3046 :: T_MinOperator_98 -> T_RawMagma_36
du_'8851''45'rawMagma_3046 T_MinOperator_98
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_36)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_36
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_36
MAlonzo.Code.Algebra.Bundles.Raw.C_RawMagma'46'constructor_341
      (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
         (T_MinOperator_98 -> T_MinOperator_98
forall a b. a -> b
coe T_MinOperator_98
v0))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-magma
d_'8851''45'magma_3048 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_68
d_'8851''45'magma_3048 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_Magma_68
d_'8851''45'magma_3048 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68
du_'8851''45'magma_3048 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'magma_3048 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_Magma_68
du_'8851''45'magma_3048 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_Magma_68
du_'8851''45'magma_3048 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Magma_68
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Magma_68
MAlonzo.Code.Algebra.Bundles.C_Magma'46'constructor_1279
      (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
         (T_MinOperator_98 -> T_MinOperator_98
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsMagma_176
du_'8851''45'isMagma_3030 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-semigroup
d_'8851''45'semigroup_3050 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
d_'8851''45'semigroup_3050 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_Semigroup_536
d_'8851''45'semigroup_3050 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536
du_'8851''45'semigroup_3050 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'semigroup_3050 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
du_'8851''45'semigroup_3050 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_Semigroup_536
du_'8851''45'semigroup_3050 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_472 -> T_Semigroup_536)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Semigroup_536
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> T_Semigroup_536
MAlonzo.Code.Algebra.Bundles.C_Semigroup'46'constructor_9793
      (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
         (T_MinOperator_98 -> T_MinOperator_98
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSemigroup_472
du_'8851''45'isSemigroup_3032 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-band
d_'8851''45'band_3052 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_596
d_'8851''45'band_3052 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_Band_596
d_'8851''45'band_3052 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596
du_'8851''45'band_3052 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'band_3052 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_Band_596
du_'8851''45'band_3052 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_Band_596
du_'8851''45'band_3052 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Band_596
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Band_596
MAlonzo.Code.Algebra.Bundles.C_Band'46'constructor_10881
      (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
         (T_MinOperator_98 -> T_MinOperator_98
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsBand_508
du_'8851''45'isBand_3034 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-commutativeSemigroup
d_'8851''45'commutativeSemigroup_3054 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_3054 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_CommutativeSemigroup_662
d_'8851''45'commutativeSemigroup_3054 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222
-> T_MinOperator_98 -> T_CommutativeSemigroup_662
du_'8851''45'commutativeSemigroup_3054 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'commutativeSemigroup_3054 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
du_'8851''45'commutativeSemigroup_3054 :: T_TotalPreorder_222
-> T_MinOperator_98 -> T_CommutativeSemigroup_662
du_'8851''45'commutativeSemigroup_3054 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeSemigroup_662
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_548 -> T_CommutativeSemigroup_662
MAlonzo.Code.Algebra.Bundles.C_CommutativeSemigroup'46'constructor_12035
      (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
         (T_MinOperator_98 -> T_MinOperator_98
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> T_IsCommutativeSemigroup_548)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> T_IsCommutativeSemigroup_548
du_'8851''45'isCommutativeSemigroup_3036 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-selectiveMagma
d_'8851''45'selectiveMagma_3056 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
d_'8851''45'selectiveMagma_3056 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> T_SelectiveMagma_122
d_'8851''45'selectiveMagma_3056 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4
  = T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122
du_'8851''45'selectiveMagma_3056 T_TotalPreorder_222
v3 T_MinOperator_98
v4
du_'8851''45'selectiveMagma_3056 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
du_'8851''45'selectiveMagma_3056 :: T_TotalPreorder_222 -> T_MinOperator_98 -> T_SelectiveMagma_122
du_'8851''45'selectiveMagma_3056 T_TotalPreorder_222
v0 T_MinOperator_98
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSelectiveMagma_436 -> T_SelectiveMagma_122)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_SelectiveMagma_122
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSelectiveMagma_436 -> T_SelectiveMagma_122
MAlonzo.Code.Algebra.Bundles.C_SelectiveMagma'46'constructor_2287
      (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
         (T_MinOperator_98 -> T_MinOperator_98
forall a b. a -> b
coe T_MinOperator_98
v1))
      ((T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> T_IsSelectiveMagma_436
du_'8851''45'isSelectiveMagma_3038 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-monoid
d_'8851''45'monoid_3060 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
d_'8851''45'monoid_3060 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_Monoid_882
d_'8851''45'monoid_3060 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_Monoid_882
du_'8851''45'monoid_3060 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny -> AgdaAny
v6
du_'8851''45'monoid_3060 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
du_'8851''45'monoid_3060 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_Monoid_882
du_'8851''45'monoid_3060 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny -> AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Monoid_882
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_686 -> T_Monoid_882
MAlonzo.Code.Algebra.Bundles.C_Monoid'46'constructor_16157
      (T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
         (T_MinOperator_98 -> T_MinOperator_98
forall a b. a -> b
coe T_MinOperator_98
v1))
      AgdaAny
v2
      ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsMonoid_686)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsMonoid_686
du_'8851''45'isMonoid_3042 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_3068 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8776'x'8658'x'8804'y_3068 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8776'x'8658'x'8804'y_3068 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_3068 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_x'8851'y'8776'x'8658'x'8804'y_3068 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_3068 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_3068 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = let v5 :: t
v5
          = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
              (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                   ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                      T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                      (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
                AgdaAny
v2 AgdaAny
v3
                (let v7 :: t
v7
                       = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                           T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                 AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   (let v8 :: t
v8
                          = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v7) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v8))
                         AgdaAny
v2
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                            AgdaAny
v2 AgdaAny
v3)
                         AgdaAny
v3
                         (let v9 :: t
v9
                                = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                                    T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            (let v10 :: t
v10
                                   = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                                       T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180
                                       (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v9) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                     (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v10))
                                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                     T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                  AgdaAny
v2 AgdaAny
v4)))
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                            T_MinOperator_98
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_3100 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8851'y'8776'y'8658'y'8804'x_3100 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8851'y'8776'y'8658'y'8804'x_3100 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'y'8658'y'8804'x_3100 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_x'8851'y'8776'y'8658'y'8804'x_3100 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'y'8658'y'8804'x_3100 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'y'8658'y'8804'x_3100 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = (T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8776'x'8658'x'8804'y_3068 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
      (let v5 :: b
v5
             = T_SubRelation_60 -> b
forall a b. a -> b
coe
                 T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)
            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
               AgdaAny
v3 AgdaAny
v2)
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
            (let v6 :: T_IsPreorder_70
v6
                   = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                       ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                          T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                          (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                  ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))
                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                     AgdaAny
v3 AgdaAny
v2)
                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                     AgdaAny
v2 AgdaAny
v3)
                  AgdaAny
v3
                  (let v7 :: T_IsPreorder_70
v7
                         = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                             ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                        ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v7))
                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                           AgdaAny
v2 AgdaAny
v3)
                        AgdaAny
v3 AgdaAny
v3
                        (let v8 :: T_IsPreorder_70
v8
                               = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                   ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                      T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                      (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                              ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                 (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v8))
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
                        AgdaAny
v4))
                  ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'comm_2856 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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'_3114 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny
d_mono'45''8804''45'distrib'45''8851'_3114 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_mono'45''8804''45'distrib'45''8851'_3114 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                                           AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_mono'45''8804''45'distrib'45''8851'_3114 T_TotalPreorder_222
v3 T_MinOperator_98
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'_3114 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny
du_mono'45''8804''45'distrib'45''8851'_3114 :: T_TotalPreorder_222
-> T_MinOperator_98
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_mono'45''8804''45'distrib'45''8851'_3114 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = let v7 :: t
v7
          = (T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
              (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                 (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
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
           -> let v9 :: b
v9
                    = T_SubRelation_60 -> b
forall a b. a -> b
coe
                        T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v9)
                   ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> AgdaAny
v2
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v5 AgdaAny
v6))
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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))
                   (let v10 :: T_IsPreorder_70
v10
                          = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                              ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                 T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                            (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            AgdaAny -> AgdaAny
v2
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v5 AgdaAny
v6))
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5)
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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))
                         (let v11 :: T_IsPreorder_70
v11
                                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11))
                               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                  ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11)))
                               ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v5)
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
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))
                               (let v12 :: T_IsPreorder_70
v12
                                      = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                          ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                             T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                     ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v12))
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                  T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v5 AgdaAny
v6)
                            AgdaAny
v5
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                               T_MinOperator_98
v1 AgdaAny
v5 AgdaAny
v6 AgdaAny
v8)))))
         MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 AgdaAny
v8
           -> let v9 :: b
v9
                    = T_SubRelation_60 -> b
forall a b. a -> b
coe
                        T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                   T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v9)
                   ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> AgdaAny
v2
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v5 AgdaAny
v6))
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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))
                   (let v10 :: T_IsPreorder_70
v10
                          = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                              ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                 T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                         ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                            (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            AgdaAny -> AgdaAny
v2
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v5 AgdaAny
v6))
                         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6)
                         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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))
                         (let v11 :: T_IsPreorder_70
v11
                                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                          AgdaAny -> AgdaAny
forall a b. a -> b
coe
                            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11))
                               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                  ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v11)))
                               ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v6)
                               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                  T_MinOperator_98
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))
                               (let v12 :: T_IsPreorder_70
v12
                                      = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                          ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                             T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                     ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v12))
                                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                        T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                  T_MinOperator_98
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_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                               AgdaAny
v5 AgdaAny
v6)
                            AgdaAny
v6
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                               T_MinOperator_98
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_3160 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8658'x'8851'z'8804'y_3160 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8658'x'8851'z'8804'y_3160 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'x'8851'z'8804'y_3160 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8658'x'8851'z'8804'y_3160 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8658'x'8851'z'8804'y_3160 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'x'8851'z'8804'y_3160 T_TotalPreorder_222
v0 T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
         ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
            (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
         AgdaAny
v2 AgdaAny
v4)
      AgdaAny
v2 AgdaAny
v3
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_2808 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_3172 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8658'z'8851'x'8804'y_3172 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8658'z'8851'x'8804'y_3172 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'z'8851'x'8804'y_3172 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8658'z'8851'x'8804'y_3172 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8658'z'8851'x'8804'y_3172 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8658'z'8851'x'8804'y_3172 T_TotalPreorder_222
v0 T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
         ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
            (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
         AgdaAny
v4 AgdaAny
v2)
      AgdaAny
v2 AgdaAny
v3
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_2834 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_3184 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'y_3184 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'y_3184 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'y_3184 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8851'z'8658'x'8804'y_3184 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'y_3184 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'y_3184 T_TotalPreorder_222
v0 T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
         ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
            (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
      AgdaAny
v2
      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
         AgdaAny
v3 AgdaAny
v4)
      AgdaAny
v3 AgdaAny
v5
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_2808 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_3198 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'z_3198 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'y'8851'z'8658'x'8804'z_3198 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'z_3198 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_x'8804'y'8851'z'8658'x'8804'z_3198 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'z_3198 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_x'8804'y'8851'z'8658'x'8804'z_3198 T_TotalPreorder_222
v0 T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
         ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
            T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
            (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
      AgdaAny
v2
      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
         AgdaAny
v3 AgdaAny
v4)
      AgdaAny
v4 AgdaAny
v5
      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_2834 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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'_3206 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'mono'45''8804'_3206 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'mono'45''8804'_3206 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
                                AgdaAny
v10
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_3206 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8851''45'mono'45''8804'_3206 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'mono'45''8804'_3206 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_3206 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = let v8 :: t
v8
          = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> T__'8846'__30 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe
              (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T__'8846'__30 -> AgdaAny
MAlonzo.Code.Data.Sum.Base.du_'91'_'44'_'93'_52
              ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                 (\ AgdaAny
v8 ->
                    (AgdaAny -> T__'8846'__30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                         T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v5 AgdaAny
v8)))
              ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                 (\ AgdaAny
v8 ->
                    (AgdaAny -> T__'8846'__30) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      AgdaAny -> T__'8846'__30
MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                         T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v5 AgdaAny
v8)))
              ((T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Relation.Binary.Structures.d_total_134
                 (T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                    (T_TotalPreorder_222 -> T_TotalPreorder_222
forall a b. a -> b
coe T_TotalPreorder_222
v0))
                 AgdaAny
v3 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
v10
                    = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_'8818''45'resp'691''45''8776'_106
                   ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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
v10))
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v4)
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v3 AgdaAny
v5)
                   (let v11 :: t
v11
                          = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (let v12 :: t
v12
                             = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                                 T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v11) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v12))
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                         ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                            T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                            (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v2 AgdaAny
v4)
                      AgdaAny
v2 AgdaAny
v3
                      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'x_2808 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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
v10
                    = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                        T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_'8818''45'resp'691''45''8776'_106
                   ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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
v10))
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v2 AgdaAny
v4)
                   (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)
                   ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                      AgdaAny
v3 AgdaAny
v5)
                   (let v11 :: t
v11
                          = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                              T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) in
                    AgdaAny -> AgdaAny
forall a b. a -> b
coe
                      (let v12 :: t
v12
                             = (T_Preorder_132 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe
                                 T_Preorder_132 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v11) 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_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> T_Setoid_44
forall a b. a -> b
coe AgdaAny
forall a. a
v12))
                            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                         ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                            T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                            (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)))
                      ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                         T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                         AgdaAny
v2 AgdaAny
v4)
                      AgdaAny
v4 AgdaAny
v5
                      ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8851'y'8804'y_2834 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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'_3256 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'mono'737''45''8804'_3256 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'mono'737''45''8804'_3256 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'737''45''8804'_3256 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'mono'737''45''8804'_3256 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'mono'737''45''8804'_3256 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'737''45''8804'_3256 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_3206 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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
v6
             = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))
-- Algebra.Construct.NaturalChoice.MinOp.⊓-monoʳ-≤
d_'8851''45'mono'691''45''8804'_3266 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'mono'691''45''8804'_3266 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'mono'691''45''8804'_3266 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'691''45''8804'_3266 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_'8851''45'mono'691''45''8804'_3266 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'mono'691''45''8804'_3266 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'691''45''8804'_3266 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_3206 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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
v6
             = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
                 T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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))
            (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_3278 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'glb_3278 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'glb_3278 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'glb_3278 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_'8851''45'glb_3278 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'glb_3278 :: T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'glb_3278 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = let v7 :: t
v7
          = (T_TotalPreorder_222 -> T_Preorder_132) -> AgdaAny -> t
forall a b. a -> b
coe
              T_TotalPreorder_222 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
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_'8818''45'resp'737''45''8776'_100
         ((T_Preorder_132 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
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_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
            AgdaAny
v3 AgdaAny
v4)
         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
            AgdaAny
v2 AgdaAny
v2)
         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny
du_'8851''45'idem_2984 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
         ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'mono'45''8804'_3206 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_3292 ::
  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_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8851''45'triangulate_3292 :: ()
-> ()
-> ()
-> T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8851''45'triangulate_3292 ~()
v0 ~()
v1 ~()
v2 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'triangulate_3292 T_TotalPreorder_222
v3 T_MinOperator_98
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_'8851''45'triangulate_3292 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
  MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'triangulate_3292 :: T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'triangulate_3292 T_TotalPreorder_222
v0 T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = let v5 :: b
v5
          = T_SubRelation_60 -> b
forall a b. a -> b
coe
              T_SubRelation_60
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
    AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_SubRelation_60 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)
         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
               AgdaAny
v2 AgdaAny
v3)
            AgdaAny
v4)
         ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
               AgdaAny
v2 AgdaAny
v3)
            ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
               AgdaAny
v3 AgdaAny
v4))
         (let v6 :: T_IsPreorder_70
v6
                = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                    ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                       T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                       (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
               ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                  ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6)))
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                     AgdaAny
v2 AgdaAny
v3)
                  AgdaAny
v4)
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                     AgdaAny
v2
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v3 AgdaAny
v3))
                  AgdaAny
v4)
               ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                     AgdaAny
v2 AgdaAny
v3)
                  ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                     AgdaAny
v3 AgdaAny
v4))
               (let v7 :: T_IsPreorder_70
v7
                      = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                          ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                             T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                             (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                     ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v7))
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                           AgdaAny
v2
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              AgdaAny
v3 AgdaAny
v3))
                        AgdaAny
v4)
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v2
                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              AgdaAny
v3 AgdaAny
v3)
                           AgdaAny
v4))
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                           AgdaAny
v2 AgdaAny
v3)
                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                           AgdaAny
v3 AgdaAny
v4))
                     (let v8 :: T_IsPreorder_70
v8
                            = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                   T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny -> AgdaAny -> AgdaAny -> 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 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v8))
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              AgdaAny
v2
                              ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v3)
                                 AgdaAny
v4))
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              AgdaAny
v2
                              ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                 AgdaAny
v3
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4)))
                           ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                              ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                 AgdaAny
v2 AgdaAny
v3)
                              ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                 AgdaAny
v3 AgdaAny
v4))
                           (let v9 :: T_IsPreorder_70
v9
                                  = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                         T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                            AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> 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 -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 ((T_IsPreorder_70
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__62
 -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsPreorder_70
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__62
-> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v9))
                                 (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    ((T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                       T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v9)))
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1 AgdaAny
v2
                                    ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       T_MinOperator_98
v1 AgdaAny
v3
                                       ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4)))
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1
                                    ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                    ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1
                                    ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                    ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                                 (let v10 :: T_IsPreorder_70
v10
                                        = T_IsTotalPreorder_124 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            ((T_TotalPreorder_222 -> T_IsTotalPreorder_124)
-> AgdaAny -> T_IsTotalPreorder_124
forall a b. a -> b
coe
                                               T_TotalPreorder_222 -> T_IsTotalPreorder_124
MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0)) in
                                  AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       ((T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_IsPreorder_70 -> AgdaAny -> T__IsRelatedTo__62
MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v10))
                                       ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          T_MinOperator_98
v1
                                          ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                             T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             T_MinOperator_98
v1 AgdaAny
v2 AgdaAny
v3)
                                          ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                             T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))))
                                 ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_2944 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                                    ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))))
                           ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                              T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                              ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v3)
                                 AgdaAny
v4)
                              ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                                 AgdaAny
v3
                                 ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    T_MinOperator_98
v1 AgdaAny
v3 AgdaAny
v4))
                              ((T_TotalPreorder_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_2944 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
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_222
 -> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_TotalPreorder_222
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8851''45'assoc_2944 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                        ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                           AgdaAny
v3 AgdaAny
v3)
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
               ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'691'_2920 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)
                  (((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'_292
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v2)
                     (\ AgdaAny
v7 AgdaAny
v8 -> AgdaAny
v7)
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
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'__298
                     (\ AgdaAny
v7 AgdaAny
v8 -> AgdaAny
v8)
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v2)
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v3 AgdaAny
v3)
                     AgdaAny
v3)
                  ((T_TotalPreorder_222
 -> T_MinOperator_98
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                     T_TotalPreorder_222
-> T_MinOperator_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8851''45'cong'737'_2882 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                     ((T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_MinOperator_98 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 T_MinOperator_98
v1
                        AgdaAny
v3 AgdaAny
v3)
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                     ((T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222 -> T_MinOperator_98 -> AgdaAny -> AgdaAny
du_'8851''45'idem_2984 (T_TotalPreorder_222 -> AgdaAny
forall a b. a -> b
coe T_TotalPreorder_222
v0) (T_MinOperator_98 -> AgdaAny
forall a b. a -> b
coe T_MinOperator_98
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))