{-# 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.Relation.Binary.Construct.NaturalOrder.Left 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.Structures
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Base.Single
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Syntax
import qualified MAlonzo.Code.Relation.Binary.Structures
import qualified MAlonzo.Code.Relation.Nullary.Decidable.Core

-- Relation.Binary.Construct.NaturalOrder.Left._.Commutative
d_Commutative_48 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Commutative_48 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Commutative_48 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Relation.Binary.Construct.NaturalOrder.Left._.Idempotent
d_Idempotent_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Idempotent_58 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Idempotent_58 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Relation.Binary.Construct.NaturalOrder.Left._.Selective
d_Selective_130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Selective_130 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Selective_130 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Relation.Binary.Construct.NaturalOrder.Left._.IsBand
d_IsBand_156 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBand_156 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Relation.Binary.Construct.NaturalOrder.Left._.IsMagma
d_IsMagma_196 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMagma_196 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Relation.Binary.Construct.NaturalOrder.Left._.IsSemigroup
d_IsSemigroup_224 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSemigroup_224 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Relation.Binary.Construct.NaturalOrder.Left._.IsBand.idem
d_idem_338 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_338 :: T_IsBand_508 -> AgdaAny -> AgdaAny
d_idem_338 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)
-- Relation.Binary.Construct.NaturalOrder.Left._.IsBand.isSemigroup
d_isSemigroup_346 ::
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
d_isSemigroup_346 :: T_IsBand_508 -> T_IsSemigroup_472
d_isSemigroup_346 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)
-- Relation.Binary.Construct.NaturalOrder.Left._.IsMagma.isEquivalence
d_isEquivalence_1496 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1496 :: T_IsMagma_176 -> T_IsEquivalence_26
d_isEquivalence_1496 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)
-- Relation.Binary.Construct.NaturalOrder.Left._.IsMagma.∙-cong
d_'8729''45'cong_1510 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1510 :: T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1510 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)
-- Relation.Binary.Construct.NaturalOrder.Left._.IsSemigroup.assoc
d_assoc_2350 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2350 :: T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2350 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)
-- Relation.Binary.Construct.NaturalOrder.Left._.IsSemigroup.isMagma
d_isMagma_2354 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176
d_isMagma_2354 :: T_IsSemigroup_472 -> T_IsMagma_176
d_isMagma_2354 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)
-- Relation.Binary.Construct.NaturalOrder.Left._.IsSemilattice
d_IsSemilattice_2682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_IsSemilattice_2682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_IsSemilattice_2682 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Relation.Binary.Construct.NaturalOrder.Left._≤_
d__'8804'__3088 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> ()
d__'8804'__3088 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8804'__3088 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Relation.Binary.Construct.NaturalOrder.Left.reflexive
d_reflexive_3094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_3094 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_reflexive_3094 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_reflexive_3094 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9
du_reflexive_3094 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_3094 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_reflexive_3094 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsMagma_176
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v8)
      AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4)
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
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
v1))))
         AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4)
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
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
v1))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4)
            (let v6 :: AgdaAny -> AgdaAny
v6
                   = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                       ((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
v1)) 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
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v6))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4)))
            ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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
v1 AgdaAny
v3 AgdaAny
v3 AgdaAny
v3 AgdaAny
v4
               ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                  (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v3)
               AgdaAny
v5))
         ((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_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3) AgdaAny
v3 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)))
-- Relation.Binary.Construct.NaturalOrder.Left.refl
d_refl_3172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_refl_3172 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
d_refl_3172 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_refl_3172 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7
du_refl_3172 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
du_refl_3172 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_refl_3172 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny
v3 = (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3) AgdaAny
v3 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Construct.NaturalOrder.Left.antisym
d_antisym_3180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_3180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_antisym_3180 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsEquivalence_26
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_antisym_3180 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsEquivalence_26
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_antisym_3180 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_3180 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_antisym_3180 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsEquivalence_26
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = ((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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v9)
      AgdaAny
v3 AgdaAny
v4
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsEquivalence_26 -> AgdaAny
forall a b. a -> b
coe T_IsEquivalence_26
v1)))
         AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4) AgdaAny
v4
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsEquivalence_26 -> AgdaAny
forall a b. a -> b
coe T_IsEquivalence_26
v1)))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v3) AgdaAny
v4
            (((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
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsEquivalence_26 -> AgdaAny
forall a b. a -> b
coe T_IsEquivalence_26
v1)))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v3) AgdaAny
v4 AgdaAny
v4
               (let v7 :: AgdaAny -> AgdaAny
v7
                      = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34 (T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v1) 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
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v7))
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
               ((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_IsEquivalence_26
v1 AgdaAny
v4
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v3) AgdaAny
v6))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4))
         AgdaAny
v5)
-- Relation.Binary.Construct.NaturalOrder.Left.total
d_total_3250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_total_3250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T__'8846'__30
d_total_3250 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> T__'8846'__30
v7 AgdaAny -> AgdaAny -> AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T__'8846'__30
du_total_3250 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny -> T__'8846'__30
v7 AgdaAny -> AgdaAny -> AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_total_3250 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
du_total_3250 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T__'8846'__30
du_total_3250 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> T__'8846'__30
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> T__'8846'__30 -> T__'8846'__30)
-> AgdaAny -> (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 ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v5 AgdaAny
v6) AgdaAny
v5)
      (\ AgdaAny
v7 ->
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v6 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v5 AgdaAny
v6) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v6 AgdaAny
v5) ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v5 AgdaAny
v6) AgdaAny
v6 AgdaAny
v7)
           ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6))
      ((AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8846'__30
v3 AgdaAny
v5 AgdaAny
v6)
-- Relation.Binary.Construct.NaturalOrder.Left.trans
d_trans_3266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_3266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_3266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_3266 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsSemigroup_472
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_trans_3266 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_3266 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_3266 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsSemigroup_472
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = ((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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v9)
      AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                     ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v1))))))
         AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                        ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v1))))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4)) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
            (((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
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                        ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v1))))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4)) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v4)
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
               (((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
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                           ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                              ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v1))))))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
                  (let v7 :: AgdaAny -> AgdaAny
v7
                         = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                             ((T_Setoid_44 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                                T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                                ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                                   ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v1)))) 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
                        (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                           ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v7))
                        ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)))
                  ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1))
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v2 AgdaAny
v4 AgdaAny
v4
                     ((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_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                           ((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
v1)))
                        AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v5)
                     ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                        (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                           ((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
v1)))
                        AgdaAny
v4)))
               ((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_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                     ((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
v1)))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4))
                  ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> 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
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4)))
            ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480 (T_IsSemigroup_472 -> T_IsSemigroup_472
forall a b. a -> b
coe T_IsSemigroup_472
v1)) AgdaAny
v2 AgdaAny
v2 AgdaAny
v3
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v4)
               ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                  (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                     ((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
v1)))
                  AgdaAny
v2)
               AgdaAny
v6))
         AgdaAny
v5)
-- Relation.Binary.Construct.NaturalOrder.Left.respʳ
d_resp'691'_3350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_resp'691'_3350 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_resp'691'_3350 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_resp'691'_3350 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_resp'691'_3350 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_resp'691'_3350 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_resp'691'_3350 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsMagma_176
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = ((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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v9)
      AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
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
v1))))
         AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
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
v1))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)
            (let v7 :: AgdaAny -> AgdaAny
v7
                   = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                       ((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
v1)) 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
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v7))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v4)))
            ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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
v1 AgdaAny
v2 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
               ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                  (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v2)
               AgdaAny
v5))
         AgdaAny
v6)
-- Relation.Binary.Construct.NaturalOrder.Left.respˡ
d_resp'737'_3430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_resp'737'_3430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_resp'737'_3430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_resp'737'_3430 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_resp'737'_3430 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_resp'737'_3430 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_resp'737'_3430 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsMagma_176
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = ((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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v9)
      AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2)
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
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
v1))))
         AgdaAny
v4 AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2)
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
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
v1))))
            AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v2) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2)
            (((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
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
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
v1))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v2) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2)
               (let v7 :: AgdaAny -> AgdaAny
v7
                      = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                          ((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
v1)) 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
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v7))
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2)))
               ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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
v1 AgdaAny
v3 AgdaAny
v4 AgdaAny
v2 AgdaAny
v2
                  AgdaAny
v5
                  ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                     (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1))
                     AgdaAny
v2)))
            AgdaAny
v6)
         ((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_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (T_IsMagma_176 -> T_IsMagma_176
forall a b. a -> b
coe T_IsMagma_176
v1)) AgdaAny
v3
            AgdaAny
v4 AgdaAny
v5))
-- Relation.Binary.Construct.NaturalOrder.Left.resp₂
d_resp'8322'_3510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_resp'8322'_3510 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> T_Σ_14
d_resp'8322'_3510 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5 = (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Σ_14
du_resp'8322'_3510 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMagma_176
v5
du_resp'8322'_3510 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_resp'8322'_3510 :: (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_176 -> T_Σ_14
du_resp'8322'_3510 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsMagma_176
v1
  = (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)
 -> T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_resp'691'_3350 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_resp'737'_3430 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsMagma_176 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_176
v1))
-- Relation.Binary.Construct.NaturalOrder.Left.dec
d_dec_3514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
d_dec_3514 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> AgdaAny
-> AgdaAny
-> T_Dec_20
d_dec_3514 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> T_Dec_20
v5 AgdaAny
v6 AgdaAny
v7 = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> AgdaAny
-> AgdaAny
-> T_Dec_20
du_dec_3514 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> T_Dec_20
v5 AgdaAny
v6 AgdaAny
v7
du_dec_3514 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  AgdaAny ->
  AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
du_dec_3514 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> AgdaAny
-> AgdaAny
-> T_Dec_20
du_dec_3514 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> T_Dec_20
v1 AgdaAny
v2 AgdaAny
v3 = (AgdaAny -> AgdaAny -> T_Dec_20) -> AgdaAny -> AgdaAny -> T_Dec_20
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Dec_20
v1 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Construct.NaturalOrder.Left._.x∙y≤x
d_x'8729'y'8804'x_3606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_x'8729'y'8804'x_3606 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8729'y'8804'x_3606 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'x_3606 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7
du_x'8729'y'8804'x_3606 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'x_3606 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'x_3606 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny
v2 AgdaAny
v3
  = ((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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v2)
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (let v4 :: T_IsBand_508
v4 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v5 :: T_IsSemigroup_472
v5
                            = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v5))))))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v2) AgdaAny
v3)
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v2)
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     (let v4 :: T_IsBand_508
v4 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v5 :: T_IsSemigroup_472
v5
                               = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                              ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v5))))))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v2) AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v2)
            (((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
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                        (let v4 :: T_IsBand_508
v4 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (let v5 :: T_IsSemigroup_472
v5
                                  = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4) in
                            AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                                 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v5))))))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3)) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v2)
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v2)
               (let v4 :: AgdaAny -> AgdaAny
v4
                      = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                          ((T_Setoid_44 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                             T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                             (let v4 :: T_IsBand_508
v4 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                (let v5 :: T_IsSemigroup_472
v5
                                       = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                                           (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4) in
                                 AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                                      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v5)))))) 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
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v4))
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v2)))
               ((T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600 T_IsCommutativeBand_590
v1 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3)))
            ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> 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_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
               AgdaAny
v2 AgdaAny
v2 AgdaAny
v3))
         ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((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_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))
            AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v2) AgdaAny
v3 AgdaAny
v3
            ((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_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                  ((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_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                        ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v2) AgdaAny
v2
               ((T_IsBand_508 -> AgdaAny -> AgdaAny)
-> T_IsBand_508 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
                  (T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)) AgdaAny
v2))
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
               (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                  ((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_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                        ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
               AgdaAny
v3)))
-- Relation.Binary.Construct.NaturalOrder.Left._.x∙y≤y
d_x'8729'y'8804'y_3616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_x'8729'y'8804'y_3616 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8729'y'8804'y_3616 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'y_3616 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7
du_x'8729'y'8804'y_3616 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'y_3616 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'y_3616 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny
v2 AgdaAny
v3
  = ((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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v3)
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (let v4 :: T_IsBand_508
v4 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v5 :: T_IsSemigroup_472
v5
                            = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v5))))))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v3)
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     (let v4 :: T_IsBand_508
v4 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v5 :: T_IsSemigroup_472
v5
                               = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                              ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v5))))))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3)) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v3)
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v3)
            (let v4 :: AgdaAny -> AgdaAny
v4
                   = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                       ((T_Setoid_44 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                          T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                          (let v4 :: T_IsBand_508
v4 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                           AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             (let v5 :: T_IsSemigroup_472
v5
                                    = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v4) in
                              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                                   ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v5)))))) 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
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v4))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v3)))
            ((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_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                  ((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_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                        ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3) AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3))
               ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> 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_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
                  AgdaAny
v2 AgdaAny
v3 AgdaAny
v3)))
         ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((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_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))
            AgdaAny
v2 AgdaAny
v2 AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3)
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
               (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                  ((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_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                        ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
               AgdaAny
v2)
            ((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_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                  ((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_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                        ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v3 AgdaAny
v3) AgdaAny
v3
               ((T_IsBand_508 -> AgdaAny -> AgdaAny)
-> T_IsBand_508 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_518
                  (T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)) AgdaAny
v3))))
-- Relation.Binary.Construct.NaturalOrder.Left._.∙-presʳ-≤
d_'8729''45'pres'691''45''8804'_3628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'pres'691''45''8804'_3628 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'pres'691''45''8804'_3628 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
                                     AgdaAny
v9 AgdaAny
v10
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'pres'691''45''8804'_3628 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8729''45'pres'691''45''8804'_3628 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'pres'691''45''8804'_3628 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'pres'691''45''8804'_3628 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = ((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.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v9)
      AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3))
      (((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
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (let v7 :: T_IsBand_508
v7 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v8 :: T_IsSemigroup_472
v8
                            = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v7) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                           ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v8))))))))
         AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3))
         (((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
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     (let v7 :: T_IsBand_508
v7 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (let v8 :: T_IsSemigroup_472
v8
                               = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v7) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                              ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v8))))))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2) AgdaAny
v3)
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3))
            (((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
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                        (let v7 :: T_IsBand_508
v7 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                         AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (let v8 :: T_IsSemigroup_472
v8
                                  = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v7) in
                            AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                                 ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v8))))))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2) AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3))
               (let v7 :: AgdaAny -> AgdaAny
v7
                      = T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                          ((T_Setoid_44 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
                             T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                             (let v7 :: T_IsBand_508
v7 = T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> T_IsCommutativeBand_590
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) in
                              AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                (let v8 :: T_IsSemigroup_472
v8
                                       = T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                                           (T_IsBand_508 -> T_IsBand_508
forall a b. a -> b
coe T_IsBand_508
v7) in
                                 AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                   ((T_IsMagma_176 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                      T_IsMagma_176 -> T_Setoid_44
MAlonzo.Code.Algebra.Structures.du_setoid_200
                                      ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
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
v8)))))) 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
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v7))
                     ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v2 AgdaAny
v3))))
               ((T_IsSemigroup_472 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472 -> 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_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508)
-> AgdaAny -> T_IsBand_508
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
                  AgdaAny
v4 AgdaAny
v2 AgdaAny
v3))
            ((T_IsMagma_176
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsMagma_176
-> 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_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((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_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))
               AgdaAny
v4 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny
v4 AgdaAny
v2) AgdaAny
v3 AgdaAny
v3 AgdaAny
v5
               ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                  (T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
                     ((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_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                           ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
                  AgdaAny
v3)))
         AgdaAny
v6)
-- Relation.Binary.Construct.NaturalOrder.Left._.infimum
d_infimum_3640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_3640 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_infimum_3640 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_3640 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny
v6 AgdaAny
v7
du_infimum_3640 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_infimum_3640 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_3640 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny
v2 AgdaAny
v3
  = (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)
 -> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'x_3606 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
      ((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)
 -> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8729'y'8804'y_3616 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8729''45'pres'691''45''8804'_3628 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
-- Relation.Binary.Construct.NaturalOrder.Left.isPreorder
d_isPreorder_3646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_3646 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_IsPreorder_70
d_isPreorder_3646 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_IsPreorder_70
du_isPreorder_3646 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
du_isPreorder_3646 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
du_isPreorder_3646 :: (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_IsPreorder_70
du_isPreorder_3646 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsBand_508
v1
  = (T_IsEquivalence_26
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsPreorder_70)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsEquivalence_26
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.C_IsPreorder'46'constructor_4003
      ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
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
v1))))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_176
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_176
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_reflexive_3094 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0)
         ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
            ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
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
v1)))
         ((T_IsBand_508 -> 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
v1)))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_472
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_472
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_3266 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0)
         ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
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
v1)))
-- Relation.Binary.Construct.NaturalOrder.Left.isPartialOrder
d_isPartialOrder_3680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_3680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_IsPartialOrder_174
d_isPartialOrder_3680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_IsPartialOrder_174
du_isPartialOrder_3680 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
du_isPartialOrder_3680 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
du_isPartialOrder_3680 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_IsPartialOrder_174
du_isPartialOrder_3680 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1
  = (T_IsPreorder_70
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsPreorder_70
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsPartialOrder_174
MAlonzo.Code.Relation.Binary.Structures.C_IsPartialOrder'46'constructor_9853
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsBand_508 -> T_IsPreorder_70)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_IsPreorder_70
du_isPreorder_3646 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0)
         ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_antisym_3180 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0)
         ((T_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
            ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
               ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                  ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))))
         ((T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Relation.Binary.Construct.NaturalOrder.Left.isDecPartialOrder
d_isDecPartialOrder_3722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecPartialOrder_224
d_isDecPartialOrder_3722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecPartialOrder_224
d_isDecPartialOrder_3722 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T_Dec_20
v6
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecPartialOrder_224
du_isDecPartialOrder_3722 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T_Dec_20
v6
du_isDecPartialOrder_3722 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecPartialOrder_224
du_isDecPartialOrder_3722 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecPartialOrder_224
du_isDecPartialOrder_3722 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny -> AgdaAny -> T_Dec_20
v2
  = (T_IsPartialOrder_174
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> T_IsDecPartialOrder_224)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsDecPartialOrder_224
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecPartialOrder_224
MAlonzo.Code.Relation.Binary.Structures.C_IsDecPartialOrder'46'constructor_11683
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_IsPartialOrder_174
du_isPartialOrder_3680 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)) ((AgdaAny -> AgdaAny -> T_Dec_20) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Dec_20
v2)
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> AgdaAny
 -> AgdaAny
 -> T_Dec_20)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> AgdaAny
-> AgdaAny
-> T_Dec_20
du_dec_3514 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny -> T_Dec_20) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Dec_20
v2))
-- Relation.Binary.Construct.NaturalOrder.Left.isTotalOrder
d_isTotalOrder_3728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_404
d_isTotalOrder_3728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalOrder_404
d_isTotalOrder_3728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalOrder_404
du_isTotalOrder_3728 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6
du_isTotalOrder_3728 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsTotalOrder_404
du_isTotalOrder_3728 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalOrder_404
du_isTotalOrder_3728 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2
  = (T_IsPartialOrder_174
 -> (AgdaAny -> AgdaAny -> T__'8846'__30) -> T_IsTotalOrder_404)
-> AgdaAny -> AgdaAny -> T_IsTotalOrder_404
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> (AgdaAny -> AgdaAny -> T__'8846'__30) -> T_IsTotalOrder_404
MAlonzo.Code.Relation.Binary.Structures.C_IsTotalOrder'46'constructor_20555
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_IsPartialOrder_174
du_isPartialOrder_3680 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> T__'8846'__30)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T__'8846'__30)
-> 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 -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T__'8846'__30
du_total_3250 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0)
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> 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_IsMagma_176 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_176 -> T_IsEquivalence_26
MAlonzo.Code.Algebra.Structures.d_isEquivalence_184
               ((T_IsSemigroup_472 -> T_IsMagma_176) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsSemigroup_472 -> T_IsMagma_176
MAlonzo.Code.Algebra.Structures.d_isMagma_480
                  ((T_IsBand_508 -> T_IsSemigroup_472) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBand_508 -> T_IsSemigroup_472
MAlonzo.Code.Algebra.Structures.d_isSemigroup_516
                     ((T_IsCommutativeBand_590 -> T_IsBand_508) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> T_IsBand_508
MAlonzo.Code.Algebra.Structures.d_isBand_598 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))))))
         ((AgdaAny -> AgdaAny -> T__'8846'__30) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8846'__30
v2) ((T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_600 (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1)))
-- Relation.Binary.Construct.NaturalOrder.Left.isDecTotalOrder
d_isDecTotalOrder_3772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_460
d_isDecTotalOrder_3772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecTotalOrder_460
d_isDecTotalOrder_3772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6 AgdaAny -> AgdaAny -> T_Dec_20
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecTotalOrder_460
du_isDecTotalOrder_3772 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6 AgdaAny -> AgdaAny -> T_Dec_20
v7
du_isDecTotalOrder_3772 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsDecTotalOrder_460
du_isDecTotalOrder_3772 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecTotalOrder_460
du_isDecTotalOrder_3772 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 AgdaAny -> AgdaAny -> T_Dec_20
v3
  = (T_IsTotalOrder_404
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> T_IsDecTotalOrder_460)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsDecTotalOrder_460
forall a b. a -> b
coe
      T_IsTotalOrder_404
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecTotalOrder_460
MAlonzo.Code.Relation.Binary.Structures.C_IsDecTotalOrder'46'constructor_22695
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590
 -> (AgdaAny -> AgdaAny -> T__'8846'__30)
 -> T_IsTotalOrder_404)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalOrder_404
du_isTotalOrder_3728 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) ((AgdaAny -> AgdaAny -> T__'8846'__30) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8846'__30
v2)) ((AgdaAny -> AgdaAny -> T_Dec_20) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Dec_20
v3)
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> AgdaAny
 -> AgdaAny
 -> T_Dec_20)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> AgdaAny
-> AgdaAny
-> T_Dec_20
du_dec_3514 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny -> T_Dec_20) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Dec_20
v3))
-- Relation.Binary.Construct.NaturalOrder.Left.preorder
d_preorder_3780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_3780 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBand_508
-> T_Preorder_132
d_preorder_3780 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5 = (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Preorder_132
du_preorder_3780 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsBand_508
v5
du_preorder_3780 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_3780 :: (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_Preorder_132
du_preorder_3780 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsBand_508
v1
  = (T_IsPreorder_70 -> T_Preorder_132) -> AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.C_Preorder'46'constructor_2267
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsBand_508 -> T_IsPreorder_70)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_508 -> T_IsPreorder_70
du_isPreorder_3646 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsBand_508 -> AgdaAny
forall a b. a -> b
coe T_IsBand_508
v1))
-- Relation.Binary.Construct.NaturalOrder.Left.poset
d_poset_3784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
d_poset_3784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> T_Poset_314
d_poset_3784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_Poset_314
du_poset_3784 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5
du_poset_3784 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
du_poset_3784 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_Poset_314
du_poset_3784 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1
  = (T_IsPartialOrder_174 -> T_Poset_314) -> AgdaAny -> T_Poset_314
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_Poset_314
MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_6389
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590 -> T_IsPartialOrder_174
du_isPartialOrder_3680 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1))
-- Relation.Binary.Construct.NaturalOrder.Left.decPoset
d_decPoset_3788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Bundles.T_DecPoset_406
d_decPoset_3788 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_DecPoset_406
d_decPoset_3788 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T_Dec_20
v6
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_DecPoset_406
du_decPoset_3788 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T_Dec_20
v6
du_decPoset_3788 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Bundles.T_DecPoset_406
du_decPoset_3788 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_DecPoset_406
du_decPoset_3788 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny -> AgdaAny -> T_Dec_20
v2
  = (T_IsDecPartialOrder_224 -> T_DecPoset_406)
-> AgdaAny -> T_DecPoset_406
forall a b. a -> b
coe
      T_IsDecPartialOrder_224 -> T_DecPoset_406
MAlonzo.Code.Relation.Binary.Bundles.C_DecPoset'46'constructor_8213
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> T_IsDecPartialOrder_224)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecPartialOrder_224
du_isDecPartialOrder_3722 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) ((AgdaAny -> AgdaAny -> T_Dec_20) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Dec_20
v2))
-- Relation.Binary.Construct.NaturalOrder.Left.totalOrder
d_totalOrder_3794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764
d_totalOrder_3794 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_TotalOrder_764
d_totalOrder_3794 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_TotalOrder_764
du_totalOrder_3794 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6
du_totalOrder_3794 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764
du_totalOrder_3794 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_TotalOrder_764
du_totalOrder_3794 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2
  = (T_IsTotalOrder_404 -> T_TotalOrder_764)
-> AgdaAny -> T_TotalOrder_764
forall a b. a -> b
coe
      T_IsTotalOrder_404 -> T_TotalOrder_764
MAlonzo.Code.Relation.Binary.Bundles.C_TotalOrder'46'constructor_15747
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590
 -> (AgdaAny -> AgdaAny -> T__'8846'__30)
 -> T_IsTotalOrder_404)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> T_IsTotalOrder_404
du_isTotalOrder_3728 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) ((AgdaAny -> AgdaAny -> T__'8846'__30) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8846'__30
v2))
-- Relation.Binary.Construct.NaturalOrder.Left.decTotalOrder
d_decTotalOrder_3800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_866
d_decTotalOrder_3800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_DecTotalOrder_866
d_decTotalOrder_3800 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~AgdaAny -> AgdaAny -> T_Level_18
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6 AgdaAny -> AgdaAny -> T_Dec_20
v7
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_DecTotalOrder_866
du_decTotalOrder_3800 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsCommutativeBand_590
v5 AgdaAny -> AgdaAny -> T__'8846'__30
v6 AgdaAny -> AgdaAny -> T_Dec_20
v7
du_decTotalOrder_3800 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590 ->
  (AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
  MAlonzo.Code.Relation.Binary.Bundles.T_DecTotalOrder_866
du_decTotalOrder_3800 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_DecTotalOrder_866
du_decTotalOrder_3800 AgdaAny -> AgdaAny -> AgdaAny
v0 T_IsCommutativeBand_590
v1 AgdaAny -> AgdaAny -> T__'8846'__30
v2 AgdaAny -> AgdaAny -> T_Dec_20
v3
  = (T_IsDecTotalOrder_460 -> T_DecTotalOrder_866)
-> AgdaAny -> T_DecTotalOrder_866
forall a b. a -> b
coe
      T_IsDecTotalOrder_460 -> T_DecTotalOrder_866
MAlonzo.Code.Relation.Binary.Bundles.C_DecTotalOrder'46'constructor_17849
      (((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_590
 -> (AgdaAny -> AgdaAny -> T__'8846'__30)
 -> (AgdaAny -> AgdaAny -> T_Dec_20)
 -> T_IsDecTotalOrder_460)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_590
-> (AgdaAny -> AgdaAny -> T__'8846'__30)
-> (AgdaAny -> AgdaAny -> T_Dec_20)
-> T_IsDecTotalOrder_460
du_isDecTotalOrder_3772 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0) (T_IsCommutativeBand_590 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_590
v1) ((AgdaAny -> AgdaAny -> T__'8846'__30) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8846'__30
v2) ((AgdaAny -> AgdaAny -> T_Dec_20) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Dec_20
v3))