{-# 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.Function.Structures 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.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Data.Product.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Function.Structures.IsCongruent
d_IsCongruent_22 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsCongruent_22 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsCongruent_22
  = C_IsCongruent'46'constructor_985 (AgdaAny ->
                                      AgdaAny -> AgdaAny -> AgdaAny)
                                     MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
                                     MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
-- Function.Structures.IsCongruent.cong
d_cong_32 ::
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 T_IsCongruent_22
v0
  = case T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v0 of
      C_IsCongruent'46'constructor_985 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 T_IsEquivalence_26
v2 T_IsEquivalence_26
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1
      T_IsCongruent_22
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsCongruent.isEquivalence₁
d_isEquivalence'8321'_34 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_34 :: T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 T_IsCongruent_22
v0
  = case T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v0 of
      C_IsCongruent'46'constructor_985 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 T_IsEquivalence_26
v2 T_IsEquivalence_26
v3 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v2
      T_IsCongruent_22
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsCongruent.isEquivalence₂
d_isEquivalence'8322'_36 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_36 :: T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 T_IsCongruent_22
v0
  = case T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v0 of
      C_IsCongruent'46'constructor_985 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 T_IsEquivalence_26
v2 T_IsEquivalence_26
v3 -> T_IsEquivalence_26 -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsEquivalence_26
v3
      T_IsCongruent_22
_ -> T_IsEquivalence_26
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsCongruent.Eq₁.setoid
d_setoid_40 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_40 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_44
d_setoid_40 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 T_IsCongruent_22
v9
du_setoid_40 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_40 :: T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_733
      (T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₁._._≈_
d__'8776'__44 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> ()
d__'8776'__44 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__44 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₁._._≉_
d__'8777'__46 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> ()
d__'8777'__46 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__46 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₁._.Carrier
d_Carrier_48 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> ()
d_Carrier_48 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> ()
d_Carrier_48 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₁._.isEquivalence
d_isEquivalence_50 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_50 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_26
d_isEquivalence_50 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_50 T_IsCongruent_22
v9
du_isEquivalence_50 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_50 :: T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_50 T_IsCongruent_22
v0 = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Structures.IsCongruent.Eq₁._.isPartialEquivalence
d_isPartialEquivalence_52 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_52 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_52 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_52 T_IsCongruent_22
v9
du_isPartialEquivalence_52 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_52 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_52 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Structures.IsCongruent.Eq₁._.partialSetoid
d_partialSetoid_54 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_54 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_54 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_54 T_IsCongruent_22
v9
du_partialSetoid_54 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_54 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_54 T_IsCongruent_22
v0
  = (T_Setoid_44 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₁._.refl
d_refl_56 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> AgdaAny -> AgdaAny
d_refl_56 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_56 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_56 T_IsCongruent_22
v9
du_refl_56 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_56 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_56 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₁._.reflexive
d_reflexive_58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_58 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_58 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_58 T_IsCongruent_22
v9
du_reflexive_58 ::
  T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_58 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_58 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))
           AgdaAny
v2)
-- Function.Structures.IsCongruent.Eq₁._.sym
d_sym_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_60 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_60 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_60 T_IsCongruent_22
v9
du_sym_60 ::
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_60 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_60 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Structures.IsCongruent.Eq₁._.trans
d_trans_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_62 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_62 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_62 T_IsCongruent_22
v9
du_trans_62 ::
  T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_62 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_62 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Structures.IsCongruent.Eq₂.setoid
d_setoid_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_66 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_44
d_setoid_66 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 T_IsCongruent_22
v9
du_setoid_66 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_66 :: T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_733
      (T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₂._._≈_
d__'8776'__70 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> ()
d__'8776'__70 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__70 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₂._._≉_
d__'8777'__72 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> ()
d__'8777'__72 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__72 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₂._.Carrier
d_Carrier_74 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> ()
d_Carrier_74 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> ()
d_Carrier_74 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₂._.isEquivalence
d_isEquivalence_76 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_76 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_26
d_isEquivalence_76 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_76 T_IsCongruent_22
v9
du_isEquivalence_76 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_76 :: T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_76 T_IsCongruent_22
v0 = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Structures.IsCongruent.Eq₂._.isPartialEquivalence
d_isPartialEquivalence_78 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_78 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_78 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_78 T_IsCongruent_22
v9
du_isPartialEquivalence_78 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_78 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_78 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Structures.IsCongruent.Eq₂._.partialSetoid
d_partialSetoid_80 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_80 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_80 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_80 T_IsCongruent_22
v9
du_partialSetoid_80 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_80 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_80 T_IsCongruent_22
v0
  = (T_Setoid_44 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₂._.refl
d_refl_82 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> AgdaAny -> AgdaAny
d_refl_82 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_82 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_82 T_IsCongruent_22
v9
du_refl_82 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_82 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_82 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₂._.reflexive
d_reflexive_84 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_84 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_84 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_84 T_IsCongruent_22
v9
du_reflexive_84 ::
  T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_84 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_84 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))
           AgdaAny
v2)
-- Function.Structures.IsCongruent.Eq₂._.sym
d_sym_86 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_86 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_86 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_86 T_IsCongruent_22
v9
du_sym_86 ::
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_86 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_86 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Structures.IsCongruent.Eq₂._.trans
d_trans_88 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_88 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_88 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_88 T_IsCongruent_22
v9
du_trans_88 ::
  T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_88 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_88 T_IsCongruent_22
v0
  = let v1 :: t
v1 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Structures.IsInjection
d_IsInjection_92 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsInjection_92 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsInjection_92
  = C_IsInjection'46'constructor_3997 T_IsCongruent_22
                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsInjection.isCongruent
d_isCongruent_100 :: T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 :: T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 T_IsInjection_92
v0
  = case T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0 of
      C_IsInjection'46'constructor_3997 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsInjection_92
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInjection.injective
d_injective_102 ::
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_102 :: T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_102 T_IsInjection_92
v0
  = case T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0 of
      C_IsInjection'46'constructor_3997 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsInjection_92
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInjection._.cong
d_cong_106 ::
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_106 :: T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_106 T_IsInjection_92
v0 = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v0))
-- Function.Structures.IsInjection._.isEquivalence₁
d_isEquivalence'8321'_108 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_108 :: T_IsInjection_92 -> T_IsEquivalence_26
d_isEquivalence'8321'_108 T_IsInjection_92
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v0))
-- Function.Structures.IsInjection._.isEquivalence₂
d_isEquivalence'8322'_110 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_110 :: T_IsInjection_92 -> T_IsEquivalence_26
d_isEquivalence'8322'_110 T_IsInjection_92
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v0))
-- Function.Structures.IsInjection._.Eq₁._≈_
d__'8776'__114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> ()
d__'8776'__114 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__114 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₁._≉_
d__'8777'__116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> ()
d__'8777'__116 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__116 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₁.Carrier
d_Carrier_118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsInjection_92 -> ()
d_Carrier_118 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> ()
d_Carrier_118 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₁.isEquivalence
d_isEquivalence_120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_120 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_IsEquivalence_26
d_isEquivalence_120 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_IsEquivalence_26
du_isEquivalence_120 T_IsInjection_92
v9
du_isEquivalence_120 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_120 :: T_IsInjection_92 -> T_IsEquivalence_26
du_isEquivalence_120 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsInjection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_122 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_122 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_122 T_IsInjection_92
v9
du_isPartialEquivalence_122 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_122 :: T_IsInjection_92 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_122 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsInjection._.Eq₁.partialSetoid
d_partialSetoid_124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_124 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_PartialSetoid_10
d_partialSetoid_124 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_PartialSetoid_10
du_partialSetoid_124 T_IsInjection_92
v9
du_partialSetoid_124 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_124 :: T_IsInjection_92 -> T_PartialSetoid_10
du_partialSetoid_124 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsInjection._.Eq₁.refl
d_refl_126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsInjection_92 -> AgdaAny -> AgdaAny
d_refl_126 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
d_refl_126 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9 = T_IsInjection_92 -> AgdaAny -> AgdaAny
du_refl_126 T_IsInjection_92
v9
du_refl_126 :: T_IsInjection_92 -> AgdaAny -> AgdaAny
du_refl_126 :: T_IsInjection_92 -> AgdaAny -> AgdaAny
du_refl_126 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsInjection._.Eq₁.reflexive
d_reflexive_128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_128 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_128 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_128 T_IsInjection_92
v9
du_reflexive_128 ::
  T_IsInjection_92 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_128 :: T_IsInjection_92 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_128 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsInjection._.Eq₁.setoid
d_setoid_130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_130 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_Setoid_44
d_setoid_130 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_Setoid_44
du_setoid_130 T_IsInjection_92
v9
du_setoid_130 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_130 :: T_IsInjection_92 -> T_Setoid_44
du_setoid_130 T_IsInjection_92
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v0))
-- Function.Structures.IsInjection._.Eq₁.sym
d_sym_132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_132 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_132 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9 = T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_132 T_IsInjection_92
v9
du_sym_132 ::
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_132 :: T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_132 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsInjection._.Eq₁.trans
d_trans_134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_134 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_134 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_134 T_IsInjection_92
v9
du_trans_134 ::
  T_IsInjection_92 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_134 :: T_IsInjection_92
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_134 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsInjection._.Eq₂._≈_
d__'8776'__138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> ()
d__'8776'__138 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__138 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₂._≉_
d__'8777'__140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> ()
d__'8777'__140 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__140 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₂.Carrier
d_Carrier_142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsInjection_92 -> ()
d_Carrier_142 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> ()
d_Carrier_142 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₂.isEquivalence
d_isEquivalence_144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_144 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_IsEquivalence_26
d_isEquivalence_144 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_IsEquivalence_26
du_isEquivalence_144 T_IsInjection_92
v9
du_isEquivalence_144 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_144 :: T_IsInjection_92 -> T_IsEquivalence_26
du_isEquivalence_144 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsInjection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_146 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_146 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_146 T_IsInjection_92
v9
du_isPartialEquivalence_146 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_146 :: T_IsInjection_92 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_146 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsInjection._.Eq₂.partialSetoid
d_partialSetoid_148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_148 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_PartialSetoid_10
d_partialSetoid_148 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_PartialSetoid_10
du_partialSetoid_148 T_IsInjection_92
v9
du_partialSetoid_148 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_148 :: T_IsInjection_92 -> T_PartialSetoid_10
du_partialSetoid_148 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsInjection._.Eq₂.refl
d_refl_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsInjection_92 -> AgdaAny -> AgdaAny
d_refl_150 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
d_refl_150 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9 = T_IsInjection_92 -> AgdaAny -> AgdaAny
du_refl_150 T_IsInjection_92
v9
du_refl_150 :: T_IsInjection_92 -> AgdaAny -> AgdaAny
du_refl_150 :: T_IsInjection_92 -> AgdaAny -> AgdaAny
du_refl_150 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsInjection._.Eq₂.reflexive
d_reflexive_152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_152 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_152 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_152 T_IsInjection_92
v9
du_reflexive_152 ::
  T_IsInjection_92 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_152 :: T_IsInjection_92 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_152 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsInjection._.Eq₂.setoid
d_setoid_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_154 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> T_Setoid_44
d_setoid_154 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92 -> T_Setoid_44
du_setoid_154 T_IsInjection_92
v9
du_setoid_154 ::
  T_IsInjection_92 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_154 :: T_IsInjection_92 -> T_Setoid_44
du_setoid_154 T_IsInjection_92
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v0))
-- Function.Structures.IsInjection._.Eq₂.sym
d_sym_156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_156 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_156 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9 = T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_156 T_IsInjection_92
v9
du_sym_156 ::
  T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_156 :: T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_156 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsInjection._.Eq₂.trans
d_trans_158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInjection_92 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_158 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_92
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_158 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_92
v9
  = T_IsInjection_92
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_158 T_IsInjection_92
v9
du_trans_158 ::
  T_IsInjection_92 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_158 :: T_IsInjection_92
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_158 T_IsInjection_92
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSurjection
d_IsSurjection_162 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsSurjection_162 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsSurjection_162
  = C_IsSurjection'46'constructor_6463 T_IsCongruent_22
                                       (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Structures.IsSurjection.isCongruent
d_isCongruent_170 :: T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 :: T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 T_IsSurjection_162
v0
  = case T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0 of
      C_IsSurjection'46'constructor_6463 T_IsCongruent_22
v1 AgdaAny -> T_Σ_14
v2 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsSurjection_162
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSurjection.surjective
d_surjective_172 ::
  T_IsSurjection_162 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_172 :: T_IsSurjection_162 -> AgdaAny -> T_Σ_14
d_surjective_172 T_IsSurjection_162
v0
  = case T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0 of
      C_IsSurjection'46'constructor_6463 T_IsCongruent_22
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsSurjection_162
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSurjection._.cong
d_cong_176 ::
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_176 :: T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_176 T_IsSurjection_162
v0 = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 ((T_IsSurjection_162 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0))
-- Function.Structures.IsSurjection._.isEquivalence₁
d_isEquivalence'8321'_178 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_178 :: T_IsSurjection_162 -> T_IsEquivalence_26
d_isEquivalence'8321'_178 T_IsSurjection_162
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsSurjection_162 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0))
-- Function.Structures.IsSurjection._.isEquivalence₂
d_isEquivalence'8322'_180 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_180 :: T_IsSurjection_162 -> T_IsEquivalence_26
d_isEquivalence'8322'_180 T_IsSurjection_162
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 ((T_IsSurjection_162 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0))
-- Function.Structures.IsSurjection._.Eq₁._≈_
d__'8776'__184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> ()
d__'8776'__184 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__184 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₁._≉_
d__'8777'__186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> ()
d__'8777'__186 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__186 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₁.Carrier
d_Carrier_188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSurjection_162 -> ()
d_Carrier_188 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> ()
d_Carrier_188 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₁.isEquivalence
d_isEquivalence_190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_190 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_IsEquivalence_26
d_isEquivalence_190 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_IsEquivalence_26
du_isEquivalence_190 T_IsSurjection_162
v9
du_isEquivalence_190 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_190 :: T_IsSurjection_162 -> T_IsEquivalence_26
du_isEquivalence_190 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsSurjection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_192 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_192 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_192 T_IsSurjection_162
v9
du_isPartialEquivalence_192 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_192 :: T_IsSurjection_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_192 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSurjection._.Eq₁.partialSetoid
d_partialSetoid_194 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_194 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_PartialSetoid_10
d_partialSetoid_194 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_PartialSetoid_10
du_partialSetoid_194 T_IsSurjection_162
v9
du_partialSetoid_194 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_194 :: T_IsSurjection_162 -> T_PartialSetoid_10
du_partialSetoid_194 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsSurjection._.Eq₁.refl
d_refl_196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSurjection_162 -> AgdaAny -> AgdaAny
d_refl_196 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
d_refl_196 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9 = T_IsSurjection_162 -> AgdaAny -> AgdaAny
du_refl_196 T_IsSurjection_162
v9
du_refl_196 :: T_IsSurjection_162 -> AgdaAny -> AgdaAny
du_refl_196 :: T_IsSurjection_162 -> AgdaAny -> AgdaAny
du_refl_196 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsSurjection._.Eq₁.reflexive
d_reflexive_198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_198 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_198 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_198 T_IsSurjection_162
v9
du_reflexive_198 ::
  T_IsSurjection_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_198 :: T_IsSurjection_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_198 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsSurjection._.Eq₁.setoid
d_setoid_200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_200 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_Setoid_44
d_setoid_200 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_Setoid_44
du_setoid_200 T_IsSurjection_162
v9
du_setoid_200 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_200 :: T_IsSurjection_162 -> T_Setoid_44
du_setoid_200 T_IsSurjection_162
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsSurjection_162 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0))
-- Function.Structures.IsSurjection._.Eq₁.sym
d_sym_202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_202 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_202 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9 = T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_202 T_IsSurjection_162
v9
du_sym_202 ::
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_202 :: T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_202 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSurjection._.Eq₁.trans
d_trans_204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_204 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_204 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_204 T_IsSurjection_162
v9
du_trans_204 ::
  T_IsSurjection_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_204 :: T_IsSurjection_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_204 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSurjection._.Eq₂._≈_
d__'8776'__208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> ()
d__'8776'__208 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__208 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₂._≉_
d__'8777'__210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> ()
d__'8777'__210 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__210 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₂.Carrier
d_Carrier_212 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSurjection_162 -> ()
d_Carrier_212 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> ()
d_Carrier_212 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₂.isEquivalence
d_isEquivalence_214 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_214 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_IsEquivalence_26
d_isEquivalence_214 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_IsEquivalence_26
du_isEquivalence_214 T_IsSurjection_162
v9
du_isEquivalence_214 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_214 :: T_IsSurjection_162 -> T_IsEquivalence_26
du_isEquivalence_214 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsSurjection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_216 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_216 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_216 T_IsSurjection_162
v9
du_isPartialEquivalence_216 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_216 :: T_IsSurjection_162 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_216 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSurjection._.Eq₂.partialSetoid
d_partialSetoid_218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_218 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_PartialSetoid_10
d_partialSetoid_218 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_PartialSetoid_10
du_partialSetoid_218 T_IsSurjection_162
v9
du_partialSetoid_218 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_218 :: T_IsSurjection_162 -> T_PartialSetoid_10
du_partialSetoid_218 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsSurjection._.Eq₂.refl
d_refl_220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSurjection_162 -> AgdaAny -> AgdaAny
d_refl_220 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
d_refl_220 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9 = T_IsSurjection_162 -> AgdaAny -> AgdaAny
du_refl_220 T_IsSurjection_162
v9
du_refl_220 :: T_IsSurjection_162 -> AgdaAny -> AgdaAny
du_refl_220 :: T_IsSurjection_162 -> AgdaAny -> AgdaAny
du_refl_220 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsSurjection._.Eq₂.reflexive
d_reflexive_222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_222 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_222 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_222 T_IsSurjection_162
v9
du_reflexive_222 ::
  T_IsSurjection_162 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_222 :: T_IsSurjection_162
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_222 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsSurjection._.Eq₂.setoid
d_setoid_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_224 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> T_Setoid_44
d_setoid_224 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162 -> T_Setoid_44
du_setoid_224 T_IsSurjection_162
v9
du_setoid_224 ::
  T_IsSurjection_162 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_224 :: T_IsSurjection_162 -> T_Setoid_44
du_setoid_224 T_IsSurjection_162
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsSurjection_162 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0))
-- Function.Structures.IsSurjection._.Eq₂.sym
d_sym_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_226 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_226 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9 = T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_226 T_IsSurjection_162
v9
du_sym_226 ::
  T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_226 :: T_IsSurjection_162 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_226 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSurjection._.Eq₂.trans
d_trans_228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_228 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_228 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9
  = T_IsSurjection_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_228 T_IsSurjection_162
v9
du_trans_228 ::
  T_IsSurjection_162 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_228 :: T_IsSurjection_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_228 T_IsSurjection_162
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> T_IsSurjection_162
forall a b. a -> b
coe T_IsSurjection_162
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSurjection.strictlySurjective
d_strictlySurjective_230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_162 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_230 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_162
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_230 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_162
v9 AgdaAny
v10
  = T_IsSurjection_162 -> AgdaAny -> T_Σ_14
du_strictlySurjective_230 T_IsSurjection_162
v9 AgdaAny
v10
du_strictlySurjective_230 ::
  T_IsSurjection_162 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_230 :: T_IsSurjection_162 -> AgdaAny -> T_Σ_14
du_strictlySurjective_230 T_IsSurjection_162
v0 AgdaAny
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Σ_14)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Σ_14
MAlonzo.Code.Data.Product.Base.du_map'8322'_150
      (\ AgdaAny
v2 AgdaAny
v3 ->
         AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           AgdaAny
v3 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_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsSurjection_162 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsSurjection_162 -> T_IsCongruent_22
d_isCongruent_170 (T_IsSurjection_162 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162
v0))) AgdaAny
v2))
      ((T_IsSurjection_162 -> AgdaAny -> T_Σ_14)
-> T_IsSurjection_162 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_162 -> AgdaAny -> T_Σ_14
d_surjective_172 T_IsSurjection_162
v0 AgdaAny
v1)
-- Function.Structures.IsBijection
d_IsBijection_238 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBijection_238 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsBijection_238
  = C_IsBijection'46'constructor_10113 T_IsInjection_92
                                       (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Structures.IsBijection.isInjection
d_isInjection_246 :: T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 :: T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 T_IsBijection_238
v0
  = case T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0 of
      C_IsBijection'46'constructor_10113 T_IsInjection_92
v1 AgdaAny -> T_Σ_14
v2 -> T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1
      T_IsBijection_238
_ -> T_IsInjection_92
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBijection.surjective
d_surjective_248 ::
  T_IsBijection_238 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_248 :: T_IsBijection_238 -> AgdaAny -> T_Σ_14
d_surjective_248 T_IsBijection_238
v0
  = case T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0 of
      C_IsBijection'46'constructor_10113 T_IsInjection_92
v1 AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v2
      T_IsBijection_238
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBijection._.cong
d_cong_252 ::
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_252 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_252 T_IsBijection_238
v0
  = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 ((T_IsBijection_238 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0)))
-- Function.Structures.IsBijection._.injective
d_injective_254 ::
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_254 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_254 T_IsBijection_238
v0
  = (T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_102 ((T_IsBijection_238 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0))
-- Function.Structures.IsBijection._.isCongruent
d_isCongruent_256 :: T_IsBijection_238 -> T_IsCongruent_22
d_isCongruent_256 :: T_IsBijection_238 -> T_IsCongruent_22
d_isCongruent_256 T_IsBijection_238
v0
  = (T_IsInjection_92 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 ((T_IsBijection_238 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0))
-- Function.Structures.IsBijection._.isEquivalence₁
d_isEquivalence'8321'_258 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_258 :: T_IsBijection_238 -> T_IsEquivalence_26
d_isEquivalence'8321'_258 T_IsBijection_238
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34
      ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 ((T_IsBijection_238 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0)))
-- Function.Structures.IsBijection._.isEquivalence₂
d_isEquivalence'8322'_260 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_260 :: T_IsBijection_238 -> T_IsEquivalence_26
d_isEquivalence'8322'_260 T_IsBijection_238
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36
      ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 ((T_IsBijection_238 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0)))
-- Function.Structures.IsBijection._.Eq₁._≈_
d__'8776'__264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> ()
d__'8776'__264 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__264 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁._≉_
d__'8777'__266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> ()
d__'8777'__266 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__266 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁.Carrier
d_Carrier_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsBijection_238 -> ()
d_Carrier_268 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> ()
d_Carrier_268 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁.isEquivalence
d_isEquivalence_270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_270 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsEquivalence_26
d_isEquivalence_270 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_270 T_IsBijection_238
v9
du_isEquivalence_270 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_270 :: T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_270 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsBijection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_272 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_272 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_272 T_IsBijection_238
v9
du_isPartialEquivalence_272 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_272 :: T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_272 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsBijection._.Eq₁.partialSetoid
d_partialSetoid_274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_274 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_PartialSetoid_10
d_partialSetoid_274 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_274 T_IsBijection_238
v9
du_partialSetoid_274 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_274 :: T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_274 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsBijection._.Eq₁.refl
d_refl_276 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsBijection_238 -> AgdaAny -> AgdaAny
d_refl_276 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
d_refl_276 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9 = T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_276 T_IsBijection_238
v9
du_refl_276 :: T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_276 :: T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_276 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsBijection._.Eq₁.reflexive
d_reflexive_278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_278 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_278 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_278 T_IsBijection_238
v9
du_reflexive_278 ::
  T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_278 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_278 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsBijection._.Eq₁.setoid
d_setoid_280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_280 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Setoid_44
d_setoid_280 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_Setoid_44
du_setoid_280 T_IsBijection_238
v9
du_setoid_280 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_280 :: T_IsBijection_238 -> T_Setoid_44
du_setoid_280 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v1)))
-- Function.Structures.IsBijection._.Eq₁.sym
d_sym_282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_282 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_282 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9 = T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_282 T_IsBijection_238
v9
du_sym_282 ::
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_282 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_282 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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_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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsBijection._.Eq₁.trans
d_trans_284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_284 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_284 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_284 T_IsBijection_238
v9
du_trans_284 ::
  T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_284 :: T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_284 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsBijection._.Eq₂._≈_
d__'8776'__288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> ()
d__'8776'__288 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__288 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂._≉_
d__'8777'__290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> ()
d__'8777'__290 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__290 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂.Carrier
d_Carrier_292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsBijection_238 -> ()
d_Carrier_292 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> ()
d_Carrier_292 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂.isEquivalence
d_isEquivalence_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_294 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsEquivalence_26
d_isEquivalence_294 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_294 T_IsBijection_238
v9
du_isEquivalence_294 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_294 :: T_IsBijection_238 -> T_IsEquivalence_26
du_isEquivalence_294 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsBijection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_296 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_296 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_296 T_IsBijection_238
v9
du_isPartialEquivalence_296 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_296 :: T_IsBijection_238 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_296 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsBijection._.Eq₂.partialSetoid
d_partialSetoid_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_298 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_PartialSetoid_10
d_partialSetoid_298 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_298 T_IsBijection_238
v9
du_partialSetoid_298 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_298 :: T_IsBijection_238 -> T_PartialSetoid_10
du_partialSetoid_298 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsBijection._.Eq₂.refl
d_refl_300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsBijection_238 -> AgdaAny -> AgdaAny
d_refl_300 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
d_refl_300 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9 = T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_300 T_IsBijection_238
v9
du_refl_300 :: T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_300 :: T_IsBijection_238 -> AgdaAny -> AgdaAny
du_refl_300 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsBijection._.Eq₂.reflexive
d_reflexive_302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_302 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_302 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_302 T_IsBijection_238
v9
du_reflexive_302 ::
  T_IsBijection_238 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_302 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_302 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsBijection._.Eq₂.setoid
d_setoid_304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_304 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Setoid_44
d_setoid_304 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_Setoid_44
du_setoid_304 T_IsBijection_238
v9
du_setoid_304 ::
  T_IsBijection_238 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_304 :: T_IsBijection_238 -> T_Setoid_44
du_setoid_304 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v1)))
-- Function.Structures.IsBijection._.Eq₂.sym
d_sym_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_306 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_306 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9 = T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_306 T_IsBijection_238
v9
du_sym_306 ::
  T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_306 :: T_IsBijection_238 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_306 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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_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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsBijection._.Eq₂.trans
d_trans_308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_308 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_308 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_308 T_IsBijection_238
v9
du_trans_308 ::
  T_IsBijection_238 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_308 :: T_IsBijection_238
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_308 T_IsBijection_238
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> T_IsBijection_238
forall a b. a -> b
coe T_IsBijection_238
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsBijection.bijective
d_bijective_310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_bijective_310 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_Σ_14
d_bijective_310 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_Σ_14
du_bijective_310 T_IsBijection_238
v9
du_bijective_310 ::
  T_IsBijection_238 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_bijective_310 :: T_IsBijection_238 -> T_Σ_14
du_bijective_310 T_IsBijection_238
v0
  = (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
      ((T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_102 ((T_IsBijection_238 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0)))
      ((T_IsBijection_238 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> AgdaAny -> T_Σ_14
d_surjective_248 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0))
-- Function.Structures.IsBijection.isSurjection
d_isSurjection_312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsBijection_238 -> T_IsSurjection_162
d_isSurjection_312 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> T_IsSurjection_162
d_isSurjection_312 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> T_IsSurjection_162
du_isSurjection_312 T_IsBijection_238
v9
du_isSurjection_312 :: T_IsBijection_238 -> T_IsSurjection_162
du_isSurjection_312 :: T_IsBijection_238 -> T_IsSurjection_162
du_isSurjection_312 T_IsBijection_238
v0
  = (T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162
C_IsSurjection'46'constructor_6463
      ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
d_isCongruent_100 ((T_IsBijection_238 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsInjection_92
d_isInjection_246 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0)))
      ((T_IsBijection_238 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> AgdaAny -> T_Σ_14
d_surjective_248 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0))
-- Function.Structures.IsBijection._.strictlySurjective
d_strictlySurjective_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_238 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_316 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_238
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_316 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_238
v9
  = T_IsBijection_238 -> AgdaAny -> T_Σ_14
du_strictlySurjective_316 T_IsBijection_238
v9
du_strictlySurjective_316 ::
  T_IsBijection_238 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_316 :: T_IsBijection_238 -> AgdaAny -> T_Σ_14
du_strictlySurjective_316 T_IsBijection_238
v0
  = (T_IsSurjection_162 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSurjection_162 -> AgdaAny -> T_Σ_14
du_strictlySurjective_230 ((T_IsBijection_238 -> T_IsSurjection_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238 -> T_IsSurjection_162
du_isSurjection_312 (T_IsBijection_238 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_238
v0))
-- Function.Structures.IsLeftInverse
d_IsLeftInverse_322 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsLeftInverse_322 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsLeftInverse_322
  = C_IsLeftInverse'46'constructor_14363 T_IsCongruent_22
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsLeftInverse.isCongruent
d_isCongruent_334 :: T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 :: T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 T_IsLeftInverse_322
v0
  = case T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0 of
      C_IsLeftInverse'46'constructor_14363 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsLeftInverse_322
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse.from-cong
d_from'45'cong_336 ::
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_336 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_336 T_IsLeftInverse_322
v0
  = case T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0 of
      C_IsLeftInverse'46'constructor_14363 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsLeftInverse_322
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse.inverseˡ
d_inverse'737'_338 ::
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_338 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_338 T_IsLeftInverse_322
v0
  = case T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0 of
      C_IsLeftInverse'46'constructor_14363 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsLeftInverse_322
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse._.isEquivalence₁
d_isEquivalence'8321'_342 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_342 :: T_IsLeftInverse_322 -> T_IsEquivalence_26
d_isEquivalence'8321'_342 T_IsLeftInverse_322
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0))
-- Function.Structures.IsLeftInverse._.isEquivalence₂
d_isEquivalence'8322'_344 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_344 :: T_IsLeftInverse_322 -> T_IsEquivalence_26
d_isEquivalence'8322'_344 T_IsLeftInverse_322
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0))
-- Function.Structures.IsLeftInverse._.cong
d_cong_346 ::
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_346 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_346 T_IsLeftInverse_322
v0 = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0))
-- Function.Structures.IsLeftInverse._.Eq₁._≈_
d__'8776'__350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> ()
d__'8776'__350 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__350 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁._≉_
d__'8777'__352 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> ()
d__'8777'__352 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__352 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁.Carrier
d_Carrier_354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> ()
d_Carrier_354 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> ()
d_Carrier_354 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁.isEquivalence
d_isEquivalence_356 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_356 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsEquivalence_26
d_isEquivalence_356 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_356 T_IsLeftInverse_322
v10
du_isEquivalence_356 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_356 :: T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_356 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsLeftInverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_358 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_358 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_358 T_IsLeftInverse_322
v10
du_isPartialEquivalence_358 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_358 :: T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_358 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsLeftInverse._.Eq₁.partialSetoid
d_partialSetoid_360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_360 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_PartialSetoid_10
d_partialSetoid_360 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_360 T_IsLeftInverse_322
v10
du_partialSetoid_360 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_360 :: T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_360 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsLeftInverse._.Eq₁.refl
d_refl_362 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
d_refl_362 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
d_refl_362 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_362 T_IsLeftInverse_322
v10
du_refl_362 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_362 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_362 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsLeftInverse._.Eq₁.reflexive
d_reflexive_364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_364 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_364 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_364 T_IsLeftInverse_322
v10
du_reflexive_364 ::
  T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_364 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_364 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsLeftInverse._.Eq₁.setoid
d_setoid_366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_366 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Setoid_44
d_setoid_366 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_366 T_IsLeftInverse_322
v10
du_setoid_366 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_366 :: T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_366 T_IsLeftInverse_322
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0))
-- Function.Structures.IsLeftInverse._.Eq₁.sym
d_sym_368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_368 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_368 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_368 T_IsLeftInverse_322
v10
du_sym_368 ::
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_368 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_368 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsLeftInverse._.Eq₁.trans
d_trans_370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_370 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_370 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_370 T_IsLeftInverse_322
v10
du_trans_370 ::
  T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_370 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_370 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsLeftInverse._.Eq₂._≈_
d__'8776'__374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> ()
d__'8776'__374 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__374 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂._≉_
d__'8777'__376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> ()
d__'8777'__376 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__376 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂.Carrier
d_Carrier_378 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> ()
d_Carrier_378 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> ()
d_Carrier_378 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂.isEquivalence
d_isEquivalence_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_380 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsEquivalence_26
d_isEquivalence_380 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_380 T_IsLeftInverse_322
v10
du_isEquivalence_380 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_380 :: T_IsLeftInverse_322 -> T_IsEquivalence_26
du_isEquivalence_380 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsLeftInverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_382 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_382 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_382 T_IsLeftInverse_322
v10
du_isPartialEquivalence_382 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_382 :: T_IsLeftInverse_322 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_382 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsLeftInverse._.Eq₂.partialSetoid
d_partialSetoid_384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_384 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_PartialSetoid_10
d_partialSetoid_384 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_384 T_IsLeftInverse_322
v10
du_partialSetoid_384 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_384 :: T_IsLeftInverse_322 -> T_PartialSetoid_10
du_partialSetoid_384 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsLeftInverse._.Eq₂.refl
d_refl_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
d_refl_386 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
d_refl_386 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_386 T_IsLeftInverse_322
v10
du_refl_386 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_386 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_refl_386 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsLeftInverse._.Eq₂.reflexive
d_reflexive_388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_388 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_388 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_388 T_IsLeftInverse_322
v10
du_reflexive_388 ::
  T_IsLeftInverse_322 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_388 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_388 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsLeftInverse._.Eq₂.setoid
d_setoid_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_390 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_Setoid_44
d_setoid_390 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_390 T_IsLeftInverse_322
v10
du_setoid_390 ::
  T_IsLeftInverse_322 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_390 :: T_IsLeftInverse_322 -> T_Setoid_44
du_setoid_390 T_IsLeftInverse_322
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v0))
-- Function.Structures.IsLeftInverse._.Eq₂.sym
d_sym_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_392 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_392 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_392 T_IsLeftInverse_322
v10
du_sym_392 ::
  T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_392 :: T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_392 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsLeftInverse._.Eq₂.trans
d_trans_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_394 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_394 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_394 T_IsLeftInverse_322
v10
du_trans_394 ::
  T_IsLeftInverse_322 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_394 :: T_IsLeftInverse_322
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_394 T_IsLeftInverse_322
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsLeftInverse.strictlyInverseˡ
d_strictlyInverse'737'_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_396 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_396 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_322
v10 AgdaAny
v11
  = (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_396 AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10 AgdaAny
v11
du_strictlyInverse'737'_396 ::
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_396 :: (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_396 AgdaAny -> AgdaAny
v0 T_IsLeftInverse_322
v1 AgdaAny
v2
  = (T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_338 T_IsLeftInverse_322
v1 AgdaAny
v2 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 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_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsLeftInverse_322 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1)))
         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2))
-- Function.Structures.IsLeftInverse.isSurjection
d_isSurjection_400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
d_isSurjection_400 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322
-> T_IsSurjection_162
d_isSurjection_400 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
  = (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
du_isSurjection_400 AgdaAny -> AgdaAny
v9 T_IsLeftInverse_322
v10
du_isSurjection_400 ::
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
du_isSurjection_400 :: (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
du_isSurjection_400 AgdaAny -> AgdaAny
v0 T_IsLeftInverse_322
v1
  = (T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162
C_IsSurjection'46'constructor_6463 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1))
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v2 ->
            (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 -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2)
              ((T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_338 T_IsLeftInverse_322
v1 AgdaAny
v2)))
-- Function.Structures.IsRightInverse
d_IsRightInverse_408 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsRightInverse_408 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsRightInverse_408
  = C_IsRightInverse'46'constructor_18837 T_IsCongruent_22
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsRightInverse.isCongruent
d_isCongruent_420 :: T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 :: T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 T_IsRightInverse_408
v0
  = case T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0 of
      C_IsRightInverse'46'constructor_18837 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsRightInverse_408
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse.from-cong
d_from'45'cong_422 ::
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_422 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_422 T_IsRightInverse_408
v0
  = case T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0 of
      C_IsRightInverse'46'constructor_18837 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsRightInverse_408
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse.inverseʳ
d_inverse'691'_424 ::
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_424 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_424 T_IsRightInverse_408
v0
  = case T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0 of
      C_IsRightInverse'46'constructor_18837 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsRightInverse_408
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse._.isEquivalence₁
d_isEquivalence'8321'_428 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_428 :: T_IsRightInverse_408 -> T_IsEquivalence_26
d_isEquivalence'8321'_428 T_IsRightInverse_408
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0))
-- Function.Structures.IsRightInverse._.isEquivalence₂
d_isEquivalence'8322'_430 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_430 :: T_IsRightInverse_408 -> T_IsEquivalence_26
d_isEquivalence'8322'_430 T_IsRightInverse_408
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0))
-- Function.Structures.IsRightInverse._.cong
d_cong_432 ::
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_432 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_432 T_IsRightInverse_408
v0 = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0))
-- Function.Structures.IsRightInverse._.Eq₁._≈_
d__'8776'__436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> ()
d__'8776'__436 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__436 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁._≉_
d__'8777'__438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> ()
d__'8777'__438 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__438 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁.Carrier
d_Carrier_440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> ()
d_Carrier_440 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> ()
d_Carrier_440 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁.isEquivalence
d_isEquivalence_442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_442 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsEquivalence_26
d_isEquivalence_442 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_442 T_IsRightInverse_408
v10
du_isEquivalence_442 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_442 :: T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_442 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsRightInverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_444 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_444 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_IsRightInverse_408
v10
du_isPartialEquivalence_444 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_444 :: T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsRightInverse._.Eq₁.partialSetoid
d_partialSetoid_446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_446 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_PartialSetoid_10
d_partialSetoid_446 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_446 T_IsRightInverse_408
v10
du_partialSetoid_446 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_446 :: T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_446 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsRightInverse._.Eq₁.refl
d_refl_448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
d_refl_448 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
d_refl_448 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_448 T_IsRightInverse_408
v10
du_refl_448 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_448 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_448 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsRightInverse._.Eq₁.reflexive
d_reflexive_450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_450 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_450 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_450 T_IsRightInverse_408
v10
du_reflexive_450 ::
  T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_450 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_450 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsRightInverse._.Eq₁.setoid
d_setoid_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_452 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Setoid_44
d_setoid_452 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_Setoid_44
du_setoid_452 T_IsRightInverse_408
v10
du_setoid_452 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_452 :: T_IsRightInverse_408 -> T_Setoid_44
du_setoid_452 T_IsRightInverse_408
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0))
-- Function.Structures.IsRightInverse._.Eq₁.sym
d_sym_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_454 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_454 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_454 T_IsRightInverse_408
v10
du_sym_454 ::
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_454 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_454 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsRightInverse._.Eq₁.trans
d_trans_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_456 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_456 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_456 T_IsRightInverse_408
v10
du_trans_456 ::
  T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_456 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_456 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsRightInverse._.Eq₂._≈_
d__'8776'__460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> ()
d__'8776'__460 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__460 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂._≉_
d__'8777'__462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> ()
d__'8777'__462 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__462 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂.Carrier
d_Carrier_464 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> ()
d_Carrier_464 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> ()
d_Carrier_464 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂.isEquivalence
d_isEquivalence_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_466 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsEquivalence_26
d_isEquivalence_466 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_466 T_IsRightInverse_408
v10
du_isEquivalence_466 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_466 :: T_IsRightInverse_408 -> T_IsEquivalence_26
du_isEquivalence_466 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsRightInverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_468 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_468 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_468 T_IsRightInverse_408
v10
du_isPartialEquivalence_468 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_468 :: T_IsRightInverse_408 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_468 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsRightInverse._.Eq₂.partialSetoid
d_partialSetoid_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_470 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_PartialSetoid_10
d_partialSetoid_470 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_470 T_IsRightInverse_408
v10
du_partialSetoid_470 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_470 :: T_IsRightInverse_408 -> T_PartialSetoid_10
du_partialSetoid_470 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsRightInverse._.Eq₂.refl
d_refl_472 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
d_refl_472 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
d_refl_472 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_472 T_IsRightInverse_408
v10
du_refl_472 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_472 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_refl_472 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsRightInverse._.Eq₂.reflexive
d_reflexive_474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_474 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_474 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_474 T_IsRightInverse_408
v10
du_reflexive_474 ::
  T_IsRightInverse_408 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_474 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_474 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsRightInverse._.Eq₂.setoid
d_setoid_476 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_476 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> T_Setoid_44
d_setoid_476 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> T_Setoid_44
du_setoid_476 T_IsRightInverse_408
v10
du_setoid_476 ::
  T_IsRightInverse_408 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_476 :: T_IsRightInverse_408 -> T_Setoid_44
du_setoid_476 T_IsRightInverse_408
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsRightInverse_408 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v0))
-- Function.Structures.IsRightInverse._.Eq₂.sym
d_sym_478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_478 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_478 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_478 T_IsRightInverse_408
v10
du_sym_478 ::
  T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_478 :: T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_478 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsRightInverse._.Eq₂.trans
d_trans_480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_480 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_480 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_408
v10
  = T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_480 T_IsRightInverse_408
v10
du_trans_480 ::
  T_IsRightInverse_408 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_480 :: T_IsRightInverse_408
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_480 T_IsRightInverse_408
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> T_IsRightInverse_408
forall a b. a -> b
coe T_IsRightInverse_408
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsRightInverse.strictlyInverseʳ
d_strictlyInverse'691'_482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_482 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_482 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_408
v10 AgdaAny
v11
  = (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_482 AgdaAny -> AgdaAny
v8 T_IsRightInverse_408
v10 AgdaAny
v11
du_strictlyInverse'691'_482 ::
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_482 :: (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_482 AgdaAny -> AgdaAny
v0 T_IsRightInverse_408
v1 AgdaAny
v2
  = (T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRightInverse_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_424 T_IsRightInverse_408
v1 AgdaAny
v2 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 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_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 ((T_IsRightInverse_408 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsRightInverse_408 -> T_IsCongruent_22
d_isCongruent_420 (T_IsRightInverse_408 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_408
v1)))
         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2))
-- Function.Structures.IsInverse
d_IsInverse_490 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsInverse_490 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsInverse_490
  = C_IsInverse'46'constructor_22449 T_IsLeftInverse_322
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsInverse.isLeftInverse
d_isLeftInverse_500 :: T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 :: T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 T_IsInverse_490
v0
  = case T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0 of
      C_IsInverse'46'constructor_22449 T_IsLeftInverse_322
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1
      T_IsInverse_490
_ -> T_IsLeftInverse_322
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInverse.inverseʳ
d_inverse'691'_502 ::
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_502 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_502 T_IsInverse_490
v0
  = case T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0 of
      C_IsInverse'46'constructor_22449 T_IsLeftInverse_322
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsInverse_490
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInverse._.from-cong
d_from'45'cong_506 ::
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_506 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_506 T_IsInverse_490
v0
  = (T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_336 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0))
-- Function.Structures.IsInverse._.inverseˡ
d_inverse'737'_508 ::
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_508 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_508 T_IsInverse_490
v0
  = (T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_338 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0))
-- Function.Structures.IsInverse._.isCongruent
d_isCongruent_510 :: T_IsInverse_490 -> T_IsCongruent_22
d_isCongruent_510 :: T_IsInverse_490 -> T_IsCongruent_22
d_isCongruent_510 T_IsInverse_490
v0
  = (T_IsLeftInverse_322 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0))
-- Function.Structures.IsInverse._.isEquivalence₁
d_isEquivalence'8321'_512 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_512 :: T_IsInverse_490 -> T_IsEquivalence_26
d_isEquivalence'8321'_512 T_IsInverse_490
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)))
-- Function.Structures.IsInverse._.isEquivalence₂
d_isEquivalence'8322'_514 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_514 :: T_IsInverse_490 -> T_IsEquivalence_26
d_isEquivalence'8322'_514 T_IsInverse_490
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)))
-- Function.Structures.IsInverse._.isSurjection
d_isSurjection_516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> T_IsSurjection_162
d_isSurjection_516 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsSurjection_162
d_isSurjection_516 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> T_IsSurjection_162
du_isSurjection_516 AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
du_isSurjection_516 ::
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> T_IsSurjection_162
du_isSurjection_516 :: (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> T_IsSurjection_162
du_isSurjection_516 AgdaAny -> AgdaAny
v0 T_IsInverse_490
v1
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
du_isSurjection_400 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v1))
-- Function.Structures.IsInverse._.strictlyInverseˡ
d_strictlyInverse'737'_518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_518 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_518 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9
                           T_IsInverse_490
v10
  = (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_518 AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
du_strictlyInverse'737'_518 ::
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_518 :: (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_518 AgdaAny -> AgdaAny
v0 T_IsInverse_490
v1
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_396 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0)
      ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v1))
-- Function.Structures.IsInverse._.cong
d_cong_520 ::
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_520 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_520 T_IsInverse_490
v0
  = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)))
-- Function.Structures.IsInverse._.Eq₁._≈_
d__'8776'__524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny -> ()
d__'8776'__524 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__524 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁._≉_
d__'8777'__526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny -> ()
d__'8777'__526 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__526 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁.Carrier
d_Carrier_528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> ()
d_Carrier_528 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> ()
d_Carrier_528 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁.isEquivalence
d_isEquivalence_530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_530 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsEquivalence_26
d_isEquivalence_530 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_530 T_IsInverse_490
v10
du_isEquivalence_530 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_530 :: T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_530 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsInverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_532 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_532 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_490
v10
  = T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_532 T_IsInverse_490
v10
du_isPartialEquivalence_532 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_532 :: T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_532 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsInverse._.Eq₁.partialSetoid
d_partialSetoid_534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_534 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_PartialSetoid_10
d_partialSetoid_534 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_534 T_IsInverse_490
v10
du_partialSetoid_534 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_534 :: T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_534 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsInverse._.Eq₁.refl
d_refl_536 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
d_refl_536 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
d_refl_536 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_536 T_IsInverse_490
v10
du_refl_536 :: T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_536 :: T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_536 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsInverse._.Eq₁.reflexive
d_reflexive_538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_538 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_538 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_538 T_IsInverse_490
v10
du_reflexive_538 ::
  T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_538 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_538 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsInverse._.Eq₁.setoid
d_setoid_540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_540 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Setoid_44
d_setoid_540 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_Setoid_44
du_setoid_540 T_IsInverse_490
v10
du_setoid_540 ::
  T_IsInverse_490 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_540 :: T_IsInverse_490 -> T_Setoid_44
du_setoid_540 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1)))
-- Function.Structures.IsInverse._.Eq₁.sym
d_sym_542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_542 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_542 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_542 T_IsInverse_490
v10
du_sym_542 ::
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_542 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_542 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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_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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsInverse._.Eq₁.trans
d_trans_544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_544 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_544 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_544 T_IsInverse_490
v10
du_trans_544 ::
  T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_544 :: T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_544 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsInverse._.Eq₂._≈_
d__'8776'__548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny -> ()
d__'8776'__548 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__548 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂._≉_
d__'8777'__550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny -> ()
d__'8777'__550 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__550 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂.Carrier
d_Carrier_552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> ()
d_Carrier_552 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> ()
d_Carrier_552 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂.isEquivalence
d_isEquivalence_554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_554 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsEquivalence_26
d_isEquivalence_554 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_554 T_IsInverse_490
v10
du_isEquivalence_554 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_554 :: T_IsInverse_490 -> T_IsEquivalence_26
du_isEquivalence_554 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsInverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_556 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_556 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_556 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_490
v10
  = T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_556 T_IsInverse_490
v10
du_isPartialEquivalence_556 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_556 :: T_IsInverse_490 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_556 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsInverse._.Eq₂.partialSetoid
d_partialSetoid_558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_558 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_PartialSetoid_10
d_partialSetoid_558 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_558 T_IsInverse_490
v10
du_partialSetoid_558 ::
  T_IsInverse_490 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_558 :: T_IsInverse_490 -> T_PartialSetoid_10
du_partialSetoid_558 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsInverse._.Eq₂.refl
d_refl_560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
d_refl_560 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
d_refl_560 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_560 T_IsInverse_490
v10
du_refl_560 :: T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_560 :: T_IsInverse_490 -> AgdaAny -> AgdaAny
du_refl_560 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsInverse._.Eq₂.reflexive
d_reflexive_562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_562 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_562 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_562 T_IsInverse_490
v10
du_reflexive_562 ::
  T_IsInverse_490 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_562 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_562 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsInverse._.Eq₂.setoid
d_setoid_564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_564 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Setoid_44
d_setoid_564 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_Setoid_44
du_setoid_564 T_IsInverse_490
v10
du_setoid_564 ::
  T_IsInverse_490 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_564 :: T_IsInverse_490 -> T_Setoid_44
du_setoid_564 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1)))
-- Function.Structures.IsInverse._.Eq₂.sym
d_sym_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_566 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_566 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_566 T_IsInverse_490
v10
du_sym_566 ::
  T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_566 :: T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_566 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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_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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsInverse._.Eq₂.trans
d_trans_568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_568 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_568 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_568 T_IsInverse_490
v10
du_trans_568 ::
  T_IsInverse_490 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_568 :: T_IsInverse_490
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_568 T_IsInverse_490
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> T_IsInverse_490
forall a b. a -> b
coe T_IsInverse_490
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsInverse.isRightInverse
d_isRightInverse_570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> T_IsRightInverse_408
d_isRightInverse_570 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_IsRightInverse_408
d_isRightInverse_570 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_IsRightInverse_408
du_isRightInverse_570 T_IsInverse_490
v10
du_isRightInverse_570 :: T_IsInverse_490 -> T_IsRightInverse_408
du_isRightInverse_570 :: T_IsInverse_490 -> T_IsRightInverse_408
du_isRightInverse_570 T_IsInverse_490
v0
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRightInverse_408)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_408
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRightInverse_408
C_IsRightInverse'46'constructor_18837
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)))
      ((T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_336 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)))
      ((T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_502 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0))
-- Function.Structures.IsInverse._.strictlyInverseʳ
d_strictlyInverse'691'_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_574 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_574 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_490
v10
  = (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_574 AgdaAny -> AgdaAny
v8 T_IsInverse_490
v10
du_strictlyInverse'691'_574 ::
  (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_574 :: (AgdaAny -> AgdaAny) -> T_IsInverse_490 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_574 AgdaAny -> AgdaAny
v0 T_IsInverse_490
v1
  = ((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsRightInverse_408 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_482 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0)
      ((T_IsInverse_490 -> T_IsRightInverse_408) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsRightInverse_408
du_isRightInverse_570 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v1))
-- Function.Structures.IsInverse.inverse
d_inverse_576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_490 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_576 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_490
-> T_Σ_14
d_inverse_576 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_490
v10
  = T_IsInverse_490 -> T_Σ_14
du_inverse_576 T_IsInverse_490
v10
du_inverse_576 ::
  T_IsInverse_490 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_576 :: T_IsInverse_490 -> T_Σ_14
du_inverse_576 T_IsInverse_490
v0
  = (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
      ((T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_338 ((T_IsInverse_490 -> T_IsLeftInverse_322) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> T_IsLeftInverse_322
d_isLeftInverse_500 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0)))
      ((T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_502 (T_IsInverse_490 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_490
v0))
-- Function.Structures.IsBiEquivalence
d_IsBiEquivalence_584 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBiEquivalence_584 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 = ()
data T_IsBiEquivalence_584
  = C_IsBiEquivalence'46'constructor_28009 T_IsCongruent_22
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsBiEquivalence.to-isCongruent
d_to'45'isCongruent_598 ::
  T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 :: T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 T_IsBiEquivalence_584
v0
  = case T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0 of
      C_IsBiEquivalence'46'constructor_28009 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsBiEquivalence_584
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence.from₁-cong
d_from'8321''45'cong_600 ::
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_600 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_600 T_IsBiEquivalence_584
v0
  = case T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0 of
      C_IsBiEquivalence'46'constructor_28009 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsBiEquivalence_584
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence.from₂-cong
d_from'8322''45'cong_602 ::
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_602 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_602 T_IsBiEquivalence_584
v0
  = case T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0 of
      C_IsBiEquivalence'46'constructor_28009 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsBiEquivalence_584
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence._.isEquivalence₁
d_isEquivalence'8321'_606 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_606 :: T_IsBiEquivalence_584 -> T_IsEquivalence_26
d_isEquivalence'8321'_606 T_IsBiEquivalence_584
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsBiEquivalence_584 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584
v0))
-- Function.Structures.IsBiEquivalence._.isEquivalence₂
d_isEquivalence'8322'_608 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_608 :: T_IsBiEquivalence_584 -> T_IsEquivalence_26
d_isEquivalence'8322'_608 T_IsBiEquivalence_584
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 ((T_IsBiEquivalence_584 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584
v0))
-- Function.Structures.IsBiEquivalence._.cong
d_cong_610 ::
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_610 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_610 T_IsBiEquivalence_584
v0
  = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 ((T_IsBiEquivalence_584 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584
v0))
-- Function.Structures.IsBiEquivalence._.Eq₁._≈_
d__'8776'__614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> ()
d__'8776'__614 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__614 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁._≉_
d__'8777'__616 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> ()
d__'8777'__616 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__616 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁.Carrier
d_Carrier_618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiEquivalence_584 -> ()
d_Carrier_618 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> ()
d_Carrier_618 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁.isEquivalence
d_isEquivalence_620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_620 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_IsEquivalence_26
d_isEquivalence_620 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_IsEquivalence_26
du_isEquivalence_620 T_IsBiEquivalence_584
v11
du_isEquivalence_620 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_620 :: T_IsBiEquivalence_584 -> T_IsEquivalence_26
du_isEquivalence_620 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsBiEquivalence._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_622 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_622 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_622 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_622 T_IsBiEquivalence_584
v11
du_isPartialEquivalence_622 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_622 :: T_IsBiEquivalence_584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_622 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₁.partialSetoid
d_partialSetoid_624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_624 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_PartialSetoid_10
d_partialSetoid_624 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_PartialSetoid_10
du_partialSetoid_624 T_IsBiEquivalence_584
v11
du_partialSetoid_624 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_624 :: T_IsBiEquivalence_584 -> T_PartialSetoid_10
du_partialSetoid_624 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiEquivalence._.Eq₁.refl
d_refl_626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
d_refl_626 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
d_refl_626 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
du_refl_626 T_IsBiEquivalence_584
v11
du_refl_626 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
du_refl_626 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
du_refl_626 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiEquivalence._.Eq₁.reflexive
d_reflexive_628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_628 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_628 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_628 T_IsBiEquivalence_584
v11
du_reflexive_628 ::
  T_IsBiEquivalence_584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_628 :: T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_628 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiEquivalence._.Eq₁.setoid
d_setoid_630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_630 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_Setoid_44
d_setoid_630 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_Setoid_44
du_setoid_630 T_IsBiEquivalence_584
v11
du_setoid_630 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_630 :: T_IsBiEquivalence_584 -> T_Setoid_44
du_setoid_630 T_IsBiEquivalence_584
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsBiEquivalence_584 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584
v0))
-- Function.Structures.IsBiEquivalence._.Eq₁.sym
d_sym_632 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_632 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_632 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_632 T_IsBiEquivalence_584
v11
du_sym_632 ::
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_632 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_632 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₁.trans
d_trans_634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_634 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_634 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_634 T_IsBiEquivalence_584
v11
du_trans_634 ::
  T_IsBiEquivalence_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_634 :: T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_634 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₂._≈_
d__'8776'__638 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> ()
d__'8776'__638 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__638 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂._≉_
d__'8777'__640 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> ()
d__'8777'__640 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__640 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂.Carrier
d_Carrier_642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiEquivalence_584 -> ()
d_Carrier_642 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> ()
d_Carrier_642 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂.isEquivalence
d_isEquivalence_644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_644 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_IsEquivalence_26
d_isEquivalence_644 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_IsEquivalence_26
du_isEquivalence_644 T_IsBiEquivalence_584
v11
du_isEquivalence_644 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_644 :: T_IsBiEquivalence_584 -> T_IsEquivalence_26
du_isEquivalence_644 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsBiEquivalence._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_646 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_646 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_646 T_IsBiEquivalence_584
v11
du_isPartialEquivalence_646 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_646 :: T_IsBiEquivalence_584 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_646 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₂.partialSetoid
d_partialSetoid_648 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_648 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_PartialSetoid_10
d_partialSetoid_648 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_PartialSetoid_10
du_partialSetoid_648 T_IsBiEquivalence_584
v11
du_partialSetoid_648 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_648 :: T_IsBiEquivalence_584 -> T_PartialSetoid_10
du_partialSetoid_648 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiEquivalence._.Eq₂.refl
d_refl_650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
d_refl_650 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
d_refl_650 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
du_refl_650 T_IsBiEquivalence_584
v11
du_refl_650 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
du_refl_650 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny
du_refl_650 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiEquivalence._.Eq₂.reflexive
d_reflexive_652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_652 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_652 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_652 T_IsBiEquivalence_584
v11
du_reflexive_652 ::
  T_IsBiEquivalence_584 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_652 :: T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_652 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiEquivalence._.Eq₂.setoid
d_setoid_654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_654 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> T_Setoid_44
d_setoid_654 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> T_Setoid_44
du_setoid_654 T_IsBiEquivalence_584
v11
du_setoid_654 ::
  T_IsBiEquivalence_584 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_654 :: T_IsBiEquivalence_584 -> T_Setoid_44
du_setoid_654 T_IsBiEquivalence_584
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsBiEquivalence_584 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_584
v0))
-- Function.Structures.IsBiEquivalence._.Eq₂.sym
d_sym_656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_656 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_656 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_656 T_IsBiEquivalence_584
v11
du_sym_656 ::
  T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_656 :: T_IsBiEquivalence_584 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_656 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₂.trans
d_trans_658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_658 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_584
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_658 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_584
v11
  = T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_658 T_IsBiEquivalence_584
v11
du_trans_658 ::
  T_IsBiEquivalence_584 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_658 :: T_IsBiEquivalence_584
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_658 T_IsBiEquivalence_584
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_584 -> T_IsCongruent_22
d_to'45'isCongruent_598 (T_IsBiEquivalence_584 -> T_IsBiEquivalence_584
forall a b. a -> b
coe T_IsBiEquivalence_584
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiInverse
d_IsBiInverse_666 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBiInverse_666 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 = ()
data T_IsBiInverse_666
  = C_IsBiInverse'46'constructor_32731 T_IsCongruent_22
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsBiInverse.to-isCongruent
d_to'45'isCongruent_684 :: T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 :: T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 T_IsBiInverse_666
v0
  = case T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0 of
      C_IsBiInverse'46'constructor_32731 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsBiInverse_666
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.from₁-cong
d_from'8321''45'cong_686 ::
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_686 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_686 T_IsBiInverse_666
v0
  = case T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0 of
      C_IsBiInverse'46'constructor_32731 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsBiInverse_666
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.from₂-cong
d_from'8322''45'cong_688 ::
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_688 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_688 T_IsBiInverse_666
v0
  = case T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0 of
      C_IsBiInverse'46'constructor_32731 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsBiInverse_666
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.inverseˡ
d_inverse'737'_690 ::
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_690 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_690 T_IsBiInverse_666
v0
  = case T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0 of
      C_IsBiInverse'46'constructor_32731 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsBiInverse_666
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.inverseʳ
d_inverse'691'_692 ::
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_692 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_692 T_IsBiInverse_666
v0
  = case T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0 of
      C_IsBiInverse'46'constructor_32731 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_IsBiInverse_666
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse._.isEquivalence₁
d_isEquivalence'8321'_696 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_696 :: T_IsBiInverse_666 -> T_IsEquivalence_26
d_isEquivalence'8321'_696 T_IsBiInverse_666
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 ((T_IsBiInverse_666 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0))
-- Function.Structures.IsBiInverse._.isEquivalence₂
d_isEquivalence'8322'_698 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_698 :: T_IsBiInverse_666 -> T_IsEquivalence_26
d_isEquivalence'8322'_698 T_IsBiInverse_666
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 ((T_IsBiInverse_666 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0))
-- Function.Structures.IsBiInverse._.cong
d_cong_700 ::
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_700 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_700 T_IsBiInverse_666
v0
  = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32 ((T_IsBiInverse_666 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0))
-- Function.Structures.IsBiInverse._.Eq₁._≈_
d__'8776'__704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> ()
d__'8776'__704 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__704 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁._≉_
d__'8777'__706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> ()
d__'8777'__706 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__706 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁.Carrier
d_Carrier_708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiInverse_666 -> ()
d_Carrier_708 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> ()
d_Carrier_708 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁.isEquivalence
d_isEquivalence_710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_710 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_IsEquivalence_26
d_isEquivalence_710 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_IsEquivalence_26
du_isEquivalence_710 T_IsBiInverse_666
v11
du_isEquivalence_710 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_710 :: T_IsBiInverse_666 -> T_IsEquivalence_26
du_isEquivalence_710 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsBiInverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_712 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_712 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_712 T_IsBiInverse_666
v11
du_isPartialEquivalence_712 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_712 :: T_IsBiInverse_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_712 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiInverse._.Eq₁.partialSetoid
d_partialSetoid_714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_714 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_PartialSetoid_10
d_partialSetoid_714 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_PartialSetoid_10
du_partialSetoid_714 T_IsBiInverse_666
v11
du_partialSetoid_714 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_714 :: T_IsBiInverse_666 -> T_PartialSetoid_10
du_partialSetoid_714 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiInverse._.Eq₁.refl
d_refl_716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiInverse_666 -> AgdaAny -> AgdaAny
d_refl_716 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
d_refl_716 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> AgdaAny -> AgdaAny
du_refl_716 T_IsBiInverse_666
v11
du_refl_716 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny
du_refl_716 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny
du_refl_716 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiInverse._.Eq₁.reflexive
d_reflexive_718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_718 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_718 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_718 T_IsBiInverse_666
v11
du_reflexive_718 ::
  T_IsBiInverse_666 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_718 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_718 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiInverse._.Eq₁.setoid
d_setoid_720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_720 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_Setoid_44
d_setoid_720 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_Setoid_44
du_setoid_720 T_IsBiInverse_666
v11
du_setoid_720 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_720 :: T_IsBiInverse_666 -> T_Setoid_44
du_setoid_720 T_IsBiInverse_666
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsBiInverse_666 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0))
-- Function.Structures.IsBiInverse._.Eq₁.sym
d_sym_722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_722 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_722 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_722 T_IsBiInverse_666
v11
du_sym_722 ::
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_722 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_722 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiInverse._.Eq₁.trans
d_trans_724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_724 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_724 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_724 T_IsBiInverse_666
v11
du_trans_724 ::
  T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_724 :: T_IsBiInverse_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_724 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiInverse._.Eq₂._≈_
d__'8776'__728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> ()
d__'8776'__728 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__728 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂._≉_
d__'8777'__730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> ()
d__'8777'__730 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__730 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂.Carrier
d_Carrier_732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiInverse_666 -> ()
d_Carrier_732 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> ()
d_Carrier_732 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂.isEquivalence
d_isEquivalence_734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_734 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_IsEquivalence_26
d_isEquivalence_734 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_IsEquivalence_26
du_isEquivalence_734 T_IsBiInverse_666
v11
du_isEquivalence_734 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_734 :: T_IsBiInverse_666 -> T_IsEquivalence_26
du_isEquivalence_734 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1))
-- Function.Structures.IsBiInverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_736 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_736 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_736 T_IsBiInverse_666
v11
du_isPartialEquivalence_736 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_736 :: T_IsBiInverse_666 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_736 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiInverse._.Eq₂.partialSetoid
d_partialSetoid_738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_738 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_PartialSetoid_10
d_partialSetoid_738 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_PartialSetoid_10
du_partialSetoid_738 T_IsBiInverse_666
v11
du_partialSetoid_738 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_738 :: T_IsBiInverse_666 -> T_PartialSetoid_10
du_partialSetoid_738 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiInverse._.Eq₂.refl
d_refl_740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiInverse_666 -> AgdaAny -> AgdaAny
d_refl_740 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
d_refl_740 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> AgdaAny -> AgdaAny
du_refl_740 T_IsBiInverse_666
v11
du_refl_740 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny
du_refl_740 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny
du_refl_740 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiInverse._.Eq₂.reflexive
d_reflexive_742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_742 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_742 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_742 T_IsBiInverse_666
v11
du_reflexive_742 ::
  T_IsBiInverse_666 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_742 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_742 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiInverse._.Eq₂.setoid
d_setoid_744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_744 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> T_Setoid_44
d_setoid_744 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> T_Setoid_44
du_setoid_744 T_IsBiInverse_666
v11
du_setoid_744 ::
  T_IsBiInverse_666 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_744 :: T_IsBiInverse_666 -> T_Setoid_44
du_setoid_744 T_IsBiInverse_666
v0
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsBiInverse_666 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_666
v0))
-- Function.Structures.IsBiInverse._.Eq₂.sym
d_sym_746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_746 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_746 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_746 T_IsBiInverse_666
v11
du_sym_746 ::
  T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_746 :: T_IsBiInverse_666 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_746 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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_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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsBiInverse._.Eq₂.trans
d_trans_748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_748 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_666
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_748 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_666
v11
  = T_IsBiInverse_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_748 T_IsBiInverse_666
v11
du_trans_748 ::
  T_IsBiInverse_666 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_748 :: T_IsBiInverse_666
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_748 T_IsBiInverse_666
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_666 -> T_IsCongruent_22
d_to'45'isCongruent_684 (T_IsBiInverse_666 -> T_IsBiInverse_666
forall a b. a -> b
coe T_IsBiInverse_666
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Function.Structures.IsSplitSurjection
d_IsSplitSurjection_752 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsSplitSurjection_752 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsSplitSurjection_752
  = C_IsSplitSurjection'46'constructor_35501 (AgdaAny -> AgdaAny)
                                             T_IsLeftInverse_322
-- Function.Structures.IsSplitSurjection.from
d_from_760 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_from_760 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_from_760 T_IsSplitSurjection_752
v0
  = case T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0 of
      C_IsSplitSurjection'46'constructor_35501 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_322
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_IsSplitSurjection_752
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSplitSurjection.isLeftInverse
d_isLeftInverse_762 ::
  T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 :: T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 T_IsSplitSurjection_752
v0
  = case T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0 of
      C_IsSplitSurjection'46'constructor_35501 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_322
v2 -> T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v2
      T_IsSplitSurjection_752
_ -> T_IsLeftInverse_322
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSplitSurjection._.from-cong
d_from'45'cong_766 ::
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_766 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_766 T_IsSplitSurjection_752
v0
  = (T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_336 ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0))
-- Function.Structures.IsSplitSurjection._.inverseˡ
d_inverse'737'_768 ::
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_768 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_768 T_IsSplitSurjection_752
v0
  = (T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_338 ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0))
-- Function.Structures.IsSplitSurjection._.isCongruent
d_isCongruent_770 :: T_IsSplitSurjection_752 -> T_IsCongruent_22
d_isCongruent_770 :: T_IsSplitSurjection_752 -> T_IsCongruent_22
d_isCongruent_770 T_IsSplitSurjection_752
v0
  = (T_IsLeftInverse_322 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0))
-- Function.Structures.IsSplitSurjection._.isEquivalence₁
d_isEquivalence'8321'_772 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_772 :: T_IsSplitSurjection_752 -> T_IsEquivalence_26
d_isEquivalence'8321'_772 T_IsSplitSurjection_752
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0)))
-- Function.Structures.IsSplitSurjection._.isEquivalence₂
d_isEquivalence'8322'_774 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_774 :: T_IsSplitSurjection_752 -> T_IsEquivalence_26
d_isEquivalence'8322'_774 T_IsSplitSurjection_752
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0)))
-- Function.Structures.IsSplitSurjection._.isSurjection
d_isSurjection_776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> T_IsSurjection_162
d_isSurjection_776 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_IsSurjection_162
d_isSurjection_776 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_IsSurjection_162
du_isSurjection_776 T_IsSplitSurjection_752
v9
du_isSurjection_776 ::
  T_IsSplitSurjection_752 -> T_IsSurjection_162
du_isSurjection_776 :: T_IsSplitSurjection_752 -> T_IsSurjection_162
du_isSurjection_776 T_IsSplitSurjection_752
v0
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> T_IsSurjection_162
du_isSurjection_400 ((T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_from_760 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0))
      ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0))
-- Function.Structures.IsSplitSurjection._.strictlyInverseˡ
d_strictlyInverse'737'_778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_778 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_778 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_778 T_IsSplitSurjection_752
v9
du_strictlyInverse'737'_778 ::
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_778 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_778 T_IsSplitSurjection_752
v0
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_322 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_396 ((T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_from_760 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0))
      ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0))
-- Function.Structures.IsSplitSurjection._.cong
d_cong_780 ::
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_780 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_780 T_IsSplitSurjection_752
v0
  = (T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_32
      ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 ((T_IsSplitSurjection_752 -> T_IsLeftInverse_322)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_752
v0)))
-- Function.Structures.IsSplitSurjection._.Eq₁._≈_
d__'8776'__784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> ()
d__'8776'__784 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__784 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₁._≉_
d__'8777'__786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> ()
d__'8777'__786 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__786 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₁.Carrier
d_Carrier_788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSplitSurjection_752 -> ()
d_Carrier_788 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> ()
d_Carrier_788 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₁.isEquivalence
d_isEquivalence_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_790 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_IsEquivalence_26
d_isEquivalence_790 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_IsEquivalence_26
du_isEquivalence_790 T_IsSplitSurjection_752
v9
du_isEquivalence_790 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_790 :: T_IsSplitSurjection_752 -> T_IsEquivalence_26
du_isEquivalence_790 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsSplitSurjection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_792 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_792 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_792 T_IsSplitSurjection_752
v9
du_isPartialEquivalence_792 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_792 :: T_IsSplitSurjection_752 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_792 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₁.partialSetoid
d_partialSetoid_794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_794 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_PartialSetoid_10
d_partialSetoid_794 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_PartialSetoid_10
du_partialSetoid_794 T_IsSplitSurjection_752
v9
du_partialSetoid_794 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_794 :: T_IsSplitSurjection_752 -> T_PartialSetoid_10
du_partialSetoid_794 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₁.refl
d_refl_796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_refl_796 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
d_refl_796 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9 = T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_refl_796 T_IsSplitSurjection_752
v9
du_refl_796 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_refl_796 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_refl_796 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₁.reflexive
d_reflexive_798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_798 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_798 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_798 T_IsSplitSurjection_752
v9
du_reflexive_798 ::
  T_IsSplitSurjection_752 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_798 :: T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_798 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsSplitSurjection._.Eq₁.setoid
d_setoid_800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_800 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_Setoid_44
d_setoid_800 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_Setoid_44
du_setoid_800 T_IsSplitSurjection_752
v9
du_setoid_800 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_800 :: T_IsSplitSurjection_752 -> T_Setoid_44
du_setoid_800 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1)))
-- Function.Structures.IsSplitSurjection._.Eq₁.sym
d_sym_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_802 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_802 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9 = T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_802 T_IsSplitSurjection_752
v9
du_sym_802 ::
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_802 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_802 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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_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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₁.trans
d_trans_804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_804 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_804 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_804 T_IsSplitSurjection_752
v9
du_trans_804 ::
  T_IsSplitSurjection_752 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_804 :: T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_804 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₂._≈_
d__'8776'__808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> ()
d__'8776'__808 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__808 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₂._≉_
d__'8777'__810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> ()
d__'8777'__810 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__810 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₂.Carrier
d_Carrier_812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSplitSurjection_752 -> ()
d_Carrier_812 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> ()
d_Carrier_812 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₂.isEquivalence
d_isEquivalence_814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_814 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_IsEquivalence_26
d_isEquivalence_814 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_IsEquivalence_26
du_isEquivalence_814 T_IsSplitSurjection_752
v9
du_isEquivalence_814 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_814 :: T_IsSplitSurjection_752 -> T_IsEquivalence_26
du_isEquivalence_814 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsSplitSurjection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_816 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_816 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_816 T_IsSplitSurjection_752
v9
du_isPartialEquivalence_816 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_816 :: T_IsSplitSurjection_752 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_816 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₂.partialSetoid
d_partialSetoid_818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_818 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_PartialSetoid_10
d_partialSetoid_818 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_PartialSetoid_10
du_partialSetoid_818 T_IsSplitSurjection_752
v9
du_partialSetoid_818 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_818 :: T_IsSplitSurjection_752 -> T_PartialSetoid_10
du_partialSetoid_818 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_70
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₂.refl
d_refl_820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
d_refl_820 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
d_refl_820 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9 = T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_refl_820 T_IsSplitSurjection_752
v9
du_refl_820 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_refl_820 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny
du_refl_820 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_26
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₂.reflexive
d_reflexive_822 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_822 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_822 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_822 T_IsSplitSurjection_752
v9
du_reflexive_822 ::
  T_IsSplitSurjection_752 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_822 :: T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_822 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((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 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsSplitSurjection._.Eq₂.setoid
d_setoid_824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_824 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> T_Setoid_44
d_setoid_824 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752 -> T_Setoid_44
du_setoid_824 T_IsSplitSurjection_752
v9
du_setoid_824 ::
  T_IsSplitSurjection_752 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_824 :: T_IsSplitSurjection_752 -> T_Setoid_44
du_setoid_824 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 ((T_IsLeftInverse_322 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_322
v1)))
-- Function.Structures.IsSplitSurjection._.Eq₂.sym
d_sym_826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_826 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_826 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9 = T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_826 T_IsSplitSurjection_752
v9
du_sym_826 ::
  T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_826 :: T_IsSplitSurjection_752 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_826 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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_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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₂.trans
d_trans_828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_752 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_828 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_752
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_828 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_752
v9
  = T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_828 T_IsSplitSurjection_752
v9
du_trans_828 ::
  T_IsSplitSurjection_752 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_828 :: T_IsSplitSurjection_752
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_828 T_IsSplitSurjection_752
v0
  = let v1 :: T_IsLeftInverse_322
v1 = T_IsSplitSurjection_752 -> T_IsLeftInverse_322
d_isLeftInverse_762 (T_IsSplitSurjection_752 -> T_IsSplitSurjection_752
forall a b. a -> b
coe T_IsSplitSurjection_752
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_322 -> T_IsCongruent_22
d_isCongruent_334 (T_IsLeftInverse_322 -> T_IsLeftInverse_322
forall a b. a -> b
coe T_IsLeftInverse_322
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((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
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))