{-# 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.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_727
      (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_74
      ((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
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> 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_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._.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
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> 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_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.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_727
      (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_74
      ((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
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> 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_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._.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
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> 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_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.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_3991 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_3991 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_3991 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_74
         ((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
      ((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_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.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
      ((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_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._.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_74
         ((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
      ((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_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.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
      ((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_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
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_6577 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_6577 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_6577 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_74
         ((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
      ((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_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.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
      ((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_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._.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_74
         ((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
      ((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_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.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
      ((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_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.IsBijection
d_IsBijection_232 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBijection_232 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsBijection_232
  = C_IsBijection'46'constructor_9159 T_IsInjection_92
                                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Structures.IsBijection.isInjection
d_isInjection_240 :: T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 :: T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 T_IsBijection_232
v0
  = case T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0 of
      C_IsBijection'46'constructor_9159 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_232
_ -> T_IsInjection_92
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBijection.surjective
d_surjective_242 ::
  T_IsBijection_232 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_242 :: T_IsBijection_232 -> AgdaAny -> T_Σ_14
d_surjective_242 T_IsBijection_232
v0
  = case T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0 of
      C_IsBijection'46'constructor_9159 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_232
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBijection._.cong
d_cong_246 ::
  T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_246 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_246 T_IsBijection_232
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_232 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0)))
-- Function.Structures.IsBijection._.injective
d_injective_248 ::
  T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_248 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_248 T_IsBijection_232
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_232 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0))
-- Function.Structures.IsBijection._.isCongruent
d_isCongruent_250 :: T_IsBijection_232 -> T_IsCongruent_22
d_isCongruent_250 :: T_IsBijection_232 -> T_IsCongruent_22
d_isCongruent_250 T_IsBijection_232
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_232 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0))
-- Function.Structures.IsBijection._.isEquivalence₁
d_isEquivalence'8321'_252 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_252 :: T_IsBijection_232 -> T_IsEquivalence_26
d_isEquivalence'8321'_252 T_IsBijection_232
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_232 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0)))
-- Function.Structures.IsBijection._.isEquivalence₂
d_isEquivalence'8322'_254 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_254 :: T_IsBijection_232 -> T_IsEquivalence_26
d_isEquivalence'8322'_254 T_IsBijection_232
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_232 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0)))
-- Function.Structures.IsBijection._.Eq₁._≈_
d__'8776'__258 ::
  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_232 -> AgdaAny -> AgdaAny -> ()
d__'8776'__258 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__258 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁._≉_
d__'8777'__260 ::
  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_232 -> AgdaAny -> AgdaAny -> ()
d__'8777'__260 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__260 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁.Carrier
d_Carrier_262 ::
  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_232 -> ()
d_Carrier_262 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> ()
d_Carrier_262 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁.isEquivalence
d_isEquivalence_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_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_264 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsEquivalence_26
d_isEquivalence_264 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_264 T_IsBijection_232
v9
du_isEquivalence_264 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_264 :: T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_264 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_266 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_266 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_266 T_IsBijection_232
v9
du_isPartialEquivalence_266 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_266 :: T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_266 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_268 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_PartialSetoid_10
d_partialSetoid_268 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_268 T_IsBijection_232
v9
du_partialSetoid_268 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_268 :: T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_268 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_74
            ((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_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_232 -> AgdaAny -> AgdaAny
d_refl_270 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
d_refl_270 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9 = T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_270 T_IsBijection_232
v9
du_refl_270 :: T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_270 :: T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_270 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_272 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_272 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_272 T_IsBijection_232
v9
du_reflexive_272 ::
  T_IsBijection_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_272 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_272 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_274 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Setoid_44
d_setoid_274 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_Setoid_44
du_setoid_274 T_IsBijection_232
v9
du_setoid_274 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_274 :: T_IsBijection_232 -> T_Setoid_44
du_setoid_274 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_276 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_276 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9 = T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_276 T_IsBijection_232
v9
du_sym_276 ::
  T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_276 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_276 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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
         ((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_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.trans
d_trans_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_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_278 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_278 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_278 T_IsBijection_232
v9
du_trans_278 ::
  T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_278 :: T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_278 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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
         ((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_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._.Eq₂._≈_
d__'8776'__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_232 -> AgdaAny -> AgdaAny -> ()
d__'8776'__282 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__282 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂._≉_
d__'8777'__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_232 -> AgdaAny -> AgdaAny -> ()
d__'8777'__284 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__284 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂.Carrier
d_Carrier_286 ::
  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_232 -> ()
d_Carrier_286 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> ()
d_Carrier_286 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂.isEquivalence
d_isEquivalence_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_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_288 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsEquivalence_26
d_isEquivalence_288 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_288 T_IsBijection_232
v9
du_isEquivalence_288 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_288 :: T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_288 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_290 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_290 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsBijection_232
v9
du_isPartialEquivalence_290 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_290 :: T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_292 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_PartialSetoid_10
d_partialSetoid_292 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_292 T_IsBijection_232
v9
du_partialSetoid_292 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_292 :: T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_292 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_74
            ((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_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_232 -> AgdaAny -> AgdaAny
d_refl_294 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
d_refl_294 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9 = T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_294 T_IsBijection_232
v9
du_refl_294 :: T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_294 :: T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_294 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_296 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_296 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_296 T_IsBijection_232
v9
du_reflexive_296 ::
  T_IsBijection_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_296 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_296 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_298 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Setoid_44
d_setoid_298 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_Setoid_44
du_setoid_298 T_IsBijection_232
v9
du_setoid_298 ::
  T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_298 :: T_IsBijection_232 -> T_Setoid_44
du_setoid_298 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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_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_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_300 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_300 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9 = T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_300 T_IsBijection_232
v9
du_sym_300 ::
  T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_300 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_300 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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
         ((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_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.trans
d_trans_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_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_302 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_302 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_302 T_IsBijection_232
v9
du_trans_302 ::
  T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_302 :: T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_302 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1 = T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
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
         ((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_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.bijective
d_bijective_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_232 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_bijective_304 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Σ_14
d_bijective_304 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_Σ_14
du_bijective_304 T_IsBijection_232
v9
du_bijective_304 ::
  T_IsBijection_232 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_bijective_304 :: T_IsBijection_232 -> T_Σ_14
du_bijective_304 T_IsBijection_232
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_232 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0)))
      ((T_IsBijection_232 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> AgdaAny -> T_Σ_14
d_surjective_242 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0))
-- Function.Structures.IsBijection.isSurjection
d_isSurjection_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_232 -> T_IsSurjection_162
d_isSurjection_306 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsSurjection_162
d_isSurjection_306 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_232
v9
  = T_IsBijection_232 -> T_IsSurjection_162
du_isSurjection_306 T_IsBijection_232
v9
du_isSurjection_306 :: T_IsBijection_232 -> T_IsSurjection_162
du_isSurjection_306 :: T_IsBijection_232 -> T_IsSurjection_162
du_isSurjection_306 T_IsBijection_232
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_6577
      ((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_232 -> T_IsInjection_92) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> T_IsInjection_92
d_isInjection_240 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0)))
      ((T_IsBijection_232 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232 -> AgdaAny -> T_Σ_14
d_surjective_242 (T_IsBijection_232 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_232
v0))
-- Function.Structures.IsLeftInverse
d_IsLeftInverse_312 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsLeftInverse_312 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsLeftInverse_312
  = C_IsLeftInverse'46'constructor_13425 T_IsCongruent_22
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny)
-- Function.Structures.IsLeftInverse.isCongruent
d_isCongruent_324 :: T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 :: T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 T_IsLeftInverse_312
v0
  = case T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v0 of
      C_IsLeftInverse'46'constructor_13425 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsLeftInverse_312
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse.cong₂
d_cong'8322'_326 ::
  T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_326 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_326 T_IsLeftInverse_312
v0
  = case T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v0 of
      C_IsLeftInverse'46'constructor_13425 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsLeftInverse_312
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse.inverseˡ
d_inverse'737'_328 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
d_inverse'737'_328 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
d_inverse'737'_328 T_IsLeftInverse_312
v0
  = case T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v0 of
      C_IsLeftInverse'46'constructor_13425 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_IsLeftInverse_312
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse._.cong
d_cong_332 ::
  T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_332 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_332 T_IsLeftInverse_312
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v0))
-- Function.Structures.IsLeftInverse._.isEquivalence₁
d_isEquivalence'8321'_334 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_334 :: T_IsLeftInverse_312 -> T_IsEquivalence_26
d_isEquivalence'8321'_334 T_IsLeftInverse_312
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v0))
-- Function.Structures.IsLeftInverse._.isEquivalence₂
d_isEquivalence'8322'_336 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_336 :: T_IsLeftInverse_312 -> T_IsEquivalence_26
d_isEquivalence'8322'_336 T_IsLeftInverse_312
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v0))
-- Function.Structures.IsLeftInverse._.Eq₁._≈_
d__'8776'__340 ::
  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_312 -> AgdaAny -> AgdaAny -> ()
d__'8776'__340 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__340 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁._≉_
d__'8777'__342 ::
  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_312 -> AgdaAny -> AgdaAny -> ()
d__'8777'__342 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__342 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁.Carrier
d_Carrier_344 ::
  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_312 -> ()
d_Carrier_344 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> ()
d_Carrier_344 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁.isEquivalence
d_isEquivalence_346 ::
  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_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_346 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_IsEquivalence_26
d_isEquivalence_346 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_IsEquivalence_26
du_isEquivalence_346 T_IsLeftInverse_312
v10
du_isEquivalence_346 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_346 :: T_IsLeftInverse_312 -> T_IsEquivalence_26
du_isEquivalence_346 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_348 ::
  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_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_348 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_348 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_348 T_IsLeftInverse_312
v10
du_isPartialEquivalence_348 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_348 :: T_IsLeftInverse_312 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_348 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_350 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_PartialSetoid_10
d_partialSetoid_350 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_PartialSetoid_10
du_partialSetoid_350 T_IsLeftInverse_312
v10
du_partialSetoid_350 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_350 :: T_IsLeftInverse_312 -> T_PartialSetoid_10
du_partialSetoid_350 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_74
         ((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_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_312 -> AgdaAny -> AgdaAny
d_refl_352 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
d_refl_352 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
du_refl_352 T_IsLeftInverse_312
v10
du_refl_352 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
du_refl_352 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
du_refl_352 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_312 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_354 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_354 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_354 T_IsLeftInverse_312
v10
du_reflexive_354 ::
  T_IsLeftInverse_312 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_354 :: T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_354 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_356 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_Setoid_44
d_setoid_356 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_Setoid_44
du_setoid_356 T_IsLeftInverse_312
v10
du_setoid_356 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_356 :: T_IsLeftInverse_312 -> T_Setoid_44
du_setoid_356 T_IsLeftInverse_312
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v0))
-- Function.Structures.IsLeftInverse._.Eq₁.sym
d_sym_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_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_358 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_358 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_358 T_IsLeftInverse_312
v10
du_sym_358 ::
  T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_358 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_358 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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.trans
d_trans_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_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_360 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_360 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_360 T_IsLeftInverse_312
v10
du_trans_360 ::
  T_IsLeftInverse_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_360 :: T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_360 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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._.Eq₂._≈_
d__'8776'__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_312 -> AgdaAny -> AgdaAny -> ()
d__'8776'__364 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__364 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂._≉_
d__'8777'__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_312 -> AgdaAny -> AgdaAny -> ()
d__'8777'__366 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__366 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂.Carrier
d_Carrier_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_312 -> ()
d_Carrier_368 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> ()
d_Carrier_368 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂.isEquivalence
d_isEquivalence_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_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_370 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_IsEquivalence_26
d_isEquivalence_370 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_IsEquivalence_26
du_isEquivalence_370 T_IsLeftInverse_312
v10
du_isEquivalence_370 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_370 :: T_IsLeftInverse_312 -> T_IsEquivalence_26
du_isEquivalence_370 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_372 ::
  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_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_372 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_372 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_372 T_IsLeftInverse_312
v10
du_isPartialEquivalence_372 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_372 :: T_IsLeftInverse_312 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_372 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_374 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_PartialSetoid_10
d_partialSetoid_374 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_PartialSetoid_10
du_partialSetoid_374 T_IsLeftInverse_312
v10
du_partialSetoid_374 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_374 :: T_IsLeftInverse_312 -> T_PartialSetoid_10
du_partialSetoid_374 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_74
         ((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_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_312 -> AgdaAny -> AgdaAny
d_refl_376 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
d_refl_376 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
du_refl_376 T_IsLeftInverse_312
v10
du_refl_376 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
du_refl_376 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
du_refl_376 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_312 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_378 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_378 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_378 T_IsLeftInverse_312
v10
du_reflexive_378 ::
  T_IsLeftInverse_312 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_378 :: T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_378 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_380 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> T_Setoid_44
d_setoid_380 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> T_Setoid_44
du_setoid_380 T_IsLeftInverse_312
v10
du_setoid_380 ::
  T_IsLeftInverse_312 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_380 :: T_IsLeftInverse_312 -> T_Setoid_44
du_setoid_380 T_IsLeftInverse_312
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v0))
-- Function.Structures.IsLeftInverse._.Eq₂.sym
d_sym_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_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_382 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_382 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_382 T_IsLeftInverse_312
v10
du_sym_382 ::
  T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_382 :: T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_382 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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.trans
d_trans_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_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_384 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_384 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_312
v10
  = T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_384 T_IsLeftInverse_312
v10
du_trans_384 ::
  T_IsLeftInverse_312 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_384 :: T_IsLeftInverse_312
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_384 T_IsLeftInverse_312
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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
d_IsRightInverse_390 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsRightInverse_390 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsRightInverse_390
  = C_IsRightInverse'46'constructor_16843 T_IsCongruent_22
                                          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny)
-- Function.Structures.IsRightInverse.isCongruent
d_isCongruent_402 :: T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 :: T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 T_IsRightInverse_390
v0
  = case T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
v0 of
      C_IsRightInverse'46'constructor_16843 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsRightInverse_390
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse.cong₂
d_cong'8322'_404 ::
  T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_404 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_404 T_IsRightInverse_390
v0
  = case T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
v0 of
      C_IsRightInverse'46'constructor_16843 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsRightInverse_390
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse.inverseʳ
d_inverse'691'_406 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny
d_inverse'691'_406 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny
d_inverse'691'_406 T_IsRightInverse_390
v0
  = case T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
v0 of
      C_IsRightInverse'46'constructor_16843 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_IsRightInverse_390
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse._.cong
d_cong_410 ::
  T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_410 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_410 T_IsRightInverse_390
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_390 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390
v0))
-- Function.Structures.IsRightInverse._.isEquivalence₁
d_isEquivalence'8321'_412 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_412 :: T_IsRightInverse_390 -> T_IsEquivalence_26
d_isEquivalence'8321'_412 T_IsRightInverse_390
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_390 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390
v0))
-- Function.Structures.IsRightInverse._.isEquivalence₂
d_isEquivalence'8322'_414 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_414 :: T_IsRightInverse_390 -> T_IsEquivalence_26
d_isEquivalence'8322'_414 T_IsRightInverse_390
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_390 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390
v0))
-- Function.Structures.IsRightInverse._.Eq₁._≈_
d__'8776'__418 ::
  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_390 -> AgdaAny -> AgdaAny -> ()
d__'8776'__418 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__418 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁._≉_
d__'8777'__420 ::
  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_390 -> AgdaAny -> AgdaAny -> ()
d__'8777'__420 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__420 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁.Carrier
d_Carrier_422 ::
  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_390 -> ()
d_Carrier_422 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> ()
d_Carrier_422 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁.isEquivalence
d_isEquivalence_424 ::
  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_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_424 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_IsEquivalence_26
d_isEquivalence_424 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_IsEquivalence_26
du_isEquivalence_424 T_IsRightInverse_390
v10
du_isEquivalence_424 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_424 :: T_IsRightInverse_390 -> T_IsEquivalence_26
du_isEquivalence_424 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_426 ::
  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_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_426 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_426 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_426 T_IsRightInverse_390
v10
du_isPartialEquivalence_426 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_426 :: T_IsRightInverse_390 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_426 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_428 ::
  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_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_428 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_PartialSetoid_10
d_partialSetoid_428 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_PartialSetoid_10
du_partialSetoid_428 T_IsRightInverse_390
v10
du_partialSetoid_428 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_428 :: T_IsRightInverse_390 -> T_PartialSetoid_10
du_partialSetoid_428 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_74
         ((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_430 ::
  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_390 -> AgdaAny -> AgdaAny
d_refl_430 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
d_refl_430 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> AgdaAny -> AgdaAny
du_refl_430 T_IsRightInverse_390
v10
du_refl_430 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny
du_refl_430 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny
du_refl_430 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_432 ::
  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_390 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_432 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_432 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_432 T_IsRightInverse_390
v10
du_reflexive_432 ::
  T_IsRightInverse_390 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_432 :: T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_432 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_434 ::
  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_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_434 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_Setoid_44
d_setoid_434 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_Setoid_44
du_setoid_434 T_IsRightInverse_390
v10
du_setoid_434 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_434 :: T_IsRightInverse_390 -> T_Setoid_44
du_setoid_434 T_IsRightInverse_390
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_390 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390
v0))
-- Function.Structures.IsRightInverse._.Eq₁.sym
d_sym_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_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_436 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_436 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_436 T_IsRightInverse_390
v10
du_sym_436 ::
  T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_436 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_436 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_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.trans
d_trans_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_390 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_438 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_438 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_438 T_IsRightInverse_390
v10
du_trans_438 ::
  T_IsRightInverse_390 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_438 :: T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_438 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_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._.Eq₂._≈_
d__'8776'__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_390 -> AgdaAny -> AgdaAny -> ()
d__'8776'__442 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__442 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂._≉_
d__'8777'__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_390 -> AgdaAny -> AgdaAny -> ()
d__'8777'__444 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__444 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂.Carrier
d_Carrier_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_390 -> ()
d_Carrier_446 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> ()
d_Carrier_446 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂.isEquivalence
d_isEquivalence_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_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_448 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_IsEquivalence_26
d_isEquivalence_448 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_IsEquivalence_26
du_isEquivalence_448 T_IsRightInverse_390
v10
du_isEquivalence_448 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_448 :: T_IsRightInverse_390 -> T_IsEquivalence_26
du_isEquivalence_448 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_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_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_450 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_450 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_450 T_IsRightInverse_390
v10
du_isPartialEquivalence_450 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_450 :: T_IsRightInverse_390 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_450 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_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_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_452 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_PartialSetoid_10
d_partialSetoid_452 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_PartialSetoid_10
du_partialSetoid_452 T_IsRightInverse_390
v10
du_partialSetoid_452 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_452 :: T_IsRightInverse_390 -> T_PartialSetoid_10
du_partialSetoid_452 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_74
         ((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_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_390 -> AgdaAny -> AgdaAny
d_refl_454 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
d_refl_454 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> AgdaAny -> AgdaAny
du_refl_454 T_IsRightInverse_390
v10
du_refl_454 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny
du_refl_454 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny
du_refl_454 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_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_390 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_456 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_456 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_456 T_IsRightInverse_390
v10
du_reflexive_456 ::
  T_IsRightInverse_390 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_456 :: T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_456 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_458 ::
  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_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_458 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> T_Setoid_44
d_setoid_458 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> T_Setoid_44
du_setoid_458 T_IsRightInverse_390
v10
du_setoid_458 ::
  T_IsRightInverse_390 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_458 :: T_IsRightInverse_390 -> T_Setoid_44
du_setoid_458 T_IsRightInverse_390
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_390 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_390
v0))
-- Function.Structures.IsRightInverse._.Eq₂.sym
d_sym_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_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_460 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_460 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_460 T_IsRightInverse_390
v10
du_sym_460 ::
  T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_460 :: T_IsRightInverse_390 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_460 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_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.trans
d_trans_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_390 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_462 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_462 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_390
v10
  = T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_462 T_IsRightInverse_390
v10
du_trans_462 ::
  T_IsRightInverse_390 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_462 :: T_IsRightInverse_390
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_462 T_IsRightInverse_390
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_390 -> T_IsCongruent_22
d_isCongruent_402 (T_IsRightInverse_390 -> T_IsRightInverse_390
forall a b. a -> b
coe T_IsRightInverse_390
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_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.IsInverse
d_IsInverse_468 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsInverse_468 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsInverse_468
  = C_IsInverse'46'constructor_19781 T_IsLeftInverse_312
                                     (AgdaAny -> AgdaAny)
-- Function.Structures.IsInverse.isLeftInverse
d_isLeftInverse_478 :: T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 :: T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 T_IsInverse_468
v0
  = case T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0 of
      C_IsInverse'46'constructor_19781 T_IsLeftInverse_312
v1 AgdaAny -> AgdaAny
v2 -> T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1
      T_IsInverse_468
_ -> T_IsLeftInverse_312
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInverse.inverseʳ
d_inverse'691'_480 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
d_inverse'691'_480 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
d_inverse'691'_480 T_IsInverse_468
v0
  = case T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0 of
      C_IsInverse'46'constructor_19781 T_IsLeftInverse_312
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsInverse_468
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInverse._.cong
d_cong_484 ::
  T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_484 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_484 T_IsInverse_468
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0)))
-- Function.Structures.IsInverse._.cong₂
d_cong'8322'_486 ::
  T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_486 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_486 T_IsInverse_468
v0
  = (T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_326 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0))
-- Function.Structures.IsInverse._.inverseˡ
d_inverse'737'_488 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
d_inverse'737'_488 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
d_inverse'737'_488 T_IsInverse_468
v0
  = (T_IsLeftInverse_312 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
d_inverse'737'_328 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0))
-- Function.Structures.IsInverse._.isCongruent
d_isCongruent_490 :: T_IsInverse_468 -> T_IsCongruent_22
d_isCongruent_490 :: T_IsInverse_468 -> T_IsCongruent_22
d_isCongruent_490 T_IsInverse_468
v0
  = (T_IsLeftInverse_312 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0))
-- Function.Structures.IsInverse._.isEquivalence₁
d_isEquivalence'8321'_492 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_492 :: T_IsInverse_468 -> T_IsEquivalence_26
d_isEquivalence'8321'_492 T_IsInverse_468
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0)))
-- Function.Structures.IsInverse._.isEquivalence₂
d_isEquivalence'8322'_494 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_494 :: T_IsInverse_468 -> T_IsEquivalence_26
d_isEquivalence'8322'_494 T_IsInverse_468
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0)))
-- Function.Structures.IsInverse._.Eq₁._≈_
d__'8776'__498 ::
  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_468 -> AgdaAny -> AgdaAny -> ()
d__'8776'__498 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__498 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁._≉_
d__'8777'__500 ::
  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_468 -> AgdaAny -> AgdaAny -> ()
d__'8777'__500 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__500 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁.Carrier
d_Carrier_502 ::
  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_468 -> ()
d_Carrier_502 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> ()
d_Carrier_502 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁.isEquivalence
d_isEquivalence_504 ::
  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_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_504 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsEquivalence_26
d_isEquivalence_504 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_504 T_IsInverse_468
v10
du_isEquivalence_504 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_504 :: T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_504 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_506 ::
  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_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_506 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_506 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_468
v10
  = T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_506 T_IsInverse_468
v10
du_isPartialEquivalence_506 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_506 :: T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_506 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_508 ::
  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_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_508 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_PartialSetoid_10
d_partialSetoid_508 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_508 T_IsInverse_468
v10
du_partialSetoid_508 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_508 :: T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_508 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_74
            ((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_510 ::
  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_468 -> AgdaAny -> AgdaAny
d_refl_510 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
d_refl_510 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_510 T_IsInverse_468
v10
du_refl_510 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_510 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_510 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_512 ::
  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_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_512 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_512 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_512 T_IsInverse_468
v10
du_reflexive_512 ::
  T_IsInverse_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_512 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_512 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_514 ::
  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_468 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_514 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Setoid_44
d_setoid_514 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_Setoid_44
du_setoid_514 T_IsInverse_468
v10
du_setoid_514 ::
  T_IsInverse_468 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_514 :: T_IsInverse_468 -> T_Setoid_44
du_setoid_514 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v1)))
-- Function.Structures.IsInverse._.Eq₁.sym
d_sym_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_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_516 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_516 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_516 T_IsInverse_468
v10
du_sym_516 ::
  T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_516 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_516 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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.trans
d_trans_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_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_518 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_518 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_518 T_IsInverse_468
v10
du_trans_518 ::
  T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_518 :: T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_518 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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._.Eq₂._≈_
d__'8776'__522 ::
  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_468 -> AgdaAny -> AgdaAny -> ()
d__'8776'__522 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__522 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂._≉_
d__'8777'__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_468 -> AgdaAny -> AgdaAny -> ()
d__'8777'__524 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__524 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂.Carrier
d_Carrier_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_468 -> ()
d_Carrier_526 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> ()
d_Carrier_526 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂.isEquivalence
d_isEquivalence_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_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_528 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsEquivalence_26
d_isEquivalence_528 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_528 T_IsInverse_468
v10
du_isEquivalence_528 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_528 :: T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_528 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_530 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_530 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_468
v10
  = T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_530 T_IsInverse_468
v10
du_isPartialEquivalence_530 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_530 :: T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_530 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_532 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_PartialSetoid_10
d_partialSetoid_532 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_532 T_IsInverse_468
v10
du_partialSetoid_532 ::
  T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_532 :: T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_532 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_74
            ((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_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_468 -> AgdaAny -> AgdaAny
d_refl_534 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
d_refl_534 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_534 T_IsInverse_468
v10
du_refl_534 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_534 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_534 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_536 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_536 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_536 T_IsInverse_468
v10
du_reflexive_536 ::
  T_IsInverse_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_536 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_536 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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_468 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_538 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Setoid_44
d_setoid_538 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_Setoid_44
du_setoid_538 T_IsInverse_468
v10
du_setoid_538 ::
  T_IsInverse_468 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_538 :: T_IsInverse_468 -> T_Setoid_44
du_setoid_538 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
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_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v1)))
-- Function.Structures.IsInverse._.Eq₂.sym
d_sym_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_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_540 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_540 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_540 T_IsInverse_468
v10
du_sym_540 ::
  T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_540 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_540 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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.trans
d_trans_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_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_542 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_542 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_542 T_IsInverse_468
v10
du_trans_542 ::
  T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_542 :: T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_542 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1 = T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
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_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.isRightInverse
d_isRightInverse_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_468 -> T_IsRightInverse_390
d_isRightInverse_544 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsRightInverse_390
d_isRightInverse_544 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_IsRightInverse_390
du_isRightInverse_544 T_IsInverse_468
v10
du_isRightInverse_544 :: T_IsInverse_468 -> T_IsRightInverse_390
du_isRightInverse_544 :: T_IsInverse_468 -> T_IsRightInverse_390
du_isRightInverse_544 T_IsInverse_468
v0
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsRightInverse_390)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_390
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
C_IsRightInverse'46'constructor_16843
      ((T_IsLeftInverse_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
d_isCongruent_324 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0)))
      ((T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_326 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0)))
      ((T_IsInverse_468 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> AgdaAny -> AgdaAny
d_inverse'691'_480 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0))
-- Function.Structures.IsInverse.inverse
d_inverse_546 ::
  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_468 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_546 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Σ_14
d_inverse_546 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_468
v10
  = T_IsInverse_468 -> T_Σ_14
du_inverse_546 T_IsInverse_468
v10
du_inverse_546 ::
  T_IsInverse_468 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_546 :: T_IsInverse_468 -> T_Σ_14
du_inverse_546 T_IsInverse_468
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_312 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> AgdaAny -> AgdaAny
d_inverse'737'_328 ((T_IsInverse_468 -> T_IsLeftInverse_312) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> T_IsLeftInverse_312
d_isLeftInverse_478 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0)))
      ((T_IsInverse_468 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468 -> AgdaAny -> AgdaAny
d_inverse'691'_480 (T_IsInverse_468 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_468
v0))
-- Function.Structures.IsBiEquivalence
d_IsBiEquivalence_554 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBiEquivalence_554 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_554
  = C_IsBiEquivalence'46'constructor_24471 T_IsCongruent_22
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsBiEquivalence.f-isCongruent
d_f'45'isCongruent_568 :: T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 :: T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 T_IsBiEquivalence_554
v0
  = case T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
v0 of
      C_IsBiEquivalence'46'constructor_24471 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_554
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence.cong₂
d_cong'8322'_570 ::
  T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_570 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_570 T_IsBiEquivalence_554
v0
  = case T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
v0 of
      C_IsBiEquivalence'46'constructor_24471 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_554
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence.cong₃
d_cong'8323'_572 ::
  T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_572 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_572 T_IsBiEquivalence_554
v0
  = case T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
v0 of
      C_IsBiEquivalence'46'constructor_24471 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_554
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence._.cong
d_cong_576 ::
  T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_576 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_576 T_IsBiEquivalence_554
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_554 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554
v0))
-- Function.Structures.IsBiEquivalence._.isEquivalence₁
d_isEquivalence'8321'_578 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_578 :: T_IsBiEquivalence_554 -> T_IsEquivalence_26
d_isEquivalence'8321'_578 T_IsBiEquivalence_554
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_554 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554
v0))
-- Function.Structures.IsBiEquivalence._.isEquivalence₂
d_isEquivalence'8322'_580 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_580 :: T_IsBiEquivalence_554 -> T_IsEquivalence_26
d_isEquivalence'8322'_580 T_IsBiEquivalence_554
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_554 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554
v0))
-- Function.Structures.IsBiEquivalence._.Eq₁._≈_
d__'8776'__584 ::
  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_554 -> AgdaAny -> AgdaAny -> ()
d__'8776'__584 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__584 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁._≉_
d__'8777'__586 ::
  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_554 -> AgdaAny -> AgdaAny -> ()
d__'8777'__586 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__586 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁.Carrier
d_Carrier_588 ::
  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_554 -> ()
d_Carrier_588 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> ()
d_Carrier_588 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁.isEquivalence
d_isEquivalence_590 ::
  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_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_590 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_IsEquivalence_26
d_isEquivalence_590 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_IsEquivalence_26
du_isEquivalence_590 T_IsBiEquivalence_554
v11
du_isEquivalence_590 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_590 :: T_IsBiEquivalence_554 -> T_IsEquivalence_26
du_isEquivalence_590 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_592 ::
  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_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_592 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_592 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_592 T_IsBiEquivalence_554
v11
du_isPartialEquivalence_592 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_592 :: T_IsBiEquivalence_554 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_592 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_594 ::
  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_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_594 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_PartialSetoid_10
d_partialSetoid_594 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_PartialSetoid_10
du_partialSetoid_594 T_IsBiEquivalence_554
v11
du_partialSetoid_594 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_594 :: T_IsBiEquivalence_554 -> T_PartialSetoid_10
du_partialSetoid_594 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_74
         ((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_596 ::
  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_554 -> AgdaAny -> AgdaAny
d_refl_596 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
d_refl_596 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny
du_refl_596 T_IsBiEquivalence_554
v11
du_refl_596 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny
du_refl_596 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny
du_refl_596 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_598 ::
  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_554 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_598 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_598 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_598 T_IsBiEquivalence_554
v11
du_reflexive_598 ::
  T_IsBiEquivalence_554 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_598 :: T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_598 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_600 ::
  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_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_600 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_Setoid_44
d_setoid_600 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_Setoid_44
du_setoid_600 T_IsBiEquivalence_554
v11
du_setoid_600 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_600 :: T_IsBiEquivalence_554 -> T_Setoid_44
du_setoid_600 T_IsBiEquivalence_554
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_554 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554
v0))
-- Function.Structures.IsBiEquivalence._.Eq₁.sym
d_sym_602 ::
  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_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_602 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_602 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_602 T_IsBiEquivalence_554
v11
du_sym_602 ::
  T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_602 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_602 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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.trans
d_trans_604 ::
  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_554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_604 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_604 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_604 T_IsBiEquivalence_554
v11
du_trans_604 ::
  T_IsBiEquivalence_554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_604 :: T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_604 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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._.Eq₂._≈_
d__'8776'__608 ::
  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_554 -> AgdaAny -> AgdaAny -> ()
d__'8776'__608 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__608 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂._≉_
d__'8777'__610 ::
  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_554 -> AgdaAny -> AgdaAny -> ()
d__'8777'__610 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__610 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂.Carrier
d_Carrier_612 ::
  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_554 -> ()
d_Carrier_612 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> ()
d_Carrier_612 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂.isEquivalence
d_isEquivalence_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_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_614 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_IsEquivalence_26
d_isEquivalence_614 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_IsEquivalence_26
du_isEquivalence_614 T_IsBiEquivalence_554
v11
du_isEquivalence_614 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_614 :: T_IsBiEquivalence_554 -> T_IsEquivalence_26
du_isEquivalence_614 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_616 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_616 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_616 T_IsBiEquivalence_554
v11
du_isPartialEquivalence_616 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_616 :: T_IsBiEquivalence_554 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_616 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_618 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_PartialSetoid_10
d_partialSetoid_618 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_PartialSetoid_10
du_partialSetoid_618 T_IsBiEquivalence_554
v11
du_partialSetoid_618 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_618 :: T_IsBiEquivalence_554 -> T_PartialSetoid_10
du_partialSetoid_618 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_74
         ((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_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_554 -> AgdaAny -> AgdaAny
d_refl_620 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
d_refl_620 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny
du_refl_620 T_IsBiEquivalence_554
v11
du_refl_620 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny
du_refl_620 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny
du_refl_620 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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_554 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_622 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_622 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_622 T_IsBiEquivalence_554
v11
du_reflexive_622 ::
  T_IsBiEquivalence_554 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_622 :: T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_622 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_624 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> T_Setoid_44
d_setoid_624 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> T_Setoid_44
du_setoid_624 T_IsBiEquivalence_554
v11
du_setoid_624 ::
  T_IsBiEquivalence_554 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_624 :: T_IsBiEquivalence_554 -> T_Setoid_44
du_setoid_624 T_IsBiEquivalence_554
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_554 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_554
v0))
-- Function.Structures.IsBiEquivalence._.Eq₂.sym
d_sym_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_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_626 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_626 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_626 T_IsBiEquivalence_554
v11
du_sym_626 ::
  T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_626 :: T_IsBiEquivalence_554 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_626 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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.trans
d_trans_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_554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_628 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_554
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_628 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_554
v11
  = T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_628 T_IsBiEquivalence_554
v11
du_trans_628 ::
  T_IsBiEquivalence_554 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_628 :: T_IsBiEquivalence_554
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_628 T_IsBiEquivalence_554
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_554 -> T_IsCongruent_22
d_f'45'isCongruent_568 (T_IsBiEquivalence_554 -> T_IsBiEquivalence_554
forall a b. a -> b
coe T_IsBiEquivalence_554
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_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
d_IsBiInverse_636 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBiInverse_636 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_636
  = C_IsBiInverse'46'constructor_29527 T_IsCongruent_22
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny)
-- Function.Structures.IsBiInverse.f-isCongruent
d_f'45'isCongruent_654 :: T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 :: T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 T_IsBiInverse_636
v0
  = case T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
v0 of
      C_IsBiInverse'46'constructor_29527 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsBiInverse_636
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.cong₂
d_cong'8322'_656 ::
  T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_656 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_656 T_IsBiInverse_636
v0
  = case T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
v0 of
      C_IsBiInverse'46'constructor_29527 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsBiInverse_636
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.inverseˡ
d_inverse'737'_658 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
d_inverse'737'_658 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
d_inverse'737'_658 T_IsBiInverse_636
v0
  = case T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
v0 of
      C_IsBiInverse'46'constructor_29527 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_IsBiInverse_636
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.cong₃
d_cong'8323'_660 ::
  T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_660 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_660 T_IsBiInverse_636
v0
  = case T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
v0 of
      C_IsBiInverse'46'constructor_29527 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsBiInverse_636
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.inverseʳ
d_inverse'691'_662 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
d_inverse'691'_662 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
d_inverse'691'_662 T_IsBiInverse_636
v0
  = case T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
v0 of
      C_IsBiInverse'46'constructor_29527 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_IsBiInverse_636
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse._.cong
d_cong_666 ::
  T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_666 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_666 T_IsBiInverse_636
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_636 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636
v0))
-- Function.Structures.IsBiInverse._.isEquivalence₁
d_isEquivalence'8321'_668 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8321'_668 :: T_IsBiInverse_636 -> T_IsEquivalence_26
d_isEquivalence'8321'_668 T_IsBiInverse_636
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_636 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636
v0))
-- Function.Structures.IsBiInverse._.isEquivalence₂
d_isEquivalence'8322'_670 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence'8322'_670 :: T_IsBiInverse_636 -> T_IsEquivalence_26
d_isEquivalence'8322'_670 T_IsBiInverse_636
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_636 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636
v0))
-- Function.Structures.IsBiInverse._.Eq₁._≈_
d__'8776'__674 ::
  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_636 -> AgdaAny -> AgdaAny -> ()
d__'8776'__674 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__674 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁._≉_
d__'8777'__676 ::
  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_636 -> AgdaAny -> AgdaAny -> ()
d__'8777'__676 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__676 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁.Carrier
d_Carrier_678 ::
  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_636 -> ()
d_Carrier_678 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> ()
d_Carrier_678 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁.isEquivalence
d_isEquivalence_680 ::
  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_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_680 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_IsEquivalence_26
d_isEquivalence_680 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_IsEquivalence_26
du_isEquivalence_680 T_IsBiInverse_636
v11
du_isEquivalence_680 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_680 :: T_IsBiInverse_636 -> T_IsEquivalence_26
du_isEquivalence_680 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_682 ::
  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_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_682 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_682 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_682 T_IsBiInverse_636
v11
du_isPartialEquivalence_682 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_682 :: T_IsBiInverse_636 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_682 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_684 ::
  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_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_684 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_PartialSetoid_10
d_partialSetoid_684 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_PartialSetoid_10
du_partialSetoid_684 T_IsBiInverse_636
v11
du_partialSetoid_684 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_684 :: T_IsBiInverse_636 -> T_PartialSetoid_10
du_partialSetoid_684 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_74
         ((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_686 ::
  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_636 -> AgdaAny -> AgdaAny
d_refl_686 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
d_refl_686 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> AgdaAny -> AgdaAny
du_refl_686 T_IsBiInverse_636
v11
du_refl_686 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
du_refl_686 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
du_refl_686 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_688 ::
  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_636 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_688 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_688 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_688 T_IsBiInverse_636
v11
du_reflexive_688 ::
  T_IsBiInverse_636 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_688 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_688 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_690 ::
  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_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_690 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_Setoid_44
d_setoid_690 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_Setoid_44
du_setoid_690 T_IsBiInverse_636
v11
du_setoid_690 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_690 :: T_IsBiInverse_636 -> T_Setoid_44
du_setoid_690 T_IsBiInverse_636
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_636 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636
v0))
-- Function.Structures.IsBiInverse._.Eq₁.sym
d_sym_692 ::
  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_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_692 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_692 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_692 T_IsBiInverse_636
v11
du_sym_692 ::
  T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_692 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_692 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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.trans
d_trans_694 ::
  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_636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_694 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_694 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_694 T_IsBiInverse_636
v11
du_trans_694 ::
  T_IsBiInverse_636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_694 :: T_IsBiInverse_636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_694 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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._.Eq₂._≈_
d__'8776'__698 ::
  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_636 -> AgdaAny -> AgdaAny -> ()
d__'8776'__698 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__698 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂._≉_
d__'8777'__700 ::
  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_636 -> AgdaAny -> AgdaAny -> ()
d__'8777'__700 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__700 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂.Carrier
d_Carrier_702 ::
  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_636 -> ()
d_Carrier_702 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> ()
d_Carrier_702 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂.isEquivalence
d_isEquivalence_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_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_704 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_IsEquivalence_26
d_isEquivalence_704 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_IsEquivalence_26
du_isEquivalence_704 T_IsBiInverse_636
v11
du_isEquivalence_704 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_704 :: T_IsBiInverse_636 -> T_IsEquivalence_26
du_isEquivalence_704 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_706 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_706 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_706 T_IsBiInverse_636
v11
du_isPartialEquivalence_706 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_706 :: T_IsBiInverse_636 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_706 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_708 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_PartialSetoid_10
d_partialSetoid_708 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_PartialSetoid_10
du_partialSetoid_708 T_IsBiInverse_636
v11
du_partialSetoid_708 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_708 :: T_IsBiInverse_636 -> T_PartialSetoid_10
du_partialSetoid_708 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_74
         ((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_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_636 -> AgdaAny -> AgdaAny
d_refl_710 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
d_refl_710 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> AgdaAny -> AgdaAny
du_refl_710 T_IsBiInverse_636
v11
du_refl_710 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
du_refl_710 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny
du_refl_710 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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_636 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_712 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_712 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_712 T_IsBiInverse_636
v11
du_reflexive_712 ::
  T_IsBiInverse_636 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_712 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_712 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_714 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> T_Setoid_44
d_setoid_714 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> T_Setoid_44
du_setoid_714 T_IsBiInverse_636
v11
du_setoid_714 ::
  T_IsBiInverse_636 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_714 :: T_IsBiInverse_636 -> T_Setoid_44
du_setoid_714 T_IsBiInverse_636
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_636 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_636
v0))
-- Function.Structures.IsBiInverse._.Eq₂.sym
d_sym_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_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_716 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_716 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_716 T_IsBiInverse_636
v11
du_sym_716 ::
  T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_716 :: T_IsBiInverse_636 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_716 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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.trans
d_trans_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_636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_718 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_718 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_636
v11
  = T_IsBiInverse_636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_718 T_IsBiInverse_636
v11
du_trans_718 ::
  T_IsBiInverse_636 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_718 :: T_IsBiInverse_636
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_718 T_IsBiInverse_636
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_636 -> T_IsCongruent_22
d_f'45'isCongruent_654 (T_IsBiInverse_636 -> T_IsBiInverse_636
forall a b. a -> b
coe T_IsBiInverse_636
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_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)))