{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}

{-# OPTIONS_GHC -Wno-overlapping-patterns #-}

module MAlonzo.Code.Function.Structures where

import MAlonzo.RTE (coe, erased, AgdaAny, addInt, subInt, mulInt,
                    quotInt, remInt, geqInt, ltInt, eqInt, add64, sub64, mul64, quot64,
                    rem64, lt64, eq64, word64FromNat, word64ToNat)
import qualified MAlonzo.RTE
import qualified Data.Text
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Data.Product.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Bundles.Raw
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_constructor_94 (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                     MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
                     MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
-- 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_constructor_94 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 T_IsEquivalence_28
v2 T_IsEquivalence_28
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_28
d_isEquivalence'8321'_34 :: T_IsCongruent_22 -> T_IsEquivalence_28
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_constructor_94 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 T_IsEquivalence_28
v2 T_IsEquivalence_28
v3 -> T_IsEquivalence_28 -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsEquivalence_28
v2
      T_IsCongruent_22
_ -> T_IsEquivalence_28
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsCongruent.isEquivalence₂
d_isEquivalence'8322'_36 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_36 :: T_IsCongruent_22 -> T_IsEquivalence_28
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_constructor_94 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v1 T_IsEquivalence_28
v2 T_IsEquivalence_28
v3 -> T_IsEquivalence_28 -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsEquivalence_28
v3
      T_IsCongruent_22
_ -> T_IsEquivalence_28
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_46
d_setoid_40 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_46
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_46
du_setoid_40 T_IsCongruent_22
v9
du_setoid_40 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_40 :: T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 T_IsCongruent_22
v0
  = (T_IsEquivalence_28 -> T_Setoid_46)
-> T_IsEquivalence_28 -> T_Setoid_46
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_Setoid_46
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_84
      (T_IsCongruent_22 -> T_IsEquivalence_28
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_28
d_isEquivalence_50 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_28
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_28
du_isEquivalence_50 T_IsCongruent_22
v9
du_isEquivalence_50 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_50 :: T_IsCongruent_22 -> T_IsEquivalence_28
du_isEquivalence_50 T_IsCongruent_22
v0 = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
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_46 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₁._.rawSetoid
d_rawSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_56 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
d_rawSetoid_56 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₁._.refl
d_refl_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
d_refl_58 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_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
du_refl_58 T_IsCongruent_22
v9
du_refl_58 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_58 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_58 T_IsCongruent_22
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_60 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_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 -> T__'8801'__12 -> AgdaAny
du_reflexive_60 T_IsCongruent_22
v9
du_reflexive_60 ::
  T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_60 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_60 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
           AgdaAny
v2)
-- Function.Structures.IsCongruent.Eq₁._.sym
d_sym_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
d_sym_62 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_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
du_sym_62 T_IsCongruent_22
v9
du_sym_62 ::
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_62 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_62 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Structures.IsCongruent.Eq₁._.trans
d_trans_64 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_64 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_64 ~()
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_64 T_IsCongruent_22
v9
du_trans_64 ::
  T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_64 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_64 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Structures.IsCongruent.Eq₂.setoid
d_setoid_68 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_46
d_setoid_68 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_46
d_setoid_68 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 T_IsCongruent_22
v9
du_setoid_68 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_68 :: T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 T_IsCongruent_22
v0
  = (T_IsEquivalence_28 -> T_Setoid_46)
-> T_IsEquivalence_28 -> T_Setoid_46
forall a b. a -> b
coe
      T_IsEquivalence_28 -> T_Setoid_46
MAlonzo.Code.Relation.Binary.Bundles.C_constructor_84
      (T_IsCongruent_22 -> T_IsEquivalence_28
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'__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__'8776'__72 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__72 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₂._._≉_
d__'8777'__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 -> AgdaAny -> AgdaAny -> ()
d__'8777'__74 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__74 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₂._.Carrier
d_Carrier_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 -> ()
d_Carrier_76 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> ()
d_Carrier_76 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> ()
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₂._.isEquivalence
d_isEquivalence_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_IsEquivalence_28
d_isEquivalence_78 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_28
d_isEquivalence_78 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsCongruent_22
v9
  = T_IsCongruent_22 -> T_IsEquivalence_28
du_isEquivalence_78 T_IsCongruent_22
v9
du_isEquivalence_78 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_78 :: T_IsCongruent_22 -> T_IsEquivalence_28
du_isEquivalence_78 T_IsCongruent_22
v0 = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_80 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_80 ~()
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_80 T_IsCongruent_22
v9
du_isPartialEquivalence_80 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_80 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_80 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Structures.IsCongruent.Eq₂._.partialSetoid
d_partialSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_82 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_82 ~()
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_82 T_IsCongruent_22
v9
du_partialSetoid_82 ::
  T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_82 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_82 T_IsCongruent_22
v0
  = (T_Setoid_46 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
      ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Structures.IsCongruent.Eq₂._.rawSetoid
d_rawSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_84 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
d_rawSetoid_84 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsCongruent.Eq₂._.refl
d_refl_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
d_refl_86 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_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
du_refl_86 T_IsCongruent_22
v9
du_refl_86 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_86 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_86 T_IsCongruent_22
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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 ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_88 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_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 -> T__'8801'__12 -> AgdaAny
du_reflexive_88 T_IsCongruent_22
v9
du_reflexive_88 ::
  T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_88 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_88 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
           AgdaAny
v2)
-- Function.Structures.IsCongruent.Eq₂._.sym
d_sym_90 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_90 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_90 ~()
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_90 T_IsCongruent_22
v9
du_sym_90 ::
  T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_90 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_90 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Structures.IsCongruent.Eq₂._.trans
d_trans_92 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_92 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_92 ~()
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_92 T_IsCongruent_22
v9
du_trans_92 ::
  T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_92 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_92 T_IsCongruent_22
v0
  = let v1 :: AgdaAny
v1 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Function.Structures.IsInjection
d_IsInjection_98 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsInjection_98 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsInjection_98
  = C_constructor_170 T_IsCongruent_22
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsInjection.isCongruent
d_isCongruent_106 :: T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 :: T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 T_IsInjection_98
v0
  = case T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0 of
      C_constructor_170 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_98
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInjection.injective
d_injective_108 ::
  T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_108 :: T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_108 T_IsInjection_98
v0
  = case T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0 of
      C_constructor_170 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_98
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInjection._.cong
d_cong_112 ::
  T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_112 :: T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_112 T_IsInjection_98
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_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v0))
-- Function.Structures.IsInjection._.isEquivalence₁
d_isEquivalence'8321'_114 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_114 :: T_IsInjection_98 -> T_IsEquivalence_28
d_isEquivalence'8321'_114 T_IsInjection_98
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v0))
-- Function.Structures.IsInjection._.isEquivalence₂
d_isEquivalence'8322'_116 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_116 :: T_IsInjection_98 -> T_IsEquivalence_28
d_isEquivalence'8322'_116 T_IsInjection_98
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v0))
-- Function.Structures.IsInjection._.Eq₁._≈_
d__'8776'__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_98 -> AgdaAny -> AgdaAny -> ()
d__'8776'__120 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__120 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₁._≉_
d__'8777'__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_98 -> AgdaAny -> AgdaAny -> ()
d__'8777'__122 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__122 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₁.Carrier
d_Carrier_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_98 -> ()
d_Carrier_124 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> ()
d_Carrier_124 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₁.isEquivalence
d_isEquivalence_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_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_126 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_IsEquivalence_28
d_isEquivalence_126 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_IsEquivalence_28
du_isEquivalence_126 T_IsInjection_98
v9
du_isEquivalence_126 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_126 :: T_IsInjection_98 -> T_IsEquivalence_28
du_isEquivalence_126 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_128 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_128 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_128 T_IsInjection_98
v9
du_isPartialEquivalence_128 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_128 :: T_IsInjection_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_128 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsInjection._.Eq₁.partialSetoid
d_partialSetoid_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_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_130 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_PartialSetoid_10
d_partialSetoid_130 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_PartialSetoid_10
du_partialSetoid_130 T_IsInjection_98
v9
du_partialSetoid_130 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_130 :: T_IsInjection_98 -> T_PartialSetoid_10
du_partialSetoid_130 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsInjection._.Eq₁.rawSetoid
d_rawSetoid_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_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_132 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_RawSetoid_12
d_rawSetoid_132 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₁.refl
d_refl_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_98 -> AgdaAny -> AgdaAny
d_refl_134 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
d_refl_134 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9 = T_IsInjection_98 -> AgdaAny -> AgdaAny
du_refl_134 T_IsInjection_98
v9
du_refl_134 :: T_IsInjection_98 -> AgdaAny -> AgdaAny
du_refl_134 :: T_IsInjection_98 -> AgdaAny -> AgdaAny
du_refl_134 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_98 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_136 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_136 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_136 T_IsInjection_98
v9
du_reflexive_136 ::
  T_IsInjection_98 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_136 :: T_IsInjection_98 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_136 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsInjection._.Eq₁.setoid
d_setoid_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_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_138 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_Setoid_46
d_setoid_138 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_Setoid_46
du_setoid_138 T_IsInjection_98
v9
du_setoid_138 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_138 :: T_IsInjection_98 -> T_Setoid_46
du_setoid_138 T_IsInjection_98
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v0))
-- Function.Structures.IsInjection._.Eq₁.sym
d_sym_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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_140 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_140 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9 = T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_140 T_IsInjection_98
v9
du_sym_140 ::
  T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_140 :: T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_140 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsInjection._.Eq₁.trans
d_trans_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_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_142 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_142 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_142 T_IsInjection_98
v9
du_trans_142 ::
  T_IsInjection_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_142 :: T_IsInjection_98
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_142 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsInjection._.Eq₂._≈_
d__'8776'__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_98 -> AgdaAny -> AgdaAny -> ()
d__'8776'__146 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__146 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₂._≉_
d__'8777'__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_98 -> AgdaAny -> AgdaAny -> ()
d__'8777'__148 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__148 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₂.Carrier
d_Carrier_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_98 -> ()
d_Carrier_150 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> ()
d_Carrier_150 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> ()
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₂.isEquivalence
d_isEquivalence_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_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_152 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_IsEquivalence_28
d_isEquivalence_152 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_IsEquivalence_28
du_isEquivalence_152 T_IsInjection_98
v9
du_isEquivalence_152 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_152 :: T_IsInjection_98 -> T_IsEquivalence_28
du_isEquivalence_152 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_154 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_154 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_154 T_IsInjection_98
v9
du_isPartialEquivalence_154 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_154 :: T_IsInjection_98 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_154 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsInjection._.Eq₂.partialSetoid
d_partialSetoid_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_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_156 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_PartialSetoid_10
d_partialSetoid_156 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_PartialSetoid_10
du_partialSetoid_156 T_IsInjection_98
v9
du_partialSetoid_156 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_156 :: T_IsInjection_98 -> T_PartialSetoid_10
du_partialSetoid_156 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsInjection._.Eq₂.rawSetoid
d_rawSetoid_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_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_158 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_RawSetoid_12
d_rawSetoid_158 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsInjection._.Eq₂.refl
d_refl_160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_98 -> AgdaAny -> AgdaAny
d_refl_160 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
d_refl_160 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9 = T_IsInjection_98 -> AgdaAny -> AgdaAny
du_refl_160 T_IsInjection_98
v9
du_refl_160 :: T_IsInjection_98 -> AgdaAny -> AgdaAny
du_refl_160 :: T_IsInjection_98 -> AgdaAny -> AgdaAny
du_refl_160 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_98 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_162 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_162 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_162 T_IsInjection_98
v9
du_reflexive_162 ::
  T_IsInjection_98 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_162 :: T_IsInjection_98 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_162 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsInjection._.Eq₂.setoid
d_setoid_164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_164 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> T_Setoid_46
d_setoid_164 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98 -> T_Setoid_46
du_setoid_164 T_IsInjection_98
v9
du_setoid_164 ::
  T_IsInjection_98 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_164 :: T_IsInjection_98 -> T_Setoid_46
du_setoid_164 T_IsInjection_98
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v0))
-- Function.Structures.IsInjection._.Eq₂.sym
d_sym_166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_166 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_166 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9 = T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_166 T_IsInjection_98
v9
du_sym_166 ::
  T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_166 :: T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_166 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsInjection._.Eq₂.trans
d_trans_168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_168 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsInjection_98
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_168 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsInjection_98
v9
  = T_IsInjection_98
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_168 T_IsInjection_98
v9
du_trans_168 ::
  T_IsInjection_98 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_168 :: T_IsInjection_98
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_168 T_IsInjection_98
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSurjection
d_IsSurjection_174 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsSurjection_174 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsSurjection_174
  = C_constructor_252 T_IsCongruent_22
                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Structures.IsSurjection.isCongruent
d_isCongruent_182 :: T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 :: T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 T_IsSurjection_174
v0
  = case T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0 of
      C_constructor_252 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_174
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSurjection.surjective
d_surjective_184 ::
  T_IsSurjection_174 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_184 :: T_IsSurjection_174 -> AgdaAny -> T_Σ_14
d_surjective_184 T_IsSurjection_174
v0
  = case T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0 of
      C_constructor_252 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_174
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSurjection._.cong
d_cong_188 ::
  T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_188 :: T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_188 T_IsSurjection_174
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_174 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0))
-- Function.Structures.IsSurjection._.isEquivalence₁
d_isEquivalence'8321'_190 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_190 :: T_IsSurjection_174 -> T_IsEquivalence_28
d_isEquivalence'8321'_190 T_IsSurjection_174
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsSurjection_174 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0))
-- Function.Structures.IsSurjection._.isEquivalence₂
d_isEquivalence'8322'_192 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_192 :: T_IsSurjection_174 -> T_IsEquivalence_28
d_isEquivalence'8322'_192 T_IsSurjection_174
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 ((T_IsSurjection_174 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0))
-- Function.Structures.IsSurjection._.Eq₁._≈_
d__'8776'__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_174 -> AgdaAny -> AgdaAny -> ()
d__'8776'__196 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__196 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₁._≉_
d__'8777'__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_174 -> AgdaAny -> AgdaAny -> ()
d__'8777'__198 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__198 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₁.Carrier
d_Carrier_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_174 -> ()
d_Carrier_200 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> ()
d_Carrier_200 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₁.isEquivalence
d_isEquivalence_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_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_202 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_IsEquivalence_28
d_isEquivalence_202 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_IsEquivalence_28
du_isEquivalence_202 T_IsSurjection_174
v9
du_isEquivalence_202 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_202 :: T_IsSurjection_174 -> T_IsEquivalence_28
du_isEquivalence_202 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_204 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_204 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_204 T_IsSurjection_174
v9
du_isPartialEquivalence_204 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_204 :: T_IsSurjection_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_204 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSurjection._.Eq₁.partialSetoid
d_partialSetoid_206 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_206 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_PartialSetoid_10
d_partialSetoid_206 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_PartialSetoid_10
du_partialSetoid_206 T_IsSurjection_174
v9
du_partialSetoid_206 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_206 :: T_IsSurjection_174 -> T_PartialSetoid_10
du_partialSetoid_206 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsSurjection._.Eq₁.rawSetoid
d_rawSetoid_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_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_208 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_RawSetoid_12
d_rawSetoid_208 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₁.refl
d_refl_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_174 -> AgdaAny -> AgdaAny
d_refl_210 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
d_refl_210 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9 = T_IsSurjection_174 -> AgdaAny -> AgdaAny
du_refl_210 T_IsSurjection_174
v9
du_refl_210 :: T_IsSurjection_174 -> AgdaAny -> AgdaAny
du_refl_210 :: T_IsSurjection_174 -> AgdaAny -> AgdaAny
du_refl_210 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_212 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_212 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_212 T_IsSurjection_174
v9
du_reflexive_212 ::
  T_IsSurjection_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_212 :: T_IsSurjection_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_212 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsSurjection._.Eq₁.setoid
d_setoid_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_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_214 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_Setoid_46
d_setoid_214 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_Setoid_46
du_setoid_214 T_IsSurjection_174
v9
du_setoid_214 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_214 :: T_IsSurjection_174 -> T_Setoid_46
du_setoid_214 T_IsSurjection_174
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsSurjection_174 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0))
-- Function.Structures.IsSurjection._.Eq₁.sym
d_sym_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_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_216 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_216 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9 = T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_216 T_IsSurjection_174
v9
du_sym_216 ::
  T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_216 :: T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_216 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSurjection._.Eq₁.trans
d_trans_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_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_218 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_218 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_218 T_IsSurjection_174
v9
du_trans_218 ::
  T_IsSurjection_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_218 :: T_IsSurjection_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_218 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSurjection._.Eq₂._≈_
d__'8776'__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_174 -> AgdaAny -> AgdaAny -> ()
d__'8776'__222 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__222 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₂._≉_
d__'8777'__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_174 -> AgdaAny -> AgdaAny -> ()
d__'8777'__224 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__224 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₂.Carrier
d_Carrier_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_174 -> ()
d_Carrier_226 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> ()
d_Carrier_226 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> ()
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₂.isEquivalence
d_isEquivalence_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_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_228 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_IsEquivalence_28
d_isEquivalence_228 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_IsEquivalence_28
du_isEquivalence_228 T_IsSurjection_174
v9
du_isEquivalence_228 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_228 :: T_IsSurjection_174 -> T_IsEquivalence_28
du_isEquivalence_228 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_230 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_230 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_IsSurjection_174
v9
du_isPartialEquivalence_230 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_230 :: T_IsSurjection_174 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSurjection._.Eq₂.partialSetoid
d_partialSetoid_232 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_232 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_PartialSetoid_10
d_partialSetoid_232 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_PartialSetoid_10
du_partialSetoid_232 T_IsSurjection_174
v9
du_partialSetoid_232 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_232 :: T_IsSurjection_174 -> T_PartialSetoid_10
du_partialSetoid_232 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsSurjection._.Eq₂.rawSetoid
d_rawSetoid_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_234 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_RawSetoid_12
d_rawSetoid_234 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsSurjection._.Eq₂.refl
d_refl_236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 -> AgdaAny -> AgdaAny
d_refl_236 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
d_refl_236 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9 = T_IsSurjection_174 -> AgdaAny -> AgdaAny
du_refl_236 T_IsSurjection_174
v9
du_refl_236 :: T_IsSurjection_174 -> AgdaAny -> AgdaAny
du_refl_236 :: T_IsSurjection_174 -> AgdaAny -> AgdaAny
du_refl_236 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_238 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_238 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_238 T_IsSurjection_174
v9
du_reflexive_238 ::
  T_IsSurjection_174 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_238 :: T_IsSurjection_174
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_238 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsSurjection._.Eq₂.setoid
d_setoid_240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_240 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> T_Setoid_46
d_setoid_240 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174 -> T_Setoid_46
du_setoid_240 T_IsSurjection_174
v9
du_setoid_240 ::
  T_IsSurjection_174 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_240 :: T_IsSurjection_174 -> T_Setoid_46
du_setoid_240 T_IsSurjection_174
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsSurjection_174 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0))
-- Function.Structures.IsSurjection._.Eq₂.sym
d_sym_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_242 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_242 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9 = T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_242 T_IsSurjection_174
v9
du_sym_242 ::
  T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_242 :: T_IsSurjection_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_242 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSurjection._.Eq₂.trans
d_trans_244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_244 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_244 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9
  = T_IsSurjection_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_244 T_IsSurjection_174
v9
du_trans_244 ::
  T_IsSurjection_174 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_244 :: T_IsSurjection_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_244 T_IsSurjection_174
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> T_IsSurjection_174
forall a b. a -> b
coe T_IsSurjection_174
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSurjection.strictlySurjective
d_strictlySurjective_246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_174 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_246 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSurjection_174
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_246 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSurjection_174
v9 AgdaAny
v10
  = T_IsSurjection_174 -> AgdaAny -> T_Σ_14
du_strictlySurjective_246 T_IsSurjection_174
v9 AgdaAny
v10
du_strictlySurjective_246 ::
  T_IsSurjection_174 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_246 :: T_IsSurjection_174 -> AgdaAny -> T_Σ_14
du_strictlySurjective_246 T_IsSurjection_174
v0 AgdaAny
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Σ_14)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Σ_14
MAlonzo.Code.Data.Product.Base.du_map'8322'_150
      (\ AgdaAny
v2 AgdaAny
v3 ->
         AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           AgdaAny
v3 AgdaAny
v2
           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsSurjection_174 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsSurjection_174 -> T_IsCongruent_22
d_isCongruent_182 (T_IsSurjection_174 -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174
v0))) AgdaAny
v2))
      ((T_IsSurjection_174 -> AgdaAny -> T_Σ_14)
-> T_IsSurjection_174 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSurjection_174 -> AgdaAny -> T_Σ_14
d_surjective_184 T_IsSurjection_174
v0 AgdaAny
v1)
-- Function.Structures.IsBijection
d_IsBijection_256 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBijection_256 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsBijection_256
  = C_constructor_340 T_IsInjection_98
                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Structures.IsBijection.isInjection
d_isInjection_264 :: T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 :: T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 T_IsBijection_256
v0
  = case T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0 of
      C_constructor_340 T_IsInjection_98
v1 AgdaAny -> T_Σ_14
v2 -> T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1
      T_IsBijection_256
_ -> T_IsInjection_98
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBijection.surjective
d_surjective_266 ::
  T_IsBijection_256 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_266 :: T_IsBijection_256 -> AgdaAny -> T_Σ_14
d_surjective_266 T_IsBijection_256
v0
  = case T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0 of
      C_constructor_340 T_IsInjection_98
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_256
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBijection._.cong
d_cong_270 ::
  T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_270 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_270 T_IsBijection_256
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_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 ((T_IsBijection_256 -> T_IsInjection_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0)))
-- Function.Structures.IsBijection._.injective
d_injective_272 ::
  T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_272 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_272 T_IsBijection_256
v0
  = (T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_108 ((T_IsBijection_256 -> T_IsInjection_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0))
-- Function.Structures.IsBijection._.isCongruent
d_isCongruent_274 :: T_IsBijection_256 -> T_IsCongruent_22
d_isCongruent_274 :: T_IsBijection_256 -> T_IsCongruent_22
d_isCongruent_274 T_IsBijection_256
v0
  = (T_IsInjection_98 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 ((T_IsBijection_256 -> T_IsInjection_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0))
-- Function.Structures.IsBijection._.isEquivalence₁
d_isEquivalence'8321'_276 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_276 :: T_IsBijection_256 -> T_IsEquivalence_28
d_isEquivalence'8321'_276 T_IsBijection_256
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34
      ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 ((T_IsBijection_256 -> T_IsInjection_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0)))
-- Function.Structures.IsBijection._.isEquivalence₂
d_isEquivalence'8322'_278 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_278 :: T_IsBijection_256 -> T_IsEquivalence_28
d_isEquivalence'8322'_278 T_IsBijection_256
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36
      ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 ((T_IsBijection_256 -> T_IsInjection_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0)))
-- Function.Structures.IsBijection._.Eq₁._≈_
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_256 -> AgdaAny -> AgdaAny -> ()
d__'8776'__282 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__282 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁._≉_
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_256 -> AgdaAny -> AgdaAny -> ()
d__'8777'__284 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__284 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁.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_256 -> ()
d_Carrier_286 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> ()
d_Carrier_286 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁.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_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_288 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsEquivalence_28
d_isEquivalence_288 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_288 T_IsBijection_256
v9
du_isEquivalence_288 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_288 :: T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_288 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_290 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_290 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsBijection_256
v9
du_isPartialEquivalence_290 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_290 :: T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsBijection._.Eq₁.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_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_292 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_PartialSetoid_10
d_partialSetoid_292 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_292 T_IsBijection_256
v9
du_partialSetoid_292 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_292 :: T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_292 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsBijection._.Eq₁.rawSetoid
d_rawSetoid_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_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_294 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
d_rawSetoid_294 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₁.refl
d_refl_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_256 -> AgdaAny -> AgdaAny
d_refl_296 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
d_refl_296 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9 = T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_296 T_IsBijection_256
v9
du_refl_296 :: T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_296 :: T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_296 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_298 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_298 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_298 T_IsBijection_256
v9
du_reflexive_298 ::
  T_IsBijection_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_298 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_298 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsBijection._.Eq₁.setoid
d_setoid_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_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_300 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Setoid_46
d_setoid_300 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_Setoid_46
du_setoid_300 T_IsBijection_256
v9
du_setoid_300 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_300 :: T_IsBijection_256 -> T_Setoid_46
du_setoid_300 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v1)))
-- Function.Structures.IsBijection._.Eq₁.sym
d_sym_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_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_302 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_302 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9 = T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_302 T_IsBijection_256
v9
du_sym_302 ::
  T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_302 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_302 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsBijection._.Eq₁.trans
d_trans_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_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_304 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_304 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_304 T_IsBijection_256
v9
du_trans_304 ::
  T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_304 :: T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_304 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsBijection._.Eq₂._≈_
d__'8776'__308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_256 -> AgdaAny -> AgdaAny -> ()
d__'8776'__308 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__308 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂._≉_
d__'8777'__310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_256 -> AgdaAny -> AgdaAny -> ()
d__'8777'__310 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__310 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂.Carrier
d_Carrier_312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsBijection_256 -> ()
d_Carrier_312 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> ()
d_Carrier_312 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> ()
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂.isEquivalence
d_isEquivalence_314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_314 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsEquivalence_28
d_isEquivalence_314 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_314 T_IsBijection_256
v9
du_isEquivalence_314 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_314 :: T_IsBijection_256 -> T_IsEquivalence_28
du_isEquivalence_314 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_316 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_316 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_316 T_IsBijection_256
v9
du_isPartialEquivalence_316 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_316 :: T_IsBijection_256 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_316 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsBijection._.Eq₂.partialSetoid
d_partialSetoid_318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_318 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_PartialSetoid_10
d_partialSetoid_318 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_318 T_IsBijection_256
v9
du_partialSetoid_318 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_318 :: T_IsBijection_256 -> T_PartialSetoid_10
du_partialSetoid_318 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsBijection._.Eq₂.rawSetoid
d_rawSetoid_320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_320 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
d_rawSetoid_320 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsBijection._.Eq₂.refl
d_refl_322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 -> AgdaAny -> AgdaAny
d_refl_322 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
d_refl_322 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9 = T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_322 T_IsBijection_256
v9
du_refl_322 :: T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_322 :: T_IsBijection_256 -> AgdaAny -> AgdaAny
du_refl_322 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_324 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_324 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_324 T_IsBijection_256
v9
du_reflexive_324 ::
  T_IsBijection_256 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_324 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_324 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsBijection._.Eq₂.setoid
d_setoid_326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_326 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Setoid_46
d_setoid_326 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_Setoid_46
du_setoid_326 T_IsBijection_256
v9
du_setoid_326 ::
  T_IsBijection_256 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_326 :: T_IsBijection_256 -> T_Setoid_46
du_setoid_326 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98
v1)))
-- Function.Structures.IsBijection._.Eq₂.sym
d_sym_328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_328 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_328 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9 = T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_328 T_IsBijection_256
v9
du_sym_328 ::
  T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_328 :: T_IsBijection_256 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_328 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsBijection._.Eq₂.trans
d_trans_330 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_330 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_330 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_330 T_IsBijection_256
v9
du_trans_330 ::
  T_IsBijection_256 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_330 :: T_IsBijection_256
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_330 T_IsBijection_256
v0
  = let v1 :: T_IsInjection_98
v1 = T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> T_IsBijection_256
forall a b. a -> b
coe T_IsBijection_256
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 (T_IsInjection_98 -> T_IsInjection_98
forall a b. a -> b
coe T_IsInjection_98
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsBijection.bijective
d_bijective_332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_bijective_332 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_Σ_14
d_bijective_332 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_Σ_14
du_bijective_332 T_IsBijection_256
v9
du_bijective_332 ::
  T_IsBijection_256 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_bijective_332 :: T_IsBijection_256 -> T_Σ_14
du_bijective_332 T_IsBijection_256
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_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_108 ((T_IsBijection_256 -> T_IsInjection_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0)))
      ((T_IsBijection_256 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> AgdaAny -> T_Σ_14
d_surjective_266 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0))
-- Function.Structures.IsBijection.isSurjection
d_isSurjection_334 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 -> T_IsSurjection_174
d_isSurjection_334 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> T_IsSurjection_174
d_isSurjection_334 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> T_IsSurjection_174
du_isSurjection_334 T_IsBijection_256
v9
du_isSurjection_334 :: T_IsBijection_256 -> T_IsSurjection_174
du_isSurjection_334 :: T_IsBijection_256 -> T_IsSurjection_174
du_isSurjection_334 T_IsBijection_256
v0
  = (T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_174
C_constructor_252
      ((T_IsInjection_98 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_98 -> T_IsCongruent_22
d_isCongruent_106 ((T_IsBijection_256 -> T_IsInjection_98) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsInjection_98
d_isInjection_264 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0)))
      ((T_IsBijection_256 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> AgdaAny -> T_Σ_14
d_surjective_266 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0))
-- Function.Structures.IsBijection._.strictlySurjective
d_strictlySurjective_338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_256 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_strictlySurjective_338 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_256
-> AgdaAny
-> T_Σ_14
d_strictlySurjective_338 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsBijection_256
v9
  = T_IsBijection_256 -> AgdaAny -> T_Σ_14
du_strictlySurjective_338 T_IsBijection_256
v9
du_strictlySurjective_338 ::
  T_IsBijection_256 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_strictlySurjective_338 :: T_IsBijection_256 -> AgdaAny -> T_Σ_14
du_strictlySurjective_338 T_IsBijection_256
v0
  = (T_IsSurjection_174 -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSurjection_174 -> AgdaAny -> T_Σ_14
du_strictlySurjective_246 ((T_IsBijection_256 -> T_IsSurjection_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256 -> T_IsSurjection_174
du_isSurjection_334 (T_IsBijection_256 -> AgdaAny
forall a b. a -> b
coe T_IsBijection_256
v0))
-- Function.Structures.IsLeftInverse
d_IsLeftInverse_346 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsLeftInverse_346 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsLeftInverse_346
  = C_constructor_432 T_IsCongruent_22
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsLeftInverse.isCongruent
d_isCongruent_358 :: T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 :: T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 T_IsLeftInverse_346
v0
  = case T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0 of
      C_constructor_432 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsLeftInverse_346
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse.from-cong
d_from'45'cong_360 ::
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_360 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_360 T_IsLeftInverse_346
v0
  = case T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0 of
      C_constructor_432 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsLeftInverse_346
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse.inverseˡ
d_inverse'737'_362 ::
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_362 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_362 T_IsLeftInverse_346
v0
  = case T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0 of
      C_constructor_432 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsLeftInverse_346
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsLeftInverse._.isEquivalence₁
d_isEquivalence'8321'_366 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_366 :: T_IsLeftInverse_346 -> T_IsEquivalence_28
d_isEquivalence'8321'_366 T_IsLeftInverse_346
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0))
-- Function.Structures.IsLeftInverse._.isEquivalence₂
d_isEquivalence'8322'_368 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_368 :: T_IsLeftInverse_346 -> T_IsEquivalence_28
d_isEquivalence'8322'_368 T_IsLeftInverse_346
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0))
-- Function.Structures.IsLeftInverse._.cong
d_cong_370 ::
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_370 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_370 T_IsLeftInverse_346
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_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0))
-- Function.Structures.IsLeftInverse._.Eq₁._≈_
d__'8776'__374 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> ()
d__'8776'__374 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__374 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁._≉_
d__'8777'__376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> ()
d__'8777'__376 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__376 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁.Carrier
d_Carrier_378 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> ()
d_Carrier_378 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> ()
d_Carrier_378 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁.isEquivalence
d_isEquivalence_380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_380 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsEquivalence_28
d_isEquivalence_380 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_380 T_IsLeftInverse_346
v10
du_isEquivalence_380 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_380 :: T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_380 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_382 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_382 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_382 T_IsLeftInverse_346
v10
du_isPartialEquivalence_382 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_382 :: T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_382 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsLeftInverse._.Eq₁.partialSetoid
d_partialSetoid_384 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_384 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_PartialSetoid_10
d_partialSetoid_384 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_384 T_IsLeftInverse_346
v10
du_partialSetoid_384 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_384 :: T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_384 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsLeftInverse._.Eq₁.rawSetoid
d_rawSetoid_386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_386 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
d_rawSetoid_386 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₁.refl
d_refl_388 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
d_refl_388 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
d_refl_388 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_388 T_IsLeftInverse_346
v10
du_refl_388 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_388 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_388 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_390 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_390 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_390 T_IsLeftInverse_346
v10
du_reflexive_390 ::
  T_IsLeftInverse_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_390 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_390 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsLeftInverse._.Eq₁.setoid
d_setoid_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_392 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Setoid_46
d_setoid_392 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_392 T_IsLeftInverse_346
v10
du_setoid_392 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_392 :: T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_392 T_IsLeftInverse_346
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0))
-- Function.Structures.IsLeftInverse._.Eq₁.sym
d_sym_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_394 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_394 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_394 T_IsLeftInverse_346
v10
du_sym_394 ::
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_394 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_394 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsLeftInverse._.Eq₁.trans
d_trans_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_396 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_396 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_396 T_IsLeftInverse_346
v10
du_trans_396 ::
  T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_396 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_396 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsLeftInverse._.Eq₂._≈_
d__'8776'__400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> ()
d__'8776'__400 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__400 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂._≉_
d__'8777'__402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 -> AgdaAny -> AgdaAny -> ()
d__'8777'__402 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__402 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂.Carrier
d_Carrier_404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 -> ()
d_Carrier_404 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> ()
d_Carrier_404 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> ()
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂.isEquivalence
d_isEquivalence_406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_406 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsEquivalence_28
d_isEquivalence_406 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_406 T_IsLeftInverse_346
v10
du_isEquivalence_406 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_406 :: T_IsLeftInverse_346 -> T_IsEquivalence_28
du_isEquivalence_406 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_408 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_408 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_408 T_IsLeftInverse_346
v10
du_isPartialEquivalence_408 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_408 :: T_IsLeftInverse_346 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_408 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsLeftInverse._.Eq₂.partialSetoid
d_partialSetoid_410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_410 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_PartialSetoid_10
d_partialSetoid_410 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_410 T_IsLeftInverse_346
v10
du_partialSetoid_410 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_410 :: T_IsLeftInverse_346 -> T_PartialSetoid_10
du_partialSetoid_410 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsLeftInverse._.Eq₂.rawSetoid
d_rawSetoid_412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_412 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
d_rawSetoid_412 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsLeftInverse._.Eq₂.refl
d_refl_414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 -> AgdaAny -> AgdaAny
d_refl_414 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
d_refl_414 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_414 T_IsLeftInverse_346
v10
du_refl_414 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_414 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_refl_414 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_416 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_416 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_416 T_IsLeftInverse_346
v10
du_reflexive_416 ::
  T_IsLeftInverse_346 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_416 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_416 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsLeftInverse._.Eq₂.setoid
d_setoid_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_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_418 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_Setoid_46
d_setoid_418 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_418 T_IsLeftInverse_346
v10
du_setoid_418 ::
  T_IsLeftInverse_346 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_418 :: T_IsLeftInverse_346 -> T_Setoid_46
du_setoid_418 T_IsLeftInverse_346
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v0))
-- Function.Structures.IsLeftInverse._.Eq₂.sym
d_sym_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_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_420 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_420 T_IsLeftInverse_346
v10
du_sym_420 ::
  T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_420 :: T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_420 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsLeftInverse._.Eq₂.trans
d_trans_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_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_422 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_422 T_IsLeftInverse_346
v10
du_trans_422 ::
  T_IsLeftInverse_346 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_422 :: T_IsLeftInverse_346
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_422 T_IsLeftInverse_346
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsLeftInverse.strictlyInverseˡ
d_strictlyInverse'737'_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_IsLeftInverse_346 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_424 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_424 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9
                           T_IsLeftInverse_346
v10 AgdaAny
v11
  = (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_424 AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10 AgdaAny
v11
du_strictlyInverse'737'_424 ::
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_424 :: (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_424 AgdaAny -> AgdaAny
v0 T_IsLeftInverse_346
v1 AgdaAny
v2
  = (T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_362 T_IsLeftInverse_346
v1 AgdaAny
v2 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2)
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         (T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsLeftInverse_346 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1)))
         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2))
-- Function.Structures.IsLeftInverse.isSurjection
d_isSurjection_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_IsLeftInverse_346 -> T_IsSurjection_174
d_isSurjection_428 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346
-> T_IsSurjection_174
d_isSurjection_428 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
  = (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
du_isSurjection_428 AgdaAny -> AgdaAny
v9 T_IsLeftInverse_346
v10
du_isSurjection_428 ::
  (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
du_isSurjection_428 :: (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
du_isSurjection_428 AgdaAny -> AgdaAny
v0 T_IsLeftInverse_346
v1
  = (T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_174
C_constructor_252 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1))
      ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v2 ->
            (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2)
              ((T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_362 T_IsLeftInverse_346
v1 AgdaAny
v2)))
-- Function.Structures.IsRightInverse
d_IsRightInverse_438 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsRightInverse_438 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsRightInverse_438
  = C_constructor_520 T_IsCongruent_22
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsRightInverse.isCongruent
d_isCongruent_450 :: T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 :: T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 T_IsRightInverse_438
v0
  = case T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0 of
      C_constructor_520 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsRightInverse_438
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse.from-cong
d_from'45'cong_452 ::
  T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_452 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_452 T_IsRightInverse_438
v0
  = case T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0 of
      C_constructor_520 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsRightInverse_438
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse.inverseʳ
d_inverse'691'_454 ::
  T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_454 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_454 T_IsRightInverse_438
v0
  = case T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0 of
      C_constructor_520 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsRightInverse_438
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsRightInverse._.isEquivalence₁
d_isEquivalence'8321'_458 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_458 :: T_IsRightInverse_438 -> T_IsEquivalence_28
d_isEquivalence'8321'_458 T_IsRightInverse_438
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0))
-- Function.Structures.IsRightInverse._.isEquivalence₂
d_isEquivalence'8322'_460 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_460 :: T_IsRightInverse_438 -> T_IsEquivalence_28
d_isEquivalence'8322'_460 T_IsRightInverse_438
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0))
-- Function.Structures.IsRightInverse._.cong
d_cong_462 ::
  T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_462 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_462 T_IsRightInverse_438
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_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0))
-- Function.Structures.IsRightInverse._.Eq₁._≈_
d__'8776'__466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> ()
d__'8776'__466 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__466 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁._≉_
d__'8777'__468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> ()
d__'8777'__468 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__468 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁.Carrier
d_Carrier_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> ()
d_Carrier_470 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> ()
d_Carrier_470 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁.isEquivalence
d_isEquivalence_472 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_472 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsEquivalence_28
d_isEquivalence_472 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_472 T_IsRightInverse_438
v10
du_isEquivalence_472 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_472 :: T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_472 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_474 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_474 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_474 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_474 T_IsRightInverse_438
v10
du_isPartialEquivalence_474 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_474 :: T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_474 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsRightInverse._.Eq₁.partialSetoid
d_partialSetoid_476 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_476 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_PartialSetoid_10
d_partialSetoid_476 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_476 T_IsRightInverse_438
v10
du_partialSetoid_476 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_476 :: T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_476 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsRightInverse._.Eq₁.rawSetoid
d_rawSetoid_478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_478 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
d_rawSetoid_478 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₁.refl
d_refl_480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
d_refl_480 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
d_refl_480 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_480 T_IsRightInverse_438
v10
du_refl_480 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_480 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_480 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_482 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_482 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_482 T_IsRightInverse_438
v10
du_reflexive_482 ::
  T_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_482 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_482 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsRightInverse._.Eq₁.setoid
d_setoid_484 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_484 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Setoid_46
d_setoid_484 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_Setoid_46
du_setoid_484 T_IsRightInverse_438
v10
du_setoid_484 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_484 :: T_IsRightInverse_438 -> T_Setoid_46
du_setoid_484 T_IsRightInverse_438
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0))
-- Function.Structures.IsRightInverse._.Eq₁.sym
d_sym_486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_486 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_486 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_486 T_IsRightInverse_438
v10
du_sym_486 ::
  T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_486 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_486 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsRightInverse._.Eq₁.trans
d_trans_488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_488 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_488 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_488 T_IsRightInverse_438
v10
du_trans_488 ::
  T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_488 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_488 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsRightInverse._.Eq₂._≈_
d__'8776'__492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_438 -> AgdaAny -> AgdaAny -> ()
d__'8776'__492 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__492 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂._≉_
d__'8777'__494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_438 -> AgdaAny -> AgdaAny -> ()
d__'8777'__494 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__494 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂.Carrier
d_Carrier_496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_438 -> ()
d_Carrier_496 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> ()
d_Carrier_496 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> ()
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂.isEquivalence
d_isEquivalence_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_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_498 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsEquivalence_28
d_isEquivalence_498 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_498 T_IsRightInverse_438
v10
du_isEquivalence_498 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_498 :: T_IsRightInverse_438 -> T_IsEquivalence_28
du_isEquivalence_498 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_500 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_500 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_500 T_IsRightInverse_438
v10
du_isPartialEquivalence_500 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_500 :: T_IsRightInverse_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_500 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsRightInverse._.Eq₂.partialSetoid
d_partialSetoid_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_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_502 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_PartialSetoid_10
d_partialSetoid_502 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_502 T_IsRightInverse_438
v10
du_partialSetoid_502 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_502 :: T_IsRightInverse_438 -> T_PartialSetoid_10
du_partialSetoid_502 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsRightInverse._.Eq₂.rawSetoid
d_rawSetoid_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_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_504 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
d_rawSetoid_504 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsRightInverse._.Eq₂.refl
d_refl_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_IsRightInverse_438 -> AgdaAny -> AgdaAny
d_refl_506 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
d_refl_506 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_506 T_IsRightInverse_438
v10
du_refl_506 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_506 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_refl_506 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_508 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_508 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_508 T_IsRightInverse_438
v10
du_reflexive_508 ::
  T_IsRightInverse_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_508 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_508 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsRightInverse._.Eq₂.setoid
d_setoid_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_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_510 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> T_Setoid_46
d_setoid_510 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> T_Setoid_46
du_setoid_510 T_IsRightInverse_438
v10
du_setoid_510 ::
  T_IsRightInverse_438 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_510 :: T_IsRightInverse_438 -> T_Setoid_46
du_setoid_510 T_IsRightInverse_438
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsRightInverse_438 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v0))
-- Function.Structures.IsRightInverse._.Eq₂.sym
d_sym_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_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_512 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_512 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_512 T_IsRightInverse_438
v10
du_sym_512 ::
  T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_512 :: T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_512 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsRightInverse._.Eq₂.trans
d_trans_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_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_514 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_514 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsRightInverse_438
v10
  = T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_514 T_IsRightInverse_438
v10
du_trans_514 ::
  T_IsRightInverse_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_514 :: T_IsRightInverse_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_514 T_IsRightInverse_438
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> T_IsRightInverse_438
forall a b. a -> b
coe T_IsRightInverse_438
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsRightInverse.strictlyInverseʳ
d_strictlyInverse'691'_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_IsRightInverse_438 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_516 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_516 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsRightInverse_438
v10 AgdaAny
v11
  = (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_516 AgdaAny -> AgdaAny
v8 T_IsRightInverse_438
v10 AgdaAny
v11
du_strictlyInverse'691'_516 ::
  (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_516 :: (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_516 AgdaAny -> AgdaAny
v0 T_IsRightInverse_438
v1 AgdaAny
v2
  = (T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsRightInverse_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_454 T_IsRightInverse_438
v1 AgdaAny
v2 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2)
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         (T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 ((T_IsRightInverse_438 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsRightInverse_438 -> T_IsCongruent_22
d_isCongruent_450 (T_IsRightInverse_438 -> AgdaAny
forall a b. a -> b
coe T_IsRightInverse_438
v1)))
         ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0 AgdaAny
v2))
-- Function.Structures.IsInverse
d_IsInverse_526 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsInverse_526 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsInverse_526
  = C_constructor_618 T_IsLeftInverse_346
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsInverse.isLeftInverse
d_isLeftInverse_536 :: T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 :: T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 T_IsInverse_526
v0
  = case T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0 of
      C_constructor_618 T_IsLeftInverse_346
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1
      T_IsInverse_526
_ -> T_IsLeftInverse_346
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInverse.inverseʳ
d_inverse'691'_538 ::
  T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_538 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_538 T_IsInverse_526
v0
  = case T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0 of
      C_constructor_618 T_IsLeftInverse_346
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsInverse_526
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsInverse._.from-cong
d_from'45'cong_542 ::
  T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_542 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_542 T_IsInverse_526
v0
  = (T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_360 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0))
-- Function.Structures.IsInverse._.inverseˡ
d_inverse'737'_544 ::
  T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_544 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_544 T_IsInverse_526
v0
  = (T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_362 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0))
-- Function.Structures.IsInverse._.isCongruent
d_isCongruent_546 :: T_IsInverse_526 -> T_IsCongruent_22
d_isCongruent_546 :: T_IsInverse_526 -> T_IsCongruent_22
d_isCongruent_546 T_IsInverse_526
v0
  = (T_IsLeftInverse_346 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0))
-- Function.Structures.IsInverse._.isEquivalence₁
d_isEquivalence'8321'_548 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_548 :: T_IsInverse_526 -> T_IsEquivalence_28
d_isEquivalence'8321'_548 T_IsInverse_526
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34
      ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)))
-- Function.Structures.IsInverse._.isEquivalence₂
d_isEquivalence'8322'_550 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_550 :: T_IsInverse_526 -> T_IsEquivalence_28
d_isEquivalence'8322'_550 T_IsInverse_526
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36
      ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)))
-- Function.Structures.IsInverse._.isSurjection
d_isSurjection_552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> T_IsSurjection_174
d_isSurjection_552 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsSurjection_174
d_isSurjection_552 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> T_IsSurjection_174
du_isSurjection_552 AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
du_isSurjection_552 ::
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> T_IsSurjection_174
du_isSurjection_552 :: (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> T_IsSurjection_174
du_isSurjection_552 AgdaAny -> AgdaAny
v0 T_IsInverse_526
v1
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
du_isSurjection_428 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v1))
-- Function.Structures.IsInverse._.strictlyInverseˡ
d_strictlyInverse'737'_554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_554 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_554 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 AgdaAny -> AgdaAny
v9
                           T_IsInverse_526
v10
  = (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_554 AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
du_strictlyInverse'737'_554 ::
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_554 :: (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_554 AgdaAny -> AgdaAny
v0 T_IsInverse_526
v1
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_424 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0)
      ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v1))
-- Function.Structures.IsInverse._.cong
d_cong_556 ::
  T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_556 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_556 T_IsInverse_526
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_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)))
-- Function.Structures.IsInverse._.Eq₁._≈_
d__'8776'__560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny -> ()
d__'8776'__560 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__560 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁._≉_
d__'8777'__562 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny -> ()
d__'8777'__562 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__562 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁.Carrier
d_Carrier_564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> ()
d_Carrier_564 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> ()
d_Carrier_564 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁.isEquivalence
d_isEquivalence_566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_566 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsEquivalence_28
d_isEquivalence_566 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_566 T_IsInverse_526
v10
du_isEquivalence_566 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_566 :: T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_566 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_568 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_568 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_526
v10
  = T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_568 T_IsInverse_526
v10
du_isPartialEquivalence_568 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_568 :: T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_568 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsInverse._.Eq₁.partialSetoid
d_partialSetoid_570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_570 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_PartialSetoid_10
d_partialSetoid_570 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_570 T_IsInverse_526
v10
du_partialSetoid_570 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_570 :: T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_570 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsInverse._.Eq₁.rawSetoid
d_rawSetoid_572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_572 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
d_rawSetoid_572 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₁.refl
d_refl_574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
d_refl_574 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
d_refl_574 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_574 T_IsInverse_526
v10
du_refl_574 :: T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_574 :: T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_574 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_576 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_576 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_576 T_IsInverse_526
v10
du_reflexive_576 ::
  T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_576 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_576 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsInverse._.Eq₁.setoid
d_setoid_578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_526 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_578 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Setoid_46
d_setoid_578 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_Setoid_46
du_setoid_578 T_IsInverse_526
v10
du_setoid_578 ::
  T_IsInverse_526 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_578 :: T_IsInverse_526 -> T_Setoid_46
du_setoid_578 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1)))
-- Function.Structures.IsInverse._.Eq₁.sym
d_sym_580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_580 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_580 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_580 T_IsInverse_526
v10
du_sym_580 ::
  T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_580 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_580 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsInverse._.Eq₁.trans
d_trans_582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_582 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_582 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_582 T_IsInverse_526
v10
du_trans_582 ::
  T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_582 :: T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_582 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsInverse._.Eq₂._≈_
d__'8776'__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) -> T_IsInverse_526 -> AgdaAny -> AgdaAny -> ()
d__'8776'__586 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__586 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂._≉_
d__'8777'__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) -> T_IsInverse_526 -> AgdaAny -> AgdaAny -> ()
d__'8777'__588 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__588 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂.Carrier
d_Carrier_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) -> T_IsInverse_526 -> ()
d_Carrier_590 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> ()
d_Carrier_590 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> ()
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂.isEquivalence
d_isEquivalence_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) ->
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_592 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsEquivalence_28
d_isEquivalence_592 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_592 T_IsInverse_526
v10
du_isEquivalence_592 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_592 :: T_IsInverse_526 -> T_IsEquivalence_28
du_isEquivalence_592 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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) ->
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_594 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_594 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_526
v10
  = T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_594 T_IsInverse_526
v10
du_isPartialEquivalence_594 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_594 :: T_IsInverse_526 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_594 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsInverse._.Eq₂.partialSetoid
d_partialSetoid_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) ->
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_596 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_PartialSetoid_10
d_partialSetoid_596 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_596 T_IsInverse_526
v10
du_partialSetoid_596 ::
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_596 :: T_IsInverse_526 -> T_PartialSetoid_10
du_partialSetoid_596 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsInverse._.Eq₂.rawSetoid
d_rawSetoid_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) ->
  T_IsInverse_526 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_598 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
d_rawSetoid_598 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsInverse._.Eq₂.refl
d_refl_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) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
d_refl_600 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
d_refl_600 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_600 T_IsInverse_526
v10
du_refl_600 :: T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_600 :: T_IsInverse_526 -> AgdaAny -> AgdaAny
du_refl_600 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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) ->
  T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_602 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_602 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_602 T_IsInverse_526
v10
du_reflexive_602 ::
  T_IsInverse_526 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_602 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_602 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsInverse._.Eq₂.setoid
d_setoid_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) ->
  T_IsInverse_526 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_604 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Setoid_46
d_setoid_604 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_Setoid_46
du_setoid_604 T_IsInverse_526
v10
du_setoid_604 ::
  T_IsInverse_526 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_604 :: T_IsInverse_526 -> T_Setoid_46
du_setoid_604 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1)))
-- Function.Structures.IsInverse._.Eq₂.sym
d_sym_606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_606 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_606 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_606 T_IsInverse_526
v10
du_sym_606 ::
  T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_606 :: T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_606 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsInverse._.Eq₂.trans
d_trans_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) ->
  T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_608 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_608 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_608 T_IsInverse_526
v10
du_trans_608 ::
  T_IsInverse_526 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_608 :: T_IsInverse_526
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_608 T_IsInverse_526
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> T_IsInverse_526
forall a b. a -> b
coe T_IsInverse_526
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsInverse.isRightInverse
d_isRightInverse_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) -> T_IsInverse_526 -> T_IsRightInverse_438
d_isRightInverse_610 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_IsRightInverse_438
d_isRightInverse_610 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_IsRightInverse_438
du_isRightInverse_610 T_IsInverse_526
v10
du_isRightInverse_610 :: T_IsInverse_526 -> T_IsRightInverse_438
du_isRightInverse_610 :: T_IsInverse_526 -> T_IsRightInverse_438
du_isRightInverse_610 T_IsInverse_526
v0
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRightInverse_438)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_438
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRightInverse_438
C_constructor_520
      ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)))
      ((T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_360 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)))
      ((T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_538 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0))
-- Function.Structures.IsInverse._.strictlyInverseʳ
d_strictlyInverse'691'_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) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
d_strictlyInverse'691'_614 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> AgdaAny
-> AgdaAny
d_strictlyInverse'691'_614 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           T_IsInverse_526
v10
  = (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_614 AgdaAny -> AgdaAny
v8 T_IsInverse_526
v10
du_strictlyInverse'691'_614 ::
  (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_614 :: (AgdaAny -> AgdaAny) -> T_IsInverse_526 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_614 AgdaAny -> AgdaAny
v0 T_IsInverse_526
v1
  = ((AgdaAny -> AgdaAny)
 -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsRightInverse_438 -> AgdaAny -> AgdaAny
du_strictlyInverse'691'_516 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0)
      ((T_IsInverse_526 -> T_IsRightInverse_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsRightInverse_438
du_isRightInverse_610 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v1))
-- Function.Structures.IsInverse.inverse
d_inverse_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) ->
  T_IsInverse_526 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_616 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_526
-> T_Σ_14
d_inverse_616 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 T_IsInverse_526
v10
  = T_IsInverse_526 -> T_Σ_14
du_inverse_616 T_IsInverse_526
v10
du_inverse_616 ::
  T_IsInverse_526 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_inverse_616 :: T_IsInverse_526 -> T_Σ_14
du_inverse_616 T_IsInverse_526
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_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_362 ((T_IsInverse_526 -> T_IsLeftInverse_346) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> T_IsLeftInverse_346
d_isLeftInverse_536 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0)))
      ((T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_538 (T_IsInverse_526 -> AgdaAny
forall a b. a -> b
coe T_IsInverse_526
v0))
-- Function.Structures.IsBiEquivalence
d_IsBiEquivalence_626 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBiEquivalence_626 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_626
  = C_constructor_706 T_IsCongruent_22
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsBiEquivalence.to-isCongruent
d_to'45'isCongruent_640 ::
  T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 :: T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 T_IsBiEquivalence_626
v0
  = case T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0 of
      C_constructor_706 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_626
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence.from₁-cong
d_from'8321''45'cong_642 ::
  T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_642 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_642 T_IsBiEquivalence_626
v0
  = case T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0 of
      C_constructor_706 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_626
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence.from₂-cong
d_from'8322''45'cong_644 ::
  T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_644 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_644 T_IsBiEquivalence_626
v0
  = case T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0 of
      C_constructor_706 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_626
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiEquivalence._.isEquivalence₁
d_isEquivalence'8321'_648 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_648 :: T_IsBiEquivalence_626 -> T_IsEquivalence_28
d_isEquivalence'8321'_648 T_IsBiEquivalence_626
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsBiEquivalence_626 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626
v0))
-- Function.Structures.IsBiEquivalence._.isEquivalence₂
d_isEquivalence'8322'_650 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_650 :: T_IsBiEquivalence_626 -> T_IsEquivalence_28
d_isEquivalence'8322'_650 T_IsBiEquivalence_626
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 ((T_IsBiEquivalence_626 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626
v0))
-- Function.Structures.IsBiEquivalence._.cong
d_cong_652 ::
  T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_652 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_652 T_IsBiEquivalence_626
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_626 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626
v0))
-- Function.Structures.IsBiEquivalence._.Eq₁._≈_
d__'8776'__656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> ()
d__'8776'__656 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__656 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁._≉_
d__'8777'__658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> ()
d__'8777'__658 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__658 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁.Carrier
d_Carrier_660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 -> ()
d_Carrier_660 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> ()
d_Carrier_660 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁.isEquivalence
d_isEquivalence_662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_662 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_IsEquivalence_28
d_isEquivalence_662 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_IsEquivalence_28
du_isEquivalence_662 T_IsBiEquivalence_626
v11
du_isEquivalence_662 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_662 :: T_IsBiEquivalence_626 -> T_IsEquivalence_28
du_isEquivalence_662 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_664 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_664 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_664 T_IsBiEquivalence_626
v11
du_isPartialEquivalence_664 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_664 :: T_IsBiEquivalence_626 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_664 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₁.partialSetoid
d_partialSetoid_666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_666 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_PartialSetoid_10
d_partialSetoid_666 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_PartialSetoid_10
du_partialSetoid_666 T_IsBiEquivalence_626
v11
du_partialSetoid_666 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_666 :: T_IsBiEquivalence_626 -> T_PartialSetoid_10
du_partialSetoid_666 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiEquivalence._.Eq₁.rawSetoid
d_rawSetoid_668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_668 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_RawSetoid_12
d_rawSetoid_668 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₁.refl
d_refl_670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 -> AgdaAny -> AgdaAny
d_refl_670 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
d_refl_670 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny
du_refl_670 T_IsBiEquivalence_626
v11
du_refl_670 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny
du_refl_670 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny
du_refl_670 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_672 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_672 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_672 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_672 T_IsBiEquivalence_626
v11
du_reflexive_672 ::
  T_IsBiEquivalence_626 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_672 :: T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_672 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiEquivalence._.Eq₁.setoid
d_setoid_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_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_674 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_Setoid_46
d_setoid_674 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_Setoid_46
du_setoid_674 T_IsBiEquivalence_626
v11
du_setoid_674 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_674 :: T_IsBiEquivalence_626 -> T_Setoid_46
du_setoid_674 T_IsBiEquivalence_626
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsBiEquivalence_626 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626
v0))
-- Function.Structures.IsBiEquivalence._.Eq₁.sym
d_sym_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_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_676 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_676 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_676 T_IsBiEquivalence_626
v11
du_sym_676 ::
  T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_676 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_676 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₁.trans
d_trans_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_IsBiEquivalence_626 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_678 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_678 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_678 T_IsBiEquivalence_626
v11
du_trans_678 ::
  T_IsBiEquivalence_626 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_678 :: T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_678 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₂._≈_
d__'8776'__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_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> ()
d__'8776'__682 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__682 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂._≉_
d__'8777'__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_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> ()
d__'8777'__684 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__684 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂.Carrier
d_Carrier_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_IsBiEquivalence_626 -> ()
d_Carrier_686 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> ()
d_Carrier_686 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> ()
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂.isEquivalence
d_isEquivalence_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_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_688 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_IsEquivalence_28
d_isEquivalence_688 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_IsEquivalence_28
du_isEquivalence_688 T_IsBiEquivalence_626
v11
du_isEquivalence_688 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_688 :: T_IsBiEquivalence_626 -> T_IsEquivalence_28
du_isEquivalence_688 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_690 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_690 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_690 T_IsBiEquivalence_626
v11
du_isPartialEquivalence_690 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_690 :: T_IsBiEquivalence_626 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_690 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₂.partialSetoid
d_partialSetoid_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_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_692 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_PartialSetoid_10
d_partialSetoid_692 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_PartialSetoid_10
du_partialSetoid_692 T_IsBiEquivalence_626
v11
du_partialSetoid_692 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_692 :: T_IsBiEquivalence_626 -> T_PartialSetoid_10
du_partialSetoid_692 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiEquivalence._.Eq₂.rawSetoid
d_rawSetoid_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_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_694 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_RawSetoid_12
d_rawSetoid_694 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsBiEquivalence._.Eq₂.refl
d_refl_696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_626 -> AgdaAny -> AgdaAny
d_refl_696 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
d_refl_696 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny
du_refl_696 T_IsBiEquivalence_626
v11
du_refl_696 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny
du_refl_696 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny
du_refl_696 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_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_IsBiEquivalence_626 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_698 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_698 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_698 T_IsBiEquivalence_626
v11
du_reflexive_698 ::
  T_IsBiEquivalence_626 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_698 :: T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_698 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiEquivalence._.Eq₂.setoid
d_setoid_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_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_700 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> T_Setoid_46
d_setoid_700 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> T_Setoid_46
du_setoid_700 T_IsBiEquivalence_626
v11
du_setoid_700 ::
  T_IsBiEquivalence_626 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_700 :: T_IsBiEquivalence_626 -> T_Setoid_46
du_setoid_700 T_IsBiEquivalence_626
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsBiEquivalence_626 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> AgdaAny
forall a b. a -> b
coe T_IsBiEquivalence_626
v0))
-- Function.Structures.IsBiEquivalence._.Eq₂.sym
d_sym_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_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_702 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_702 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_702 T_IsBiEquivalence_626
v11
du_sym_702 ::
  T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_702 :: T_IsBiEquivalence_626 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_702 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiEquivalence._.Eq₂.trans
d_trans_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_IsBiEquivalence_626 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_704 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiEquivalence_626
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_704 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiEquivalence_626
v11
  = T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_704 T_IsBiEquivalence_626
v11
du_trans_704 ::
  T_IsBiEquivalence_626 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_704 :: T_IsBiEquivalence_626
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_704 T_IsBiEquivalence_626
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiEquivalence_626 -> T_IsCongruent_22
d_to'45'isCongruent_640 (T_IsBiEquivalence_626 -> T_IsBiEquivalence_626
forall a b. a -> b
coe T_IsBiEquivalence_626
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiInverse
d_IsBiInverse_714 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBiInverse_714 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_714
  = C_constructor_802 T_IsCongruent_22
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Structures.IsBiInverse.to-isCongruent
d_to'45'isCongruent_732 :: T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 :: T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 T_IsBiInverse_714
v0
  = case T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0 of
      C_constructor_802 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> T_IsCongruent_22 -> T_IsCongruent_22
forall a b. a -> b
coe T_IsCongruent_22
v1
      T_IsBiInverse_714
_ -> T_IsCongruent_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.from₁-cong
d_from'8321''45'cong_734 ::
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_734 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8321''45'cong_734 T_IsBiInverse_714
v0
  = case T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0 of
      C_constructor_802 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsBiInverse_714
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.from₂-cong
d_from'8322''45'cong_736 ::
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_736 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'8322''45'cong_736 T_IsBiInverse_714
v0
  = case T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0 of
      C_constructor_802 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IsBiInverse_714
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.inverseˡ
d_inverse'737'_738 ::
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_738 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_738 T_IsBiInverse_714
v0
  = case T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0 of
      C_constructor_802 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_IsBiInverse_714
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse.inverseʳ
d_inverse'691'_740 ::
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_740 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'691'_740 T_IsBiInverse_714
v0
  = case T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0 of
      C_constructor_802 T_IsCongruent_22
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_IsBiInverse_714
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsBiInverse._.isEquivalence₁
d_isEquivalence'8321'_744 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_744 :: T_IsBiInverse_714 -> T_IsEquivalence_28
d_isEquivalence'8321'_744 T_IsBiInverse_714
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 ((T_IsBiInverse_714 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0))
-- Function.Structures.IsBiInverse._.isEquivalence₂
d_isEquivalence'8322'_746 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_746 :: T_IsBiInverse_714 -> T_IsEquivalence_28
d_isEquivalence'8322'_746 T_IsBiInverse_714
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 ((T_IsBiInverse_714 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0))
-- Function.Structures.IsBiInverse._.cong
d_cong_748 ::
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_748 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_748 T_IsBiInverse_714
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_714 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0))
-- Function.Structures.IsBiInverse._.Eq₁._≈_
d__'8776'__752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 -> AgdaAny -> AgdaAny -> ()
d__'8776'__752 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__752 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁._≉_
d__'8777'__754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 -> AgdaAny -> AgdaAny -> ()
d__'8777'__754 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__754 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁.Carrier
d_Carrier_756 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 -> ()
d_Carrier_756 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> ()
d_Carrier_756 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁.isEquivalence
d_isEquivalence_758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_758 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_IsEquivalence_28
d_isEquivalence_758 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_IsEquivalence_28
du_isEquivalence_758 T_IsBiInverse_714
v11
du_isEquivalence_758 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_758 :: T_IsBiInverse_714 -> T_IsEquivalence_28
du_isEquivalence_758 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_760 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_760 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_760 T_IsBiInverse_714
v11
du_isPartialEquivalence_760 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_760 :: T_IsBiInverse_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_760 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiInverse._.Eq₁.partialSetoid
d_partialSetoid_762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_762 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_PartialSetoid_10
d_partialSetoid_762 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_PartialSetoid_10
du_partialSetoid_762 T_IsBiInverse_714
v11
du_partialSetoid_762 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_762 :: T_IsBiInverse_714 -> T_PartialSetoid_10
du_partialSetoid_762 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiInverse._.Eq₁.rawSetoid
d_rawSetoid_764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_764 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_RawSetoid_12
d_rawSetoid_764 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₁.refl
d_refl_766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 -> AgdaAny -> AgdaAny
d_refl_766 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
d_refl_766 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> AgdaAny -> AgdaAny
du_refl_766 T_IsBiInverse_714
v11
du_refl_766 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny
du_refl_766 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny
du_refl_766 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_768 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_768 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_768 T_IsBiInverse_714
v11
du_reflexive_768 ::
  T_IsBiInverse_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_768 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_768 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiInverse._.Eq₁.setoid
d_setoid_770 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_770 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_Setoid_46
d_setoid_770 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_Setoid_46
du_setoid_770 T_IsBiInverse_714
v11
du_setoid_770 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_770 :: T_IsBiInverse_714 -> T_Setoid_46
du_setoid_770 T_IsBiInverse_714
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsBiInverse_714 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0))
-- Function.Structures.IsBiInverse._.Eq₁.sym
d_sym_772 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_772 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_772 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_772 T_IsBiInverse_714
v11
du_sym_772 ::
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_772 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_772 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiInverse._.Eq₁.trans
d_trans_774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_774 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_774 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_774 T_IsBiInverse_714
v11
du_trans_774 ::
  T_IsBiInverse_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_774 :: T_IsBiInverse_714
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_774 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiInverse._.Eq₂._≈_
d__'8776'__778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> ()
d__'8776'__778 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__778 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂._≉_
d__'8777'__780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 -> AgdaAny -> AgdaAny -> ()
d__'8777'__780 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__780 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂.Carrier
d_Carrier_782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.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_714 -> ()
d_Carrier_782 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> ()
d_Carrier_782 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> ()
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂.isEquivalence
d_isEquivalence_784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_784 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_IsEquivalence_28
d_isEquivalence_784 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_IsEquivalence_28
du_isEquivalence_784 T_IsBiInverse_714
v11
du_isEquivalence_784 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_784 :: T_IsBiInverse_714 -> T_IsEquivalence_28
du_isEquivalence_784 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_786 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_786 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9
                           ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_786 T_IsBiInverse_714
v11
du_isPartialEquivalence_786 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_786 :: T_IsBiInverse_714 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_786 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiInverse._.Eq₂.partialSetoid
d_partialSetoid_788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_788 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_PartialSetoid_10
d_partialSetoid_788 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10
                    T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_PartialSetoid_10
du_partialSetoid_788 T_IsBiInverse_714
v11
du_partialSetoid_788 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_788 :: T_IsBiInverse_714 -> T_PartialSetoid_10
du_partialSetoid_788 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
         ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v1)))
-- Function.Structures.IsBiInverse._.Eq₂.rawSetoid
d_rawSetoid_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_790 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_RawSetoid_12
d_rawSetoid_790 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsBiInverse._.Eq₂.refl
d_refl_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> T_IsBiInverse_714 -> AgdaAny -> AgdaAny
d_refl_792 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
d_refl_792 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> AgdaAny -> AgdaAny
du_refl_792 T_IsBiInverse_714
v11
du_refl_792 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny
du_refl_792 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny
du_refl_792 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
         ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
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_794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_794 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_794 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_794 T_IsBiInverse_714
v11
du_reflexive_794 ::
  T_IsBiInverse_714 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_794 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_794 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
              AgdaAny
v3))
-- Function.Structures.IsBiInverse._.Eq₂.setoid
d_setoid_796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_796 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> T_Setoid_46
d_setoid_796 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> T_Setoid_46
du_setoid_796 T_IsBiInverse_714
v11
du_setoid_796 ::
  T_IsBiInverse_714 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_796 :: T_IsBiInverse_714 -> T_Setoid_46
du_setoid_796 T_IsBiInverse_714
v0
  = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsBiInverse_714 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> AgdaAny
forall a b. a -> b
coe T_IsBiInverse_714
v0))
-- Function.Structures.IsBiInverse._.Eq₂.sym
d_sym_798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_798 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_798 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_798 T_IsBiInverse_714
v11
du_sym_798 ::
  T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_798 :: T_IsBiInverse_714 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_798 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsBiInverse._.Eq₂.trans
d_trans_800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  T_IsBiInverse_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_800 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_714
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_800 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny -> AgdaAny
v9 ~AgdaAny -> AgdaAny
v10 T_IsBiInverse_714
v11
  = T_IsBiInverse_714
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_800 T_IsBiInverse_714
v11
du_trans_800 ::
  T_IsBiInverse_714 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_800 :: T_IsBiInverse_714
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_800 T_IsBiInverse_714
v0
  = let v1 :: T_IsCongruent_22
v1 = T_IsBiInverse_714 -> T_IsCongruent_22
d_to'45'isCongruent_732 (T_IsBiInverse_714 -> T_IsBiInverse_714
forall a b. a -> b
coe T_IsBiInverse_714
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
            ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Function.Structures.IsSplitSurjection
d_IsSplitSurjection_806 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsSplitSurjection_806 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
data T_IsSplitSurjection_806
  = C_constructor_888 (AgdaAny -> AgdaAny) T_IsLeftInverse_346
-- Function.Structures.IsSplitSurjection.from
d_from_814 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_from_814 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_from_814 T_IsSplitSurjection_806
v0
  = case T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0 of
      C_constructor_888 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_346
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_IsSplitSurjection_806
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSplitSurjection.isLeftInverse
d_isLeftInverse_816 ::
  T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 :: T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 T_IsSplitSurjection_806
v0
  = case T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0 of
      C_constructor_888 AgdaAny -> AgdaAny
v1 T_IsLeftInverse_346
v2 -> T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v2
      T_IsSplitSurjection_806
_ -> T_IsLeftInverse_346
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Structures.IsSplitSurjection._.from-cong
d_from'45'cong_820 ::
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_820 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_820 T_IsSplitSurjection_806
v0
  = (T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_from'45'cong_360 ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0))
-- Function.Structures.IsSplitSurjection._.inverseˡ
d_inverse'737'_822 ::
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_822 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_822 T_IsSplitSurjection_806
v0
  = (T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_inverse'737'_362 ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0))
-- Function.Structures.IsSplitSurjection._.isCongruent
d_isCongruent_824 :: T_IsSplitSurjection_806 -> T_IsCongruent_22
d_isCongruent_824 :: T_IsSplitSurjection_806 -> T_IsCongruent_22
d_isCongruent_824 T_IsSplitSurjection_806
v0
  = (T_IsLeftInverse_346 -> T_IsCongruent_22)
-> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0))
-- Function.Structures.IsSplitSurjection._.isEquivalence₁
d_isEquivalence'8321'_826 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8321'_826 :: T_IsSplitSurjection_806 -> T_IsEquivalence_28
d_isEquivalence'8321'_826 T_IsSplitSurjection_806
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34
      ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0)))
-- Function.Structures.IsSplitSurjection._.isEquivalence₂
d_isEquivalence'8322'_828 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence'8322'_828 :: T_IsSplitSurjection_806 -> T_IsEquivalence_28
d_isEquivalence'8322'_828 T_IsSplitSurjection_806
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36
      ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0)))
-- Function.Structures.IsSplitSurjection._.isSurjection
d_isSurjection_830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> T_IsSurjection_174
d_isSurjection_830 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_IsSurjection_174
d_isSurjection_830 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_IsSurjection_174
du_isSurjection_830 T_IsSplitSurjection_806
v9
du_isSurjection_830 ::
  T_IsSplitSurjection_806 -> T_IsSurjection_174
du_isSurjection_830 :: T_IsSplitSurjection_806 -> T_IsSurjection_174
du_isSurjection_830 T_IsSplitSurjection_806
v0
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174)
-> AgdaAny -> AgdaAny -> T_IsSurjection_174
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> T_IsSurjection_174
du_isSurjection_428 ((T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_from_814 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0))
      ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0))
-- Function.Structures.IsSplitSurjection._.strictlyInverseˡ
d_strictlyInverse'737'_832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_strictlyInverse'737'_832 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
d_strictlyInverse'737'_832 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_832 T_IsSplitSurjection_806
v9
du_strictlyInverse'737'_832 ::
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_832 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_832 T_IsSplitSurjection_806
v0
  = ((AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> T_IsLeftInverse_346 -> AgdaAny -> AgdaAny
du_strictlyInverse'737'_424 ((T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_from_814 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0))
      ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0))
-- Function.Structures.IsSplitSurjection._.cong
d_cong_834 ::
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_834 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_834 T_IsSplitSurjection_806
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_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 ((T_IsSplitSurjection_806 -> T_IsLeftInverse_346)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> AgdaAny
forall a b. a -> b
coe T_IsSplitSurjection_806
v0)))
-- Function.Structures.IsSplitSurjection._.Eq₁._≈_
d__'8776'__838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> ()
d__'8776'__838 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__838 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₁._≉_
d__'8777'__840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> ()
d__'8777'__840 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__840 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₁.Carrier
d_Carrier_842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSplitSurjection_806 -> ()
d_Carrier_842 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> ()
d_Carrier_842 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₁.isEquivalence
d_isEquivalence_844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_844 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_IsEquivalence_28
d_isEquivalence_844 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_IsEquivalence_28
du_isEquivalence_844 T_IsSplitSurjection_806
v9
du_isEquivalence_844 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_844 :: T_IsSplitSurjection_806 -> T_IsEquivalence_28
du_isEquivalence_844 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsSplitSurjection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_846 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_846 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_846 T_IsSplitSurjection_806
v9
du_isPartialEquivalence_846 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_846 :: T_IsSplitSurjection_806 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_846 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₁.partialSetoid
d_partialSetoid_848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_848 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_PartialSetoid_10
d_partialSetoid_848 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_PartialSetoid_10
du_partialSetoid_848 T_IsSplitSurjection_806
v9
du_partialSetoid_848 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_848 :: T_IsSplitSurjection_806 -> T_PartialSetoid_10
du_partialSetoid_848 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₁.rawSetoid
d_rawSetoid_850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_850 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_RawSetoid_12
d_rawSetoid_850 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₁.refl
d_refl_852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_refl_852 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
d_refl_852 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9 = T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_refl_852 T_IsSplitSurjection_806
v9
du_refl_852 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_refl_852 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_refl_852 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₁.reflexive
d_reflexive_854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_854 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_854 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_854 T_IsSplitSurjection_806
v9
du_reflexive_854 ::
  T_IsSplitSurjection_806 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_854 :: T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_854 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsSplitSurjection._.Eq₁.setoid
d_setoid_856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_856 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_Setoid_46
d_setoid_856 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_Setoid_46
du_setoid_856 T_IsSplitSurjection_806
v9
du_setoid_856 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_856 :: T_IsSplitSurjection_806 -> T_Setoid_46
du_setoid_856 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_40 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1)))
-- Function.Structures.IsSplitSurjection._.Eq₁.sym
d_sym_858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_858 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_858 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9 = T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_858 T_IsSplitSurjection_806
v9
du_sym_858 ::
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_858 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_858 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₁.trans
d_trans_860 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_860 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_860 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_860 T_IsSplitSurjection_806
v9
du_trans_860 ::
  T_IsSplitSurjection_806 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_860 :: T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_860 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₂._≈_
d__'8776'__864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> ()
d__'8776'__864 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
d__'8776'__864 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₂._≉_
d__'8777'__866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> ()
d__'8777'__866 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__866 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₂.Carrier
d_Carrier_868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) -> T_IsSplitSurjection_806 -> ()
d_Carrier_868 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> ()
d_Carrier_868 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> ()
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₂.isEquivalence
d_isEquivalence_870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_870 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_IsEquivalence_28
d_isEquivalence_870 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_IsEquivalence_28
du_isEquivalence_870 T_IsSplitSurjection_806
v9
du_isEquivalence_870 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
du_isEquivalence_870 :: T_IsSplitSurjection_806 -> T_IsEquivalence_28
du_isEquivalence_870 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Structures.IsSplitSurjection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_872 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_872 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_872 T_IsSplitSurjection_806
v9
du_isPartialEquivalence_872 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_872 :: T_IsSplitSurjection_806 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_872 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₂.partialSetoid
d_partialSetoid_874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_874 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_PartialSetoid_10
d_partialSetoid_874 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_PartialSetoid_10
du_partialSetoid_874 T_IsSplitSurjection_806
v9
du_partialSetoid_874 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_874 :: T_IsSplitSurjection_806 -> T_PartialSetoid_10
du_partialSetoid_874 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_46 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_46 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_72
            ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₂.rawSetoid
d_rawSetoid_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_876 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_RawSetoid_12
d_rawSetoid_876 = ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_RawSetoid_12
forall a. a
erased
-- Function.Structures.IsSplitSurjection._.Eq₂.refl
d_refl_878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
d_refl_878 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
d_refl_878 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9 = T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_refl_878 T_IsSplitSurjection_806
v9
du_refl_878 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_refl_878 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny
du_refl_878 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
            ((T_IsCongruent_22 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_IsEquivalence_28
d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Structures.IsSplitSurjection._.Eq₂.reflexive
d_reflexive_880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_880 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_880 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_880 T_IsSplitSurjection_806
v9
du_reflexive_880 ::
  T_IsSplitSurjection_806 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_880 :: T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_880 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                 AgdaAny
v4)))
-- Function.Structures.IsSplitSurjection._.Eq₂.setoid
d_setoid_882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_882 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> T_Setoid_46
d_setoid_882 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806 -> T_Setoid_46
du_setoid_882 T_IsSplitSurjection_806
v9
du_setoid_882 ::
  T_IsSplitSurjection_806 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_882 :: T_IsSplitSurjection_806 -> T_Setoid_46
du_setoid_882 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe ((T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 ((T_IsLeftInverse_346 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_346
v1)))
-- Function.Structures.IsSplitSurjection._.Eq₂.sym
d_sym_884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_884 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_884 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9 = T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_884 T_IsSplitSurjection_806
v9
du_sym_884 ::
  T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_884 :: T_IsSplitSurjection_806 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_884 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Function.Structures.IsSplitSurjection._.Eq₂.trans
d_trans_886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny) ->
  T_IsSplitSurjection_806 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_886 :: ()
-> ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny)
-> T_IsSplitSurjection_806
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_886 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~()
v6 ~AgdaAny -> AgdaAny -> ()
v7 ~AgdaAny -> AgdaAny
v8 T_IsSplitSurjection_806
v9
  = T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_886 T_IsSplitSurjection_806
v9
du_trans_886 ::
  T_IsSplitSurjection_806 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_886 :: T_IsSplitSurjection_806
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_886 T_IsSplitSurjection_806
v0
  = let v1 :: T_IsLeftInverse_346
v1 = T_IsSplitSurjection_806 -> T_IsLeftInverse_346
d_isLeftInverse_816 (T_IsSplitSurjection_806 -> T_IsSplitSurjection_806
forall a b. a -> b
coe T_IsSplitSurjection_806
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2 = T_IsLeftInverse_346 -> T_IsCongruent_22
d_isCongruent_358 (T_IsLeftInverse_346 -> T_IsLeftInverse_346
forall a b. a -> b
coe T_IsLeftInverse_346
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_IsCongruent_22 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_46
du_setoid_68 (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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))