{-# 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.Bundles 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.Function.Structures
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Function.Bundles._._._≈_
d__'8776'__30 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__30 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__30 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Carrier
d_Carrier_32 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 -> ()
d_Carrier_32 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
d_Carrier_32 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Bijective
d_Bijective_42 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) -> ()
d_Bijective_42 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Bijective_42 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Injective
d_Injective_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) -> ()
d_Injective_46 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Injective_46 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Inverseʳ
d_Inverse'691'_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Inverse'691'_48 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse'691'_48 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Inverseˡ
d_Inverse'737'_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Inverse'737'_50 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse'737'_50 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Inverseᵇ
d_Inverse'7495'_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Inverse'7495'_52 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse'7495'_52 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Surjective
d_Surjective_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny) -> ()
d_Surjective_54 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Surjective_54 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBiInverse
d_IsBiInverse_60 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBiInverse_60 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 = ()
-- Function.Bundles._._.IsBijection
d_IsBijection_62 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBijection_62 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsCongruent
d_IsCongruent_64 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsCongruent_64 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsInjection
d_IsInjection_66 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInjection_66 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsInverse
d_IsInverse_68 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsInverse_68 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsLeftInverse
d_IsLeftInverse_70 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLeftInverse_70 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsRightInverse
d_IsRightInverse_72 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsRightInverse_72 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Function.Bundles._._.IsSurjection
d_IsSurjection_74 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsSurjection_74 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Function.Bundles._._.IsBijection.Eq₁._≈_
d__'8776'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__226 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁._≉_
d__'8777'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__228 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__228 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁.Carrier
d_Carrier_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 -> ()
d_Carrier_230 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Level_18
d_Carrier_230 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₁.isEquivalence
d_isEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_232 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsEquivalence_26
d_isEquivalence_232 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_232 T_IsBijection_232
v7
du_isEquivalence_232 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_232 :: T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_232 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsBijection.Eq₁.isPartialEquivalence
d_isPartialEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_234 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_234 T_IsBijection_232
v7
du_isPartialEquivalence_234 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_234 :: T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_234 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Bundles._._.IsBijection.Eq₁.partialSetoid
d_partialSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_236 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_PartialSetoid_10
d_partialSetoid_236 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_236 T_IsBijection_232
v7
du_partialSetoid_236 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_236 :: T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_236 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₁.refl
d_refl_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny
d_refl_238 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
d_refl_238 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_238 T_IsBijection_232
v7
du_refl_238 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny
du_refl_238 :: T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_238 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₁.reflexive
d_reflexive_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_240 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_240 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_240 T_IsBijection_232
v7
du_reflexive_240 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_240 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_240 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsBijection.Eq₁.setoid
d_setoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_242 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Setoid_44
d_setoid_242 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232 -> T_Setoid_44
du_setoid_242 T_IsBijection_232
v7
du_setoid_242 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_242 :: T_IsBijection_232 -> T_Setoid_44
du_setoid_242 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v1)))
-- Function.Bundles._._.IsBijection.Eq₁.sym
d_sym_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_244 T_IsBijection_232
v7
du_sym_244 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_244 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_244 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₁.trans
d_trans_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_246 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_246 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_246 T_IsBijection_232
v7
du_trans_246 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_246 :: T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_246 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₂._≈_
d__'8776'__250 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__250 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__250 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂._≉_
d__'8777'__252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__252 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__252 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂.Carrier
d_Carrier_254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 -> ()
d_Carrier_254 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Level_18
d_Carrier_254 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsBijection.Eq₂.isEquivalence
d_isEquivalence_256 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_256 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsEquivalence_26
d_isEquivalence_256 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_256 T_IsBijection_232
v7
du_isEquivalence_256 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_256 :: T_IsBijection_232 -> T_IsEquivalence_26
du_isEquivalence_256 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsBijection.Eq₂.isPartialEquivalence
d_isPartialEquivalence_258 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_258 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_258 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_258 T_IsBijection_232
v7
du_isPartialEquivalence_258 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_258 :: T_IsBijection_232 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_258 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Bundles._._.IsBijection.Eq₂.partialSetoid
d_partialSetoid_260 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_260 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_PartialSetoid_10
d_partialSetoid_260 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_260 T_IsBijection_232
v7
du_partialSetoid_260 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_260 :: T_IsBijection_232 -> T_PartialSetoid_10
du_partialSetoid_260 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₂.refl
d_refl_262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny
d_refl_262 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
d_refl_262 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_262 T_IsBijection_232
v7
du_refl_262 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny
du_refl_262 :: T_IsBijection_232 -> AgdaAny -> AgdaAny
du_refl_262 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₂.reflexive
d_reflexive_264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_264 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_264 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7
  = T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_264 T_IsBijection_232
v7
du_reflexive_264 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_264 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_264 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsBijection.Eq₂.setoid
d_setoid_266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_266 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> T_Setoid_44
d_setoid_266 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232 -> T_Setoid_44
du_setoid_266 T_IsBijection_232
v7
du_setoid_266 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_266 :: T_IsBijection_232 -> T_Setoid_44
du_setoid_266 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v1)))
-- Function.Bundles._._.IsBijection.Eq₂.sym
d_sym_268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_268 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_268 T_IsBijection_232
v7
du_sym_268 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_268 :: T_IsBijection_232 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_268 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsBijection.Eq₂.trans
d_trans_270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsBijection_232
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsBijection_232
v7 = T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_270 T_IsBijection_232
v7
du_trans_270 ::
  MAlonzo.Code.Function.Structures.T_IsBijection_232 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_270 :: T_IsBijection_232
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_270 T_IsBijection_232
v0
  = let v1 :: T_IsInjection_92
v1
          = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (T_IsBijection_232 -> T_IsBijection_232
forall a b. a -> b
coe T_IsBijection_232
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsCongruent.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__282 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__284 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 -> ()
d_Carrier_286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
d_Carrier_286 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_26
d_isEquivalence_288 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_288 T_IsCongruent_22
v7
du_isEquivalence_288 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_288 :: T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_288 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsCongruent_22
v7
du_isPartialEquivalence_290 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_290 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_290 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Bundles._._.IsCongruent.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_292 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_292 T_IsCongruent_22
v7
du_partialSetoid_292 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_292 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_292 T_IsCongruent_22
v0
  = (T_Setoid_44 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₁.refl
d_refl_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
d_refl_294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_294 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_294 T_IsCongruent_22
v7
du_refl_294 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
du_refl_294 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_294 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₁.reflexive
d_reflexive_296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_296 T_IsCongruent_22
v7
du_reflexive_296 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_296 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_296 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))
           AgdaAny
v2)
-- Function.Bundles._._.IsCongruent.Eq₁.setoid
d_setoid_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_44
d_setoid_298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 = (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_298
du_setoid_298 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_298 :: (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_298 AgdaAny -> AgdaAny
v0 T_IsCongruent_22
v1
  = (T_IsCongruent_22 -> T_Setoid_44)
-> T_IsCongruent_22 -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 T_IsCongruent_22
v1
-- Function.Bundles._._.IsCongruent.Eq₁.sym
d_sym_300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_300 T_IsCongruent_22
v7
du_sym_300 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_300 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_300 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₁.trans
d_trans_302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_302 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_302 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_302 T_IsCongruent_22
v7
du_trans_302 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_302 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_302 T_IsCongruent_22
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₂._≈_
d__'8776'__306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__306 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂._≉_
d__'8777'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__308 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂.Carrier
d_Carrier_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 -> ()
d_Carrier_310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
d_Carrier_310 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsCongruent.Eq₂.isEquivalence
d_isEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsEquivalence_26
d_isEquivalence_312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_312 T_IsCongruent_22
v7
du_isEquivalence_312 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_312 :: T_IsCongruent_22 -> T_IsEquivalence_26
du_isEquivalence_312 T_IsCongruent_22
v0
  = (T_IsCongruent_22 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0)
-- Function.Bundles._._.IsCongruent.Eq₂.isPartialEquivalence
d_isPartialEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_314 T_IsCongruent_22
v7
du_isPartialEquivalence_314 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_314 :: T_IsCongruent_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_314 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
         ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Function.Bundles._._.IsCongruent.Eq₂.partialSetoid
d_partialSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_PartialSetoid_10
d_partialSetoid_316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_316 T_IsCongruent_22
v7
du_partialSetoid_316 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_316 :: T_IsCongruent_22 -> T_PartialSetoid_10
du_partialSetoid_316 T_IsCongruent_22
v0
  = (T_Setoid_44 -> T_PartialSetoid_10)
-> AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₂.refl
d_refl_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
d_refl_318 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
d_refl_318 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_318 T_IsCongruent_22
v7
du_refl_318 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny
du_refl_318 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny
du_refl_318 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₂.reflexive
d_reflexive_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_320 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7
  = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_320 T_IsCongruent_22
v7
du_reflexive_320 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_320 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_320 T_IsCongruent_22
v0
  = let v1 :: t
v1
          = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
           ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))
           AgdaAny
v2)
-- Function.Bundles._._.IsCongruent.Eq₂.setoid
d_setoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_322 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> T_Setoid_44
d_setoid_322 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 = (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_322
du_setoid_322 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_322 :: (AgdaAny -> AgdaAny) -> T_IsCongruent_22 -> T_Setoid_44
du_setoid_322 AgdaAny -> AgdaAny
v0 T_IsCongruent_22
v1
  = (T_IsCongruent_22 -> T_Setoid_44)
-> T_IsCongruent_22 -> T_Setoid_44
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 T_IsCongruent_22
v1
-- Function.Bundles._._.IsCongruent.Eq₂.sym
d_sym_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_324 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_324 T_IsCongruent_22
v7
du_sym_324 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_324 :: T_IsCongruent_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_324 T_IsCongruent_22
v0
  = (T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsCongruent.Eq₂.trans
d_trans_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_326 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> T_IsCongruent_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_326 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 T_IsCongruent_22
v7 = T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_326 T_IsCongruent_22
v7
du_trans_326 ::
  MAlonzo.Code.Function.Structures.T_IsCongruent_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_326 :: T_IsCongruent_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_326 T_IsCongruent_22
v0
  = (T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v0))
-- Function.Bundles._._.IsInverse.Eq₁._≈_
d__'8776'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__412 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁._≉_
d__'8777'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__414 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__414 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁.Carrier
d_Carrier_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 -> ()
d_Carrier_416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Level_18
d_Carrier_416 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₁.isEquivalence
d_isEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsEquivalence_26
d_isEquivalence_418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_418 T_IsInverse_468
v8
du_isEquivalence_418 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_418 :: T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_418 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsInverse.Eq₁.isPartialEquivalence
d_isPartialEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_420 T_IsInverse_468
v8
du_isPartialEquivalence_420 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_420 :: T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_420 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Bundles._._.IsInverse.Eq₁.partialSetoid
d_partialSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_PartialSetoid_10
d_partialSetoid_422 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_422 T_IsInverse_468
v8
du_partialSetoid_422 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_422 :: T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_422 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₁.refl
d_refl_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny
d_refl_424 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
d_refl_424 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_424 T_IsInverse_468
v8
du_refl_424 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny
du_refl_424 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_424 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₁.reflexive
d_reflexive_426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_426 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_426 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_426 T_IsInverse_468
v8
du_reflexive_426 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_426 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_426 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsInverse.Eq₁.setoid
d_setoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Setoid_44
d_setoid_428 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468 -> T_Setoid_44
du_setoid_428 T_IsInverse_468
v8
du_setoid_428 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_428 :: T_IsInverse_468 -> T_Setoid_44
du_setoid_428 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_IsLeftInverse_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v1)))
-- Function.Bundles._._.IsInverse.Eq₁.sym
d_sym_430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_430 T_IsInverse_468
v8
du_sym_430 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_430 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_430 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₁.trans
d_trans_432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_432 T_IsInverse_468
v8
du_trans_432 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_432 :: T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_432 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₂._≈_
d__'8776'__436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> ()
d__'8776'__436 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__436 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂._≉_
d__'8777'__438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> ()
d__'8777'__438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__438 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂.Carrier
d_Carrier_440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 -> ()
d_Carrier_440 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Level_18
d_Carrier_440 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.IsInverse.Eq₂.isEquivalence
d_isEquivalence_442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsEquivalence_26
d_isEquivalence_442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_442 T_IsInverse_468
v8
du_isEquivalence_442 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_442 :: T_IsInverse_468 -> T_IsEquivalence_26
du_isEquivalence_442 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2)))
-- Function.Bundles._._.IsInverse.Eq₂.isPartialEquivalence
d_isPartialEquivalence_444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_444 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_444 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_IsInverse_468
v8
du_isPartialEquivalence_444 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_444 :: T_IsInverse_468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_444 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Function.Bundles._._.IsInverse.Eq₂.partialSetoid
d_partialSetoid_446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_446 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_PartialSetoid_10
d_partialSetoid_446 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_446 T_IsInverse_468
v8
du_partialSetoid_446 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_446 :: T_IsInverse_468 -> T_PartialSetoid_10
du_partialSetoid_446 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₂.refl
d_refl_448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny
d_refl_448 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
d_refl_448 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_448 T_IsInverse_468
v8
du_refl_448 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny
du_refl_448 :: T_IsInverse_468 -> AgdaAny -> AgdaAny
du_refl_448 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₂.reflexive
d_reflexive_450 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_450 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_450 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8
  = T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_450 T_IsInverse_468
v8
du_reflexive_450 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_450 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_450 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
                 AgdaAny
v4)))
-- Function.Bundles._._.IsInverse.Eq₂.setoid
d_setoid_452 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_452 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> T_Setoid_44
d_setoid_452 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468 -> T_Setoid_44
du_setoid_452 T_IsInverse_468
v8
du_setoid_452 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_452 :: T_IsInverse_468 -> T_Setoid_44
du_setoid_452 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_IsLeftInverse_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v1)))
-- Function.Bundles._._.IsInverse.Eq₂.sym
d_sym_454 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_454 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_454 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_454 T_IsInverse_468
v8
du_sym_454 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_454 :: T_IsInverse_468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_454 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._._.IsInverse.Eq₂.trans
d_trans_456 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_456 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsInverse_468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_456 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 ~AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny
v7 T_IsInverse_468
v8 = T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_456 T_IsInverse_468
v8
du_trans_456 ::
  MAlonzo.Code.Function.Structures.T_IsInverse_468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_456 :: T_IsInverse_468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_456 T_IsInverse_468
v0
  = let v1 :: T_IsLeftInverse_312
v1
          = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (T_IsInverse_468 -> T_IsInverse_468
forall a b. a -> b
coe T_IsInverse_468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCongruent_22
v2
             = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v2))))
-- Function.Bundles._.Func
d_Func_642 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Func_642 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Func_642
  = C_Func'46'constructor_5949 (AgdaAny -> AgdaAny)
                               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Func.f
d_f_648 :: T_Func_642 -> AgdaAny -> AgdaAny
d_f_648 :: T_Func_642 -> AgdaAny -> AgdaAny
d_f_648 T_Func_642
v0
  = case T_Func_642 -> T_Func_642
forall a b. a -> b
coe T_Func_642
v0 of
      C_Func'46'constructor_5949 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Func_642
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Func.cong
d_cong_650 ::
  T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_650 :: T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_650 T_Func_642
v0
  = case T_Func_642 -> T_Func_642
forall a b. a -> b
coe T_Func_642
v0 of
      C_Func'46'constructor_5949 AgdaAny -> AgdaAny
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_Func_642
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Func.isCongruent
d_isCongruent_652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_652 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_IsCongruent_22
d_isCongruent_652 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_isCongruent_652 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_652 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_650 (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1))
-- Function.Bundles._.Func._.Eq₁._≈_
d__'8776'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> ()
d__'8776'__658 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__658 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁._≉_
d__'8777'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> ()
d__'8777'__660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__660 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁.Carrier
d_Carrier_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> ()
d_Carrier_662 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_Level_18
d_Carrier_662 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.Eq₁.isEquivalence
d_isEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_664 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_IsEquivalence_26
d_isEquivalence_664 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsEquivalence_26
du_isEquivalence_664 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_isEquivalence_664 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_664 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsEquivalence_26
du_isEquivalence_664 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.Func._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_666 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_666 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Func_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_666 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_isPartialEquivalence_666 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_666 :: T_Setoid_44
-> T_Setoid_44 -> T_Func_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_666 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Func._.Eq₁.partialSetoid
d_partialSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_668 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_PartialSetoid_10
d_partialSetoid_668 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_PartialSetoid_10
du_partialSetoid_668 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_partialSetoid_668 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_668 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_PartialSetoid_10
du_partialSetoid_668 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny
d_refl_670 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
d_refl_670 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> AgdaAny -> AgdaAny
du_refl_670 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_refl_670 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny
du_refl_670 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> AgdaAny -> AgdaAny
du_refl_670 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_672 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_672 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_672 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_reflexive_672 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_672 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_672 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))
              AgdaAny
v5))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_674 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_Setoid_44
d_setoid_674 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_Setoid_44
du_setoid_674 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_setoid_674 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_674 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_Setoid_44
du_setoid_674 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_676 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_676 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_sym_676 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_676 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_676 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_678 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_678 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_trans_678 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_678 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_678 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> ()
d__'8776'__682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__682 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> ()
d__'8777'__684 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__684 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> ()
d_Carrier_686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_Level_18
d_Carrier_686 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_688 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_IsEquivalence_26
d_isEquivalence_688 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsEquivalence_26
du_isEquivalence_688 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_isEquivalence_688 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_688 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsEquivalence_26
du_isEquivalence_688 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_690 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_690 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Func_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_690 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_isPartialEquivalence_690 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_690 :: T_Setoid_44
-> T_Setoid_44 -> T_Func_642 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_690 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Func._.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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_692 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_PartialSetoid_10
d_partialSetoid_692 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_PartialSetoid_10
du_partialSetoid_692 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_partialSetoid_692 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_692 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_PartialSetoid_10
du_partialSetoid_692 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.Eq₂.refl
d_refl_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny
d_refl_694 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
d_refl_694 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> AgdaAny -> AgdaAny
du_refl_694 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_refl_694 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny
du_refl_694 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> AgdaAny -> AgdaAny
du_refl_694 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.Eq₂.reflexive
d_reflexive_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_696 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_696 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_696 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_reflexive_696 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_696 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_696 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))
              AgdaAny
v5))
-- Function.Bundles._.Func._.Eq₂.setoid
d_setoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> T_Setoid_44
d_setoid_698 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_Setoid_44
du_setoid_698 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_setoid_698 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_698 :: T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_Setoid_44
du_setoid_698 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
      ((T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2))
-- Function.Bundles._.Func._.Eq₂.sym
d_sym_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_700 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_700 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_700 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_sym_700 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_700 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_700 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Func._.Eq₂.trans
d_trans_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_702 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_702 T_Setoid_44
v4 T_Setoid_44
v5 T_Func_642
v6
du_trans_702 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Func_642 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_702 :: T_Setoid_44
-> T_Setoid_44
-> T_Func_642
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_702 T_Setoid_44
v0 T_Setoid_44
v1 T_Func_642
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Func_642 -> AgdaAny
forall a b. a -> b
coe T_Func_642
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Injection
d_Injection_704 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Injection_704 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Injection_704
  = C_Injection'46'constructor_8015 (AgdaAny -> AgdaAny)
                                    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Injection.f
d_f_712 :: T_Injection_704 -> AgdaAny -> AgdaAny
d_f_712 :: T_Injection_704 -> AgdaAny -> AgdaAny
d_f_712 T_Injection_704
v0
  = case T_Injection_704 -> T_Injection_704
forall a b. a -> b
coe T_Injection_704
v0 of
      C_Injection'46'constructor_8015 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Injection_704
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.cong
d_cong_714 ::
  T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_714 :: T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_714 T_Injection_704
v0
  = case T_Injection_704 -> T_Injection_704
forall a b. a -> b
coe T_Injection_704
v0 of
      C_Injection'46'constructor_8015 AgdaAny -> AgdaAny
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_Injection_704
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.injective
d_injective_716 ::
  T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_716 :: T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_716 T_Injection_704
v0
  = case T_Injection_704 -> T_Injection_704
forall a b. a -> b
coe T_Injection_704
v0 of
      C_Injection'46'constructor_8015 AgdaAny -> AgdaAny
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_Injection_704
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Injection.function
d_function_718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> T_Func_642
d_function_718 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_Func_642
d_function_718 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Injection_704
v6 = T_Injection_704 -> T_Func_642
du_function_718 T_Injection_704
v6
du_function_718 :: T_Injection_704 -> T_Func_642
du_function_718 :: T_Injection_704 -> T_Func_642
du_function_718 T_Injection_704
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_642)
-> AgdaAny -> AgdaAny -> T_Func_642
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_642
C_Func'46'constructor_5949 ((T_Injection_704 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_704 -> AgdaAny -> AgdaAny
d_f_712 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v0))
      ((T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_714 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v0))
-- Function.Bundles._.Injection._.isCongruent
d_isCongruent_722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_IsCongruent_22
d_isCongruent_722 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsCongruent_22
du_isCongruent_722 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_isCongruent_722 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_722 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsCongruent_22
du_isCongruent_722 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) ((T_Injection_704 -> T_Func_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2))
-- Function.Bundles._.Injection._.Eq₁._≈_
d__'8776'__726 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> ()
d__'8776'__726 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__726 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁._≉_
d__'8777'__728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> ()
d__'8777'__728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__728 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁.Carrier
d_Carrier_730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> ()
d_Carrier_730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_Level_18
d_Carrier_730 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₁.isEquivalence
d_isEquivalence_732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_IsEquivalence_26
d_isEquivalence_732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsEquivalence_26
du_isEquivalence_732 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_isEquivalence_732 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_732 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsEquivalence_26
du_isEquivalence_732 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Injection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_734 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Injection_704 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_734 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_isPartialEquivalence_734 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_734 :: T_Setoid_44
-> T_Setoid_44 -> T_Injection_704 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_734 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))
-- Function.Bundles._.Injection._.Eq₁.partialSetoid
d_partialSetoid_736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_736 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_PartialSetoid_10
d_partialSetoid_736 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_PartialSetoid_10
du_partialSetoid_736 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_partialSetoid_736 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_736 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_PartialSetoid_10
du_partialSetoid_736 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₁.refl
d_refl_738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny
d_refl_738 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
d_refl_738 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> AgdaAny -> AgdaAny
du_refl_738 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_refl_738 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny
du_refl_738 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> AgdaAny -> AgdaAny
du_refl_738 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₁.reflexive
d_reflexive_740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_740 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_740 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_740 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_reflexive_740 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_740 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_740 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Injection._.Eq₁.setoid
d_setoid_742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_742 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_Setoid_44
d_setoid_742 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_Setoid_44
du_setoid_742 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_setoid_742 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_742 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_Setoid_44
du_setoid_742 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Injection._.Eq₁.sym
d_sym_744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_744 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_744 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_744 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_sym_744 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_744 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_744 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₁.trans
d_trans_746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_746 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_746 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_746 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_trans_746 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_746 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_746 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₂._≈_
d__'8776'__750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> ()
d__'8776'__750 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__750 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂._≉_
d__'8777'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> ()
d__'8777'__752 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__752 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂.Carrier
d_Carrier_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> ()
d_Carrier_754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_Level_18
d_Carrier_754 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Injection._.Eq₂.isEquivalence
d_isEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_756 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_IsEquivalence_26
d_isEquivalence_756 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsEquivalence_26
du_isEquivalence_756 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_isEquivalence_756 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_756 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsEquivalence_26
du_isEquivalence_756 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4)))
-- Function.Bundles._.Injection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_758 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_758 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Injection_704 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_758 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_isPartialEquivalence_758 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_758 :: T_Setoid_44
-> T_Setoid_44 -> T_Injection_704 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_758 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
               ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5)))))
-- Function.Bundles._.Injection._.Eq₂.partialSetoid
d_partialSetoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_760 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_PartialSetoid_10
d_partialSetoid_760 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_PartialSetoid_10
du_partialSetoid_760 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_partialSetoid_760 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_760 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_PartialSetoid_10
du_partialSetoid_760 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
            ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₂.refl
d_refl_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny
d_refl_762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
d_refl_762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> AgdaAny -> AgdaAny
du_refl_762 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_refl_762 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny
du_refl_762 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> AgdaAny -> AgdaAny
du_refl_762 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₂.reflexive
d_reflexive_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_764 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_reflexive_764 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_764 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_764 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: t
v5
                = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
               (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                 ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v5))
                 AgdaAny
v6)))
-- Function.Bundles._.Injection._.Eq₂.setoid
d_setoid_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_Setoid_44
d_setoid_766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_Setoid_44
du_setoid_766 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_setoid_766 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_766 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_Setoid_44
du_setoid_766 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
         ((T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Injection._.Eq₂.sym
d_sym_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_768 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_sym_768 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_768 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_768 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection._.Eq₂.trans
d_trans_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_770 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_770 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_770 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_trans_770 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_770 :: T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_770 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = let v3 :: t
v3 = (T_Injection_704 -> T_Func_642) -> AgdaAny -> t
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4 = (T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Injection.isInjection
d_isInjection_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
d_isInjection_772 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Injection_704
-> T_IsInjection_92
d_isInjection_772 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsInjection_92
du_isInjection_772 T_Setoid_44
v4 T_Setoid_44
v5 T_Injection_704
v6
du_isInjection_772 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Injection_704 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
du_isInjection_772 :: T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsInjection_92
du_isInjection_772 T_Setoid_44
v0 T_Setoid_44
v1 T_Injection_704
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInjection_92)
-> AgdaAny -> AgdaAny -> T_IsInjection_92
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsInjection_92
MAlonzo.Code.Function.Structures.C_IsInjection'46'constructor_3991
      ((T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_Setoid_44 -> T_Func_642 -> T_IsCongruent_22
du_isCongruent_652 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
         ((T_Injection_704 -> T_Func_642) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_704 -> T_Func_642
du_function_718 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2)))
      ((T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Injection_704 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_716 (T_Injection_704 -> AgdaAny
forall a b. a -> b
coe T_Injection_704
v2))
-- Function.Bundles._.Surjection
d_Surjection_774 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Surjection_774 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Surjection_774
  = C_Surjection'46'constructor_10327 (AgdaAny -> AgdaAny)
                                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                      (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Function.Bundles._.Surjection.f
d_f_782 :: T_Surjection_774 -> AgdaAny -> AgdaAny
d_f_782 :: T_Surjection_774 -> AgdaAny -> AgdaAny
d_f_782 T_Surjection_774
v0
  = case T_Surjection_774 -> T_Surjection_774
forall a b. a -> b
coe T_Surjection_774
v0 of
      C_Surjection'46'constructor_10327 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Surjection_774
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.cong
d_cong_784 ::
  T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_784 :: T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_784 T_Surjection_774
v0
  = case T_Surjection_774 -> T_Surjection_774
forall a b. a -> b
coe T_Surjection_774
v0 of
      C_Surjection'46'constructor_10327 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_Surjection_774
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.surjective
d_surjective_786 ::
  T_Surjection_774 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_786 :: T_Surjection_774 -> AgdaAny -> T_Σ_14
d_surjective_786 T_Surjection_774
v0
  = case T_Surjection_774 -> T_Surjection_774
forall a b. a -> b
coe T_Surjection_774
v0 of
      C_Surjection'46'constructor_10327 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v3
      T_Surjection_774
_ -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Surjection.isCongruent
d_isCongruent_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_788 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_IsCongruent_22
d_isCongruent_788 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_isCongruent_788 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_788 :: T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_784 (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1))
-- Function.Bundles._.Surjection._.Eq₁._≈_
d__'8776'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> ()
d__'8776'__794 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__794 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁._≉_
d__'8777'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> ()
d__'8777'__796 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__796 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁.Carrier
d_Carrier_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> ()
d_Carrier_798 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_Level_18
d_Carrier_798 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₁.isEquivalence
d_isEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_800 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_IsEquivalence_26
d_isEquivalence_800 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsEquivalence_26
du_isEquivalence_800 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_isEquivalence_800 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_800 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsEquivalence_26
du_isEquivalence_800 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.Surjection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_802 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_802 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_802 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_isPartialEquivalence_802 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_802 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_802 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Surjection._.Eq₁.partialSetoid
d_partialSetoid_804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_804 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_PartialSetoid_10
d_partialSetoid_804 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_PartialSetoid_10
du_partialSetoid_804 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_partialSetoid_804 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_804 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_PartialSetoid_10
du_partialSetoid_804 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₁.refl
d_refl_806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny
d_refl_806 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
d_refl_806 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> AgdaAny -> AgdaAny
du_refl_806 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_refl_806 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny
du_refl_806 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> AgdaAny -> AgdaAny
du_refl_806 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₁.reflexive
d_reflexive_808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_808 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_808 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_reflexive_808 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_808 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_808 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))
              AgdaAny
v5))
-- Function.Bundles._.Surjection._.Eq₁.setoid
d_setoid_810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_810 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_Setoid_44
d_setoid_810 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_Setoid_44
du_setoid_810 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_setoid_810 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_810 :: T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_Setoid_44
du_setoid_810 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2))
-- Function.Bundles._.Surjection._.Eq₁.sym
d_sym_812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_812 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_812 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_sym_812 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_812 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_812 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₁.trans
d_trans_814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_814 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_814 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_814 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_trans_814 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_814 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_814 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₂._≈_
d__'8776'__818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> ()
d__'8776'__818 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__818 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂._≉_
d__'8777'__820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> ()
d__'8777'__820 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__820 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂.Carrier
d_Carrier_822 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> ()
d_Carrier_822 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_Level_18
d_Carrier_822 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Surjection._.Eq₂.isEquivalence
d_isEquivalence_824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_824 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_IsEquivalence_26
d_isEquivalence_824 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsEquivalence_26
du_isEquivalence_824 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_isEquivalence_824 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_824 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsEquivalence_26
du_isEquivalence_824 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.Surjection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_826 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_826 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_826 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_isPartialEquivalence_826 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_826 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_826 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.Surjection._.Eq₂.partialSetoid
d_partialSetoid_828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_828 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_PartialSetoid_10
d_partialSetoid_828 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_PartialSetoid_10
du_partialSetoid_828 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_partialSetoid_828 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_828 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_PartialSetoid_10
du_partialSetoid_828 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₂.refl
d_refl_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny
d_refl_830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
d_refl_830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> AgdaAny -> AgdaAny
du_refl_830 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_refl_830 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny
du_refl_830 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> AgdaAny -> AgdaAny
du_refl_830 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₂.reflexive
d_reflexive_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_832 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_832 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_832 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_reflexive_832 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_832 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_832 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))
              AgdaAny
v5))
-- Function.Bundles._.Surjection._.Eq₂.setoid
d_setoid_834 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_834 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_Setoid_44
d_setoid_834 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_Setoid_44
du_setoid_834 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_setoid_834 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_834 :: T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_Setoid_44
du_setoid_834 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
      ((T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2))
-- Function.Bundles._.Surjection._.Eq₂.sym
d_sym_836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_836 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_836 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_836 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_sym_836 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_836 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_836 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection._.Eq₂.trans
d_trans_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_838 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_trans_838 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_838 :: T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_838 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.Surjection.isSurjection
d_isSurjection_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
d_isSurjection_840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Surjection_774
-> T_IsSurjection_162
d_isSurjection_840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsSurjection_162
du_isSurjection_840 T_Setoid_44
v4 T_Setoid_44
v5 T_Surjection_774
v6
du_isSurjection_840 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Surjection_774 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
du_isSurjection_840 :: T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsSurjection_162
du_isSurjection_840 T_Setoid_44
v0 T_Setoid_44
v1 T_Surjection_774
v2
  = (T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      T_IsCongruent_22 -> (AgdaAny -> T_Σ_14) -> T_IsSurjection_162
MAlonzo.Code.Function.Structures.C_IsSurjection'46'constructor_6577
      ((T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Surjection_774 -> T_IsCongruent_22
du_isCongruent_788 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2))
      ((T_Surjection_774 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Surjection_774 -> AgdaAny -> T_Σ_14
d_surjective_786 (T_Surjection_774 -> AgdaAny
forall a b. a -> b
coe T_Surjection_774
v2))
-- Function.Bundles._.Bijection
d_Bijection_842 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Bijection_842 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Bijection_842
  = C_Bijection'46'constructor_12595 (AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Function.Bundles._.Bijection.f
d_f_850 :: T_Bijection_842 -> AgdaAny -> AgdaAny
d_f_850 :: T_Bijection_842 -> AgdaAny -> AgdaAny
d_f_850 T_Bijection_842
v0
  = case T_Bijection_842 -> T_Bijection_842
forall a b. a -> b
coe T_Bijection_842
v0 of
      C_Bijection'46'constructor_12595 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Bijection_842
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.cong
d_cong_852 ::
  T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 :: T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 T_Bijection_842
v0
  = case T_Bijection_842 -> T_Bijection_842
forall a b. a -> b
coe T_Bijection_842
v0 of
      C_Bijection'46'constructor_12595 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_Bijection_842
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.bijective
d_bijective_854 ::
  T_Bijection_842 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_bijective_854 :: T_Bijection_842 -> T_Σ_14
d_bijective_854 T_Bijection_842
v0
  = case T_Bijection_842 -> T_Bijection_842
forall a b. a -> b
coe T_Bijection_842
v0 of
      C_Bijection'46'constructor_12595 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 T_Σ_14
v3 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v3
      T_Bijection_842
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Bijection.injective
d_injective_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_injective_856 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_injective_856 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_842
v6 AgdaAny
v7 AgdaAny
v8
  = T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_856 T_Bijection_842
v6 AgdaAny
v7 AgdaAny
v8
du_injective_856 ::
  T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_856 :: T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_856 T_Bijection_842
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny)
-> T_Σ_14 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 (T_Bijection_842 -> T_Σ_14
d_bijective_854 (T_Bijection_842 -> T_Bijection_842
forall a b. a -> b
coe T_Bijection_842
v0))
      AgdaAny
v1 AgdaAny
v2
-- Function.Bundles._.Bijection.surjective
d_surjective_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_surjective_858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> T_Σ_14
d_surjective_858 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_842
v6 = T_Bijection_842 -> AgdaAny -> T_Σ_14
du_surjective_858 T_Bijection_842
v6
du_surjective_858 ::
  T_Bijection_842 ->
  AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_surjective_858 :: T_Bijection_842 -> AgdaAny -> T_Σ_14
du_surjective_858 T_Bijection_842
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_Bijection_842 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> T_Σ_14
d_bijective_854 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v0))
-- Function.Bundles._.Bijection.injection
d_injection_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> T_Injection_704
d_injection_860 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Injection_704
d_injection_860 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_842
v6 = T_Bijection_842 -> T_Injection_704
du_injection_860 T_Bijection_842
v6
du_injection_860 :: T_Bijection_842 -> T_Injection_704
du_injection_860 :: T_Bijection_842 -> T_Injection_704
du_injection_860 T_Bijection_842
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Injection_704)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Injection_704
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Injection_704
C_Injection'46'constructor_8015 ((T_Bijection_842 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> AgdaAny -> AgdaAny
d_f_850 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v0))
      ((T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v0)) ((T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_injective_856 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v0))
-- Function.Bundles._.Bijection.surjection
d_surjection_862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> T_Surjection_774
d_surjection_862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Surjection_774
d_surjection_862 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Bijection_842
v6 = T_Bijection_842 -> T_Surjection_774
du_surjection_862 T_Bijection_842
v6
du_surjection_862 :: T_Bijection_842 -> T_Surjection_774
du_surjection_862 :: T_Bijection_842 -> T_Surjection_774
du_surjection_862 T_Bijection_842
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_774)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_774
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_774
C_Surjection'46'constructor_10327 ((T_Bijection_842 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> AgdaAny -> AgdaAny
d_f_850 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v0))
      ((T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong_852 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v0)) ((T_Bijection_842 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> AgdaAny -> T_Σ_14
du_surjective_858 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v0))
-- Function.Bundles._.Bijection._.isInjection
d_isInjection_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
d_isInjection_866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_IsInjection_92
d_isInjection_866 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsInjection_92
du_isInjection_866 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_isInjection_866 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Function.Structures.T_IsInjection_92
du_isInjection_866 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsInjection_92
du_isInjection_866 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = (T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsInjection_92)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsInjection_92
forall a b. a -> b
coe
      T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsInjection_92
du_isInjection_772 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Bijection_842 -> T_Injection_704) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> T_Injection_704
du_injection_860 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2))
-- Function.Bundles._.Bijection._.isSurjection
d_isSurjection_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
d_isSurjection_870 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_IsSurjection_162
d_isSurjection_870 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsSurjection_162
du_isSurjection_870 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_isSurjection_870 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Function.Structures.T_IsSurjection_162
du_isSurjection_870 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsSurjection_162
du_isSurjection_870 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_Surjection_774 -> T_IsSurjection_162)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsSurjection_162
forall a b. a -> b
coe
      T_Setoid_44
-> T_Setoid_44 -> T_Surjection_774 -> T_IsSurjection_162
du_isSurjection_840 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Bijection_842 -> T_Surjection_774) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> T_Surjection_774
du_surjection_862 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2))
-- Function.Bundles._.Bijection.isBijection
d_isBijection_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232
d_isBijection_872 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_IsBijection_232
d_isBijection_872 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_isBijection_872 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Function.Structures.T_IsBijection_232
du_isBijection_872 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = (T_IsInjection_92 -> (AgdaAny -> T_Σ_14) -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe
      T_IsInjection_92 -> (AgdaAny -> T_Σ_14) -> T_IsBijection_232
MAlonzo.Code.Function.Structures.C_IsBijection'46'constructor_9159
      ((T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsInjection_92)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_Setoid_44 -> T_Injection_704 -> T_IsInjection_92
du_isInjection_772 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
         ((T_Bijection_842 -> T_Injection_704) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> T_Injection_704
du_injection_860 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2)))
      ((T_Bijection_842 -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Bijection_842 -> AgdaAny -> T_Σ_14
du_surjective_858 (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2))
-- Function.Bundles._.Bijection._.Eq₁._≈_
d__'8776'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> ()
d__'8776'__878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__878 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁._≉_
d__'8777'__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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> ()
d__'8777'__880 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__880 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁.Carrier
d_Carrier_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> ()
d_Carrier_882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Level_18
d_Carrier_882 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₁.isEquivalence
d_isEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_884 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_IsEquivalence_26
d_isEquivalence_884 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsEquivalence_26
du_isEquivalence_884 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_isEquivalence_884 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_884 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsEquivalence_26
du_isEquivalence_884 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Bijection._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_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 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Bijection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_886 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_isPartialEquivalence_886 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_886 :: T_Setoid_44
-> T_Setoid_44 -> T_Bijection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_886 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))
-- Function.Bundles._.Bijection._.Eq₁.partialSetoid
d_partialSetoid_888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_888 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_PartialSetoid_10
d_partialSetoid_888 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_PartialSetoid_10
du_partialSetoid_888 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_partialSetoid_888 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_888 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_PartialSetoid_10
du_partialSetoid_888 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₁.refl
d_refl_890 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny
d_refl_890 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
d_refl_890 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> AgdaAny -> AgdaAny
du_refl_890 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_refl_890 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny
du_refl_890 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> AgdaAny -> AgdaAny
du_refl_890 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₁.reflexive
d_reflexive_892 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_892 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_892 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_892 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_reflexive_892 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_892 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_892 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Bijection._.Eq₁.setoid
d_setoid_894 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_894 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Setoid_44
d_setoid_894 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_Setoid_44
du_setoid_894 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_setoid_894 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_894 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_Setoid_44
du_setoid_894 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
            ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v4))))
-- Function.Bundles._.Bijection._.Eq₁.sym
d_sym_896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_896 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_896 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_896 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_sym_896 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_896 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_896 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₁.trans
d_trans_898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_898 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_898 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_898 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_trans_898 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_898 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_898 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₂._≈_
d__'8776'__902 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> ()
d__'8776'__902 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__902 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂._≉_
d__'8777'__904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> ()
d__'8777'__904 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__904 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂.Carrier
d_Carrier_906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> ()
d_Carrier_906 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Level_18
d_Carrier_906 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Bijection._.Eq₂.isEquivalence
d_isEquivalence_908 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_908 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_IsEquivalence_26
d_isEquivalence_908 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsEquivalence_26
du_isEquivalence_908 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_isEquivalence_908 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_908 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsEquivalence_26
du_isEquivalence_908 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Bijection._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_910 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_910 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_910 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Bijection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_910 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_isPartialEquivalence_910 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_910 :: T_Setoid_44
-> T_Setoid_44 -> T_Bijection_842 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_910 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))
-- Function.Bundles._.Bijection._.Eq₂.partialSetoid
d_partialSetoid_912 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_912 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_PartialSetoid_10
d_partialSetoid_912 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_PartialSetoid_10
du_partialSetoid_912 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_partialSetoid_912 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_912 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_PartialSetoid_10
du_partialSetoid_912 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₂.refl
d_refl_914 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny
d_refl_914 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
d_refl_914 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> AgdaAny -> AgdaAny
du_refl_914 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_refl_914 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny
du_refl_914 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> AgdaAny -> AgdaAny
du_refl_914 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₂.reflexive
d_reflexive_916 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_916 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_916 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_916 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_reflexive_916 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_916 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_916 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Bijection._.Eq₂.setoid
d_setoid_918 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_918 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> T_Setoid_44
d_setoid_918 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_Setoid_44
du_setoid_918 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_setoid_918 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_918 :: T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_Setoid_44
du_setoid_918 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
            ((T_IsInjection_92 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> AgdaAny
forall a b. a -> b
coe T_IsInjection_92
v4))))
-- Function.Bundles._.Bijection._.Eq₂.sym
d_sym_920 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_920 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_920 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_920 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_sym_920 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_920 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_920 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Bijection._.Eq₂.trans
d_trans_922 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_922 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_922 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_922 T_Setoid_44
v4 T_Setoid_44
v5 T_Bijection_842
v6
du_trans_922 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Bijection_842 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_922 :: T_Setoid_44
-> T_Setoid_44
-> T_Bijection_842
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_922 T_Setoid_44
v0 T_Setoid_44
v1 T_Bijection_842
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Bijection_842 -> T_IsBijection_232
du_isBijection_872 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Bijection_842 -> AgdaAny
forall a b. a -> b
coe T_Bijection_842
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsInjection_92
v4
             = T_IsBijection_232 -> T_IsInjection_92
MAlonzo.Code.Function.Structures.d_isInjection_240 (AgdaAny -> T_IsBijection_232
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsInjection_92 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_100 (T_IsInjection_92 -> T_IsInjection_92
forall a b. a -> b
coe T_IsInjection_92
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Equivalence
d_Equivalence_924 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Equivalence_924 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Equivalence_924
  = C_Equivalence'46'constructor_16599 (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.Equivalence.f
d_f_934 :: T_Equivalence_924 -> AgdaAny -> AgdaAny
d_f_934 :: T_Equivalence_924 -> AgdaAny -> AgdaAny
d_f_934 T_Equivalence_924
v0
  = case T_Equivalence_924 -> T_Equivalence_924
forall a b. a -> b
coe T_Equivalence_924
v0 of
      C_Equivalence'46'constructor_16599 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Equivalence_924
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.g
d_g_936 :: T_Equivalence_924 -> AgdaAny -> AgdaAny
d_g_936 :: T_Equivalence_924 -> AgdaAny -> AgdaAny
d_g_936 T_Equivalence_924
v0
  = case T_Equivalence_924 -> T_Equivalence_924
forall a b. a -> b
coe T_Equivalence_924
v0 of
      C_Equivalence'46'constructor_16599 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_Equivalence_924
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.cong₁
d_cong'8321'_938 ::
  T_Equivalence_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_938 :: T_Equivalence_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_938 T_Equivalence_924
v0
  = case T_Equivalence_924 -> T_Equivalence_924
forall a b. a -> b
coe T_Equivalence_924
v0 of
      C_Equivalence'46'constructor_16599 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Equivalence_924
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Equivalence.cong₂
d_cong'8322'_940 ::
  T_Equivalence_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_940 :: T_Equivalence_924 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_940 T_Equivalence_924
v0
  = case T_Equivalence_924 -> T_Equivalence_924
forall a b. a -> b
coe T_Equivalence_924
v0 of
      C_Equivalence'46'constructor_16599 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Equivalence_924
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse
d_LeftInverse_942 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_LeftInverse_942 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_LeftInverse_942
  = C_LeftInverse'46'constructor_17795 (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny -> AgdaAny)
-- Function.Bundles._.LeftInverse.f
d_f_954 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_f_954 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_f_954 T_LeftInverse_942
v0
  = case T_LeftInverse_942 -> T_LeftInverse_942
forall a b. a -> b
coe T_LeftInverse_942
v0 of
      C_LeftInverse'46'constructor_17795 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_LeftInverse_942
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.g
d_g_956 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_g_956 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_g_956 T_LeftInverse_942
v0
  = case T_LeftInverse_942 -> T_LeftInverse_942
forall a b. a -> b
coe T_LeftInverse_942
v0 of
      C_LeftInverse'46'constructor_17795 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_LeftInverse_942
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.cong₁
d_cong'8321'_958 ::
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_958 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_958 T_LeftInverse_942
v0
  = case T_LeftInverse_942 -> T_LeftInverse_942
forall a b. a -> b
coe T_LeftInverse_942
v0 of
      C_LeftInverse'46'constructor_17795 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_LeftInverse_942
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.cong₂
d_cong'8322'_960 ::
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_960 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_960 T_LeftInverse_942
v0
  = case T_LeftInverse_942 -> T_LeftInverse_942
forall a b. a -> b
coe T_LeftInverse_942
v0 of
      C_LeftInverse'46'constructor_17795 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_LeftInverse_942
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.inverseˡ
d_inverse'737'_962 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_inverse'737'_962 :: T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_inverse'737'_962 T_LeftInverse_942
v0
  = case T_LeftInverse_942 -> T_LeftInverse_942
forall a b. a -> b
coe T_LeftInverse_942
v0 of
      C_LeftInverse'46'constructor_17795 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_LeftInverse_942
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.LeftInverse.isCongruent
d_isCongruent_964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_IsCongruent_22
d_isCongruent_964 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_isCongruent_964 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_964 :: T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_958 (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1))
-- Function.Bundles._.LeftInverse._.Eq₁._≈_
d__'8776'__970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> ()
d__'8776'__970 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__970 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁._≉_
d__'8777'__972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> ()
d__'8777'__972 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__972 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁.Carrier
d_Carrier_974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> ()
d_Carrier_974 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_Level_18
d_Carrier_974 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₁.isEquivalence
d_isEquivalence_976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_IsEquivalence_26
d_isEquivalence_976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsEquivalence_26
du_isEquivalence_976 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_isEquivalence_976 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_976 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsEquivalence_26
du_isEquivalence_976 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.LeftInverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_978 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_978 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_isPartialEquivalence_978 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_978 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_978 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.LeftInverse._.Eq₁.partialSetoid
d_partialSetoid_980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_PartialSetoid_10
d_partialSetoid_980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_PartialSetoid_10
du_partialSetoid_980 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_partialSetoid_980 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_980 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_PartialSetoid_10
du_partialSetoid_980 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₁.refl
d_refl_982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_refl_982 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
d_refl_982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> AgdaAny -> AgdaAny
du_refl_982 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_refl_982 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny
du_refl_982 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> AgdaAny -> AgdaAny
du_refl_982 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₁.reflexive
d_reflexive_984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_984 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_reflexive_984 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_984 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_984 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))
              AgdaAny
v5))
-- Function.Bundles._.LeftInverse._.Eq₁.setoid
d_setoid_986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_Setoid_44
d_setoid_986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_Setoid_44
du_setoid_986 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_setoid_986 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_986 :: T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_Setoid_44
du_setoid_986 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2))
-- Function.Bundles._.LeftInverse._.Eq₁.sym
d_sym_988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_988 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_sym_988 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_988 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_988 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₁.trans
d_trans_990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_990 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_trans_990 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_990 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_990 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₂._≈_
d__'8776'__994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> ()
d__'8776'__994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__994 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂._≉_
d__'8777'__996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> ()
d__'8777'__996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__996 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂.Carrier
d_Carrier_998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> ()
d_Carrier_998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_Level_18
d_Carrier_998 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.LeftInverse._.Eq₂.isEquivalence
d_isEquivalence_1000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_IsEquivalence_26
d_isEquivalence_1000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsEquivalence_26
du_isEquivalence_1000 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_isEquivalence_1000 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1000 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsEquivalence_26
du_isEquivalence_1000 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3))
-- Function.Bundles._.LeftInverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1002 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_isPartialEquivalence_1002 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1002 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1002 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
            ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))
-- Function.Bundles._.LeftInverse._.Eq₂.partialSetoid
d_partialSetoid_1004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1004 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_PartialSetoid_10
d_partialSetoid_1004 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_PartialSetoid_10
du_partialSetoid_1004 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_partialSetoid_1004 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1004 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_PartialSetoid_10
du_partialSetoid_1004 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₂.refl
d_refl_1006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_refl_1006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
d_refl_1006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> AgdaAny -> AgdaAny
du_refl_1006 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_refl_1006 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny
du_refl_1006 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> AgdaAny -> AgdaAny
du_refl_1006 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₂.reflexive
d_reflexive_1008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1008 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1008 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_reflexive_1008 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1008 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1008 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: t
v4
             = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
            (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
              ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))
              AgdaAny
v5))
-- Function.Bundles._.LeftInverse._.Eq₂.setoid
d_setoid_1010 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1010 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_Setoid_44
d_setoid_1010 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_Setoid_44
du_setoid_1010 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_setoid_1010 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1010 :: T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_Setoid_44
du_setoid_1010 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2))
-- Function.Bundles._.LeftInverse._.Eq₂.sym
d_sym_1012 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1012 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1012 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_sym_1012 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1012 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1012 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse._.Eq₂.trans
d_trans_1014 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1014 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6 = T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1014 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_trans_1014 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1014 :: T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1014 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = let v3 :: t
v3 = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
         ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))
-- Function.Bundles._.LeftInverse.isLeftInverse
d_isLeftInverse_1016 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_312
d_isLeftInverse_1016 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_IsLeftInverse_312
d_isLeftInverse_1016 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsLeftInverse_312
du_isLeftInverse_1016 T_Setoid_44
v4 T_Setoid_44
v5 T_LeftInverse_942
v6
du_isLeftInverse_1016 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_312
du_isLeftInverse_1016 :: T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsLeftInverse_312
du_isLeftInverse_1016 T_Setoid_44
v0 T_Setoid_44
v1 T_LeftInverse_942
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsLeftInverse_312)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_312
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.C_IsLeftInverse'46'constructor_13425
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsCongruent_22
du_isCongruent_964 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2))
      ((T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_960 (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2)) ((T_LeftInverse_942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_inverse'737'_962 (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v2))
-- Function.Bundles._.LeftInverse.equivalence
d_equivalence_1018 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_LeftInverse_942 -> T_Equivalence_924
d_equivalence_1018 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_LeftInverse_942
-> T_Equivalence_924
d_equivalence_1018 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_LeftInverse_942
v6
  = T_LeftInverse_942 -> T_Equivalence_924
du_equivalence_1018 T_LeftInverse_942
v6
du_equivalence_1018 :: T_LeftInverse_942 -> T_Equivalence_924
du_equivalence_1018 :: T_LeftInverse_942 -> T_Equivalence_924
du_equivalence_1018 T_LeftInverse_942
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_924)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_924
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_924
C_Equivalence'46'constructor_16599 ((T_LeftInverse_942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_f_954 (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v0))
      ((T_LeftInverse_942 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942 -> AgdaAny -> AgdaAny
d_g_956 (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v0)) ((T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_958 (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v0))
      ((T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_960 (T_LeftInverse_942 -> AgdaAny
forall a b. a -> b
coe T_LeftInverse_942
v0))
-- Function.Bundles._.RightInverse
d_RightInverse_1020 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_RightInverse_1020 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_RightInverse_1020
  = C_RightInverse'46'constructor_21353 (AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                        (AgdaAny -> AgdaAny)
-- Function.Bundles._.RightInverse.f
d_f_1032 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_f_1032 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_f_1032 T_RightInverse_1020
v0
  = case T_RightInverse_1020 -> T_RightInverse_1020
forall a b. a -> b
coe T_RightInverse_1020
v0 of
      C_RightInverse'46'constructor_21353 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_RightInverse_1020
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.g
d_g_1034 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_g_1034 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_g_1034 T_RightInverse_1020
v0
  = case T_RightInverse_1020 -> T_RightInverse_1020
forall a b. a -> b
coe T_RightInverse_1020
v0 of
      C_RightInverse'46'constructor_21353 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_RightInverse_1020
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.cong₁
d_cong'8321'_1036 ::
  T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1036 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1036 T_RightInverse_1020
v0
  = case T_RightInverse_1020 -> T_RightInverse_1020
forall a b. a -> b
coe T_RightInverse_1020
v0 of
      C_RightInverse'46'constructor_21353 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_RightInverse_1020
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.cong₂
d_cong'8322'_1038 ::
  T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1038 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1038 T_RightInverse_1020
v0
  = case T_RightInverse_1020 -> T_RightInverse_1020
forall a b. a -> b
coe T_RightInverse_1020
v0 of
      C_RightInverse'46'constructor_21353 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_RightInverse_1020
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.inverseʳ
d_inverse'691'_1040 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_inverse'691'_1040 :: T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_inverse'691'_1040 T_RightInverse_1020
v0
  = case T_RightInverse_1020 -> T_RightInverse_1020
forall a b. a -> b
coe T_RightInverse_1020
v0 of
      C_RightInverse'46'constructor_21353 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_RightInverse_1020
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.RightInverse.isCongruent
d_isCongruent_1042 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1020 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_isCongruent_1042 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1020
-> T_IsCongruent_22
d_isCongruent_1042 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1020
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1020 -> T_IsCongruent_22
du_isCongruent_1042 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1020
v6
du_isCongruent_1042 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1020 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_isCongruent_1042 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1020 -> T_IsCongruent_22
du_isCongruent_1042 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1020
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1036 (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v2))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1))
-- Function.Bundles._.RightInverse.isRightInverse
d_isRightInverse_1044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1020 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_390
d_isRightInverse_1044 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1020
-> T_IsRightInverse_390
d_isRightInverse_1044 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1020
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1020 -> T_IsRightInverse_390
du_isRightInverse_1044 T_Setoid_44
v4 T_Setoid_44
v5 T_RightInverse_1020
v6
du_isRightInverse_1044 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1020 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_390
du_isRightInverse_1044 :: T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1020 -> T_IsRightInverse_390
du_isRightInverse_1044 T_Setoid_44
v0 T_Setoid_44
v1 T_RightInverse_1020
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsRightInverse_390)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_390
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsRightInverse_390
MAlonzo.Code.Function.Structures.C_IsRightInverse'46'constructor_16843
      ((T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1020 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1020 -> T_IsCongruent_22
du_isCongruent_1042 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v2))
      ((T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1038 (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v2)) ((T_RightInverse_1020 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_inverse'691'_1040 (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v2))
-- Function.Bundles._.RightInverse.equivalence
d_equivalence_1046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_RightInverse_1020 -> T_Equivalence_924
d_equivalence_1046 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_RightInverse_1020
-> T_Equivalence_924
d_equivalence_1046 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_RightInverse_1020
v6
  = T_RightInverse_1020 -> T_Equivalence_924
du_equivalence_1046 T_RightInverse_1020
v6
du_equivalence_1046 :: T_RightInverse_1020 -> T_Equivalence_924
du_equivalence_1046 :: T_RightInverse_1020 -> T_Equivalence_924
du_equivalence_1046 T_RightInverse_1020
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_924)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_924
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_924
C_Equivalence'46'constructor_16599 ((T_RightInverse_1020 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_f_1032 (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v0))
      ((T_RightInverse_1020 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020 -> AgdaAny -> AgdaAny
d_g_1034 (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v0)) ((T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1036 (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v0))
      ((T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1038 (T_RightInverse_1020 -> AgdaAny
forall a b. a -> b
coe T_RightInverse_1020
v0))
-- Function.Bundles._.Inverse
d_Inverse_1048 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_Inverse_1048 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_Inverse_1048
  = C_Inverse'46'constructor_23693 (AgdaAny -> AgdaAny)
                                   (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                   MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
-- Function.Bundles._.Inverse.f
d_f_1060 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f_1060 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f_1060 T_Inverse_1048
v0
  = case T_Inverse_1048 -> T_Inverse_1048
forall a b. a -> b
coe T_Inverse_1048
v0 of
      C_Inverse'46'constructor_23693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_Inverse_1048
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.f⁻¹
d_f'8315''185'_1062 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f'8315''185'_1062 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f'8315''185'_1062 T_Inverse_1048
v0
  = case T_Inverse_1048 -> T_Inverse_1048
forall a b. a -> b
coe T_Inverse_1048
v0 of
      C_Inverse'46'constructor_23693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_Inverse_1048
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.cong₁
d_cong'8321'_1064 ::
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1064 :: T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1064 T_Inverse_1048
v0
  = case T_Inverse_1048 -> T_Inverse_1048
forall a b. a -> b
coe T_Inverse_1048
v0 of
      C_Inverse'46'constructor_23693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Inverse_1048
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.cong₂
d_cong'8322'_1066 ::
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1066 :: T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1066 T_Inverse_1048
v0
  = case T_Inverse_1048 -> T_Inverse_1048
forall a b. a -> b
coe T_Inverse_1048
v0 of
      C_Inverse'46'constructor_23693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Inverse_1048
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.inverse
d_inverse_1068 ::
  T_Inverse_1048 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1068 :: T_Inverse_1048 -> T_Σ_14
d_inverse_1068 T_Inverse_1048
v0
  = case T_Inverse_1048 -> T_Inverse_1048
forall a b. a -> b
coe T_Inverse_1048
v0 of
      C_Inverse'46'constructor_23693 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 T_Σ_14
v5 -> T_Σ_14 -> T_Σ_14
forall a b. a -> b
coe T_Σ_14
v5
      T_Inverse_1048
_ -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.Inverse.inverseˡ
d_inverse'737'_1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny
d_inverse'737'_1070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
d_inverse'737'_1070 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'737'_1070 T_Inverse_1048
v6
du_inverse'737'_1070 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'737'_1070 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'737'_1070 T_Inverse_1048
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_Inverse_1048 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> T_Σ_14
d_inverse_1068 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
-- Function.Bundles._.Inverse.inverseʳ
d_inverse'691'_1072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny
d_inverse'691'_1072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
d_inverse'691'_1072 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'691'_1072 T_Inverse_1048
v6
du_inverse'691'_1072 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'691'_1072 :: T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'691'_1072 T_Inverse_1048
v0
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
      ((T_Inverse_1048 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> T_Σ_14
d_inverse_1068 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
-- Function.Bundles._.Inverse.leftInverse
d_leftInverse_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> T_LeftInverse_942
d_leftInverse_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_LeftInverse_942
d_leftInverse_1074 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Inverse_1048 -> T_LeftInverse_942
du_leftInverse_1074 T_Inverse_1048
v6
du_leftInverse_1074 :: T_Inverse_1048 -> T_LeftInverse_942
du_leftInverse_1074 :: T_Inverse_1048 -> T_LeftInverse_942
du_leftInverse_1074 T_Inverse_1048
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_LeftInverse_942)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_LeftInverse_942
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_LeftInverse_942
C_LeftInverse'46'constructor_17795 ((T_Inverse_1048 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f_1060 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
      ((T_Inverse_1048 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f'8315''185'_1062 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0)) ((T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1064 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
      ((T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1066 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
      ((T_Inverse_1048 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'737'_1070 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
-- Function.Bundles._.Inverse.rightInverse
d_rightInverse_1076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> T_RightInverse_1020
d_rightInverse_1076 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_RightInverse_1020
d_rightInverse_1076 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Inverse_1048 -> T_RightInverse_1020
du_rightInverse_1076 T_Inverse_1048
v6
du_rightInverse_1076 :: T_Inverse_1048 -> T_RightInverse_1020
du_rightInverse_1076 :: T_Inverse_1048 -> T_RightInverse_1020
du_rightInverse_1076 T_Inverse_1048
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_RightInverse_1020)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_RightInverse_1020
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_RightInverse_1020
C_RightInverse'46'constructor_21353 ((T_Inverse_1048 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f_1060 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
      ((T_Inverse_1048 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny
d_f'8315''185'_1062 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0)) ((T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1064 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
      ((T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1066 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
      ((T_Inverse_1048 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'691'_1072 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v0))
-- Function.Bundles._.Inverse._.isLeftInverse
d_isLeftInverse_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_312
d_isLeftInverse_1080 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_IsLeftInverse_312
d_isLeftInverse_1080 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsLeftInverse_312
du_isLeftInverse_1080 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_isLeftInverse_1080 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Function.Structures.T_IsLeftInverse_312
du_isLeftInverse_1080 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsLeftInverse_312
du_isLeftInverse_1080 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsLeftInverse_312)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsLeftInverse_312
forall a b. a -> b
coe
      T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsLeftInverse_312
du_isLeftInverse_1016 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Inverse_1048 -> T_LeftInverse_942) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> T_LeftInverse_942
du_leftInverse_1074 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2))
-- Function.Bundles._.Inverse._.isRightInverse
d_isRightInverse_1084 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_390
d_isRightInverse_1084 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_IsRightInverse_390
d_isRightInverse_1084 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1048 -> T_IsRightInverse_390
du_isRightInverse_1084 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_isRightInverse_1084 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Function.Structures.T_IsRightInverse_390
du_isRightInverse_1084 :: T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1048 -> T_IsRightInverse_390
du_isRightInverse_1084 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = (T_Setoid_44
 -> T_Setoid_44 -> T_RightInverse_1020 -> T_IsRightInverse_390)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRightInverse_390
forall a b. a -> b
coe
      T_Setoid_44
-> T_Setoid_44 -> T_RightInverse_1020 -> T_IsRightInverse_390
du_isRightInverse_1044 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
      ((T_Inverse_1048 -> T_RightInverse_1020) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> T_RightInverse_1020
du_rightInverse_1076 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2))
-- Function.Bundles._.Inverse.isInverse
d_isInverse_1086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> MAlonzo.Code.Function.Structures.T_IsInverse_468
d_isInverse_1086 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_IsInverse_468
d_isInverse_1086 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_isInverse_1086 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> MAlonzo.Code.Function.Structures.T_IsInverse_468
du_isInverse_1086 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = (T_IsLeftInverse_312 -> (AgdaAny -> AgdaAny) -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe
      T_IsLeftInverse_312 -> (AgdaAny -> AgdaAny) -> T_IsInverse_468
MAlonzo.Code.Function.Structures.C_IsInverse'46'constructor_19781
      ((T_Setoid_44
 -> T_Setoid_44 -> T_LeftInverse_942 -> T_IsLeftInverse_312)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44
-> T_Setoid_44 -> T_LeftInverse_942 -> T_IsLeftInverse_312
du_isLeftInverse_1016 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1)
         ((T_Inverse_1048 -> T_LeftInverse_942) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> T_LeftInverse_942
du_leftInverse_1074 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2)))
      ((T_Inverse_1048 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048 -> AgdaAny -> AgdaAny
du_inverse'691'_1072 (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2))
-- Function.Bundles._.Inverse._.Eq₁._≈_
d__'8776'__1092 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1092 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1092 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁._≉_
d__'8777'__1094 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1094 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1094 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁.Carrier
d_Carrier_1096 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> ()
d_Carrier_1096 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_Level_18
d_Carrier_1096 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₁.isEquivalence
d_isEquivalence_1098 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1098 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_IsEquivalence_26
d_isEquivalence_1098 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsEquivalence_26
du_isEquivalence_1098 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_isEquivalence_1098 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1098 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsEquivalence_26
du_isEquivalence_1098 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Inverse._.Eq₁.isPartialEquivalence
d_isPartialEquivalence_1100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1100 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1100 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1048 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1100 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_isPartialEquivalence_1100 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1100 :: T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1048 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1100 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))
-- Function.Bundles._.Inverse._.Eq₁.partialSetoid
d_partialSetoid_1102 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1102 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_PartialSetoid_10
d_partialSetoid_1102 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_PartialSetoid_10
du_partialSetoid_1102 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_partialSetoid_1102 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1102 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_PartialSetoid_10
du_partialSetoid_1102 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₁.refl
d_refl_1104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny
d_refl_1104 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
d_refl_1104 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> AgdaAny -> AgdaAny
du_refl_1104 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_refl_1104 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny
du_refl_1104 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> AgdaAny -> AgdaAny
du_refl_1104 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₁.reflexive
d_reflexive_1106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1106 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1106 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1106 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_reflexive_1106 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1106 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1106 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Inverse._.Eq₁.setoid
d_setoid_1108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_Setoid_44
d_setoid_1108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_Setoid_44
du_setoid_1108 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_setoid_1108 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1108 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_Setoid_44
du_setoid_1108 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_40
            ((T_IsLeftInverse_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v4))))
-- Function.Bundles._.Inverse._.Eq₁.sym
d_sym_1110 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1110 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1110 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1110 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_sym_1110 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1110 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1110 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₁.trans
d_trans_1112 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1112 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1112 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1112 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_trans_1112 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1112 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1112 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8321'_34
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₂._≈_
d__'8776'__1116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1116 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8776'__1116 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂._≉_
d__'8777'__1118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1118 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
d__'8777'__1118 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂.Carrier
d_Carrier_1120 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> ()
d_Carrier_1120 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_Level_18
d_Carrier_1120 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.Inverse._.Eq₂.isEquivalence
d_isEquivalence_1122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1122 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_IsEquivalence_26
d_isEquivalence_1122 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsEquivalence_26
du_isEquivalence_1122 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_isEquivalence_1122 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1122 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsEquivalence_26
du_isEquivalence_1122 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
               (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5))))
-- Function.Bundles._.Inverse._.Eq₂.isPartialEquivalence
d_isPartialEquivalence_1124 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1124 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1124 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1048 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1124 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_isPartialEquivalence_1124 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1124 :: T_Setoid_44
-> T_Setoid_44 -> T_Inverse_1048 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1124 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                  ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))))))
-- Function.Bundles._.Inverse._.Eq₂.partialSetoid
d_partialSetoid_1126 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
d_partialSetoid_1126 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_PartialSetoid_10
d_partialSetoid_1126 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_PartialSetoid_10
du_partialSetoid_1126 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_partialSetoid_1126 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_PartialSetoid_10
du_partialSetoid_1126 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_PartialSetoid_10
du_partialSetoid_1126 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_PartialSetoid_10
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Setoid_44 -> T_PartialSetoid_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Setoid_44 -> T_PartialSetoid_10
MAlonzo.Code.Relation.Binary.Bundles.du_partialSetoid_74
               ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₂.refl
d_refl_1128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny
d_refl_1128 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
d_refl_1128 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> AgdaAny -> AgdaAny
du_refl_1128 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_refl_1128 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny
du_refl_1128 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> AgdaAny -> AgdaAny
du_refl_1128 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_34
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₂.reflexive
d_reflexive_1130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1130 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1130 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
  = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1130 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_reflexive_1130 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1130 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
du_reflexive_1130 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v6 :: t
v6
                   = (T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> t
forall a b. a -> b
coe T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66 (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                  (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                    ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v6))
                    AgdaAny
v7))))
-- Function.Bundles._.Inverse._.Eq₂.setoid
d_setoid_1132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1132 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> T_Setoid_44
d_setoid_1132 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_Setoid_44
du_setoid_1132 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_setoid_1132 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1132 :: T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_Setoid_44
du_setoid_1132 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCongruent_22 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCongruent_22 -> T_Setoid_44
MAlonzo.Code.Function.Structures.du_setoid_66
            ((T_IsLeftInverse_312 -> T_IsCongruent_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> AgdaAny
forall a b. a -> b
coe T_IsLeftInverse_312
v4))))
-- Function.Bundles._.Inverse._.Eq₂.sym
d_sym_1134 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1134 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1134 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1134 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_sym_1134 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1134 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_sym_1134 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_36
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.Inverse._.Eq₂.trans
d_trans_1136 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1136 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1136 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6 = T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1136 T_Setoid_44
v4 T_Setoid_44
v5 T_Inverse_1048
v6
du_trans_1136 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_Inverse_1048 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1136 :: T_Setoid_44
-> T_Setoid_44
-> T_Inverse_1048
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_trans_1136 T_Setoid_44
v0 T_Setoid_44
v1 T_Inverse_1048
v2
  = let v3 :: t
v3 = (T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468)
-> AgdaAny -> AgdaAny -> AgdaAny -> t
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_Inverse_1048 -> T_IsInverse_468
du_isInverse_1086 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_Inverse_1048 -> AgdaAny
forall a b. a -> b
coe T_Inverse_1048
v2) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v4 :: T_IsLeftInverse_312
v4
             = T_IsInverse_468 -> T_IsLeftInverse_312
MAlonzo.Code.Function.Structures.d_isLeftInverse_478 (AgdaAny -> T_IsInverse_468
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v5 :: T_IsCongruent_22
v5
                = T_IsLeftInverse_312 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.d_isCongruent_324 (T_IsLeftInverse_312 -> T_IsLeftInverse_312
forall a b. a -> b
coe T_IsLeftInverse_312
v4) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_26
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_26
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_38
               ((T_IsCongruent_22 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCongruent_22 -> T_IsEquivalence_26
MAlonzo.Code.Function.Structures.d_isEquivalence'8322'_36
                  (T_IsCongruent_22 -> AgdaAny
forall a b. a -> b
coe T_IsCongruent_22
v5)))))
-- Function.Bundles._.BiEquivalence
d_BiEquivalence_1138 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_BiEquivalence_1138 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_BiEquivalence_1138
  = C_BiEquivalence'46'constructor_28533 (AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Function.Bundles._.BiEquivalence.f
d_f_1152 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny
d_f_1152 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny
d_f_1152 T_BiEquivalence_1138
v0
  = case T_BiEquivalence_1138 -> T_BiEquivalence_1138
forall a b. a -> b
coe T_BiEquivalence_1138
v0 of
      C_BiEquivalence'46'constructor_28533 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_BiEquivalence_1138
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.g₁
d_g'8321'_1154 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny
d_g'8321'_1154 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny
d_g'8321'_1154 T_BiEquivalence_1138
v0
  = case T_BiEquivalence_1138 -> T_BiEquivalence_1138
forall a b. a -> b
coe T_BiEquivalence_1138
v0 of
      C_BiEquivalence'46'constructor_28533 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_BiEquivalence_1138
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.g₂
d_g'8322'_1156 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny
d_g'8322'_1156 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny
d_g'8322'_1156 T_BiEquivalence_1138
v0
  = case T_BiEquivalence_1138 -> T_BiEquivalence_1138
forall a b. a -> b
coe T_BiEquivalence_1138
v0 of
      C_BiEquivalence'46'constructor_28533 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_BiEquivalence_1138
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.cong₁
d_cong'8321'_1158 ::
  T_BiEquivalence_1138 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1158 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1158 T_BiEquivalence_1138
v0
  = case T_BiEquivalence_1138 -> T_BiEquivalence_1138
forall a b. a -> b
coe T_BiEquivalence_1138
v0 of
      C_BiEquivalence'46'constructor_28533 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BiEquivalence_1138
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.cong₂
d_cong'8322'_1160 ::
  T_BiEquivalence_1138 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1160 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1160 T_BiEquivalence_1138
v0
  = case T_BiEquivalence_1138 -> T_BiEquivalence_1138
forall a b. a -> b
coe T_BiEquivalence_1138
v0 of
      C_BiEquivalence'46'constructor_28533 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_BiEquivalence_1138
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiEquivalence.cong₃
d_cong'8323'_1162 ::
  T_BiEquivalence_1138 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_1162 :: T_BiEquivalence_1138 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_1162 T_BiEquivalence_1138
v0
  = case T_BiEquivalence_1138 -> T_BiEquivalence_1138
forall a b. a -> b
coe T_BiEquivalence_1138
v0 of
      C_BiEquivalence'46'constructor_28533 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
      T_BiEquivalence_1138
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse
d_BiInverse_1164 :: p -> p -> p -> p -> p -> p -> T_Level_18
d_BiInverse_1164 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
data T_BiInverse_1164
  = C_BiInverse'46'constructor_30623 (AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                     (AgdaAny -> AgdaAny)
-- Function.Bundles._.BiInverse.f
d_f_1182 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_f_1182 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_f_1182 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.g₁
d_g'8321'_1184 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_g'8321'_1184 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_g'8321'_1184 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.g₂
d_g'8322'_1186 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_g'8322'_1186 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_g'8322'_1186 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.cong₁
d_cong'8321'_1188 ::
  T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1188 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1188 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.cong₂
d_cong'8322'_1190 ::
  T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1190 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1190 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.cong₃
d_cong'8323'_1192 ::
  T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_1192 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_1192 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.inverseˡ
d_inverse'737'_1194 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_inverse'737'_1194 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_inverse'737'_1194 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v7
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.inverseʳ
d_inverse'691'_1196 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_inverse'691'_1196 :: T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_inverse'691'_1196 T_BiInverse_1164
v0
  = case T_BiInverse_1164 -> T_BiInverse_1164
forall a b. a -> b
coe T_BiInverse_1164
v0 of
      C_BiInverse'46'constructor_30623 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v8
      T_BiInverse_1164
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Function.Bundles._.BiInverse.f-isCongruent
d_f'45'isCongruent_1198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_BiInverse_1164 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
d_f'45'isCongruent_1198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_BiInverse_1164
-> T_IsCongruent_22
d_f'45'isCongruent_1198 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_1164
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_1164 -> T_IsCongruent_22
du_f'45'isCongruent_1198 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_1164
v6
du_f'45'isCongruent_1198 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_BiInverse_1164 ->
  MAlonzo.Code.Function.Structures.T_IsCongruent_22
du_f'45'isCongruent_1198 :: T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_1164 -> T_IsCongruent_22
du_f'45'isCongruent_1198 T_Setoid_44
v0 T_Setoid_44
v1 T_BiInverse_1164
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCongruent_22
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_26 -> T_IsEquivalence_26 -> T_IsCongruent_22
MAlonzo.Code.Function.Structures.C_IsCongruent'46'constructor_985
      ((T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1188 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v2))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0))
      ((T_Setoid_44 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Setoid_44 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1))
-- Function.Bundles._.BiInverse.isBiInverse
d_isBiInverse_1200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_BiInverse_1164 ->
  MAlonzo.Code.Function.Structures.T_IsBiInverse_636
d_isBiInverse_1200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_BiInverse_1164
-> T_IsBiInverse_636
d_isBiInverse_1200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_1164
v6
  = T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_1164 -> T_IsBiInverse_636
du_isBiInverse_1200 T_Setoid_44
v4 T_Setoid_44
v5 T_BiInverse_1164
v6
du_isBiInverse_1200 ::
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_BiInverse_1164 ->
  MAlonzo.Code.Function.Structures.T_IsBiInverse_636
du_isBiInverse_1200 :: T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_1164 -> T_IsBiInverse_636
du_isBiInverse_1200 T_Setoid_44
v0 T_Setoid_44
v1 T_BiInverse_1164
v2
  = (T_IsCongruent_22
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_IsBiInverse_636)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsBiInverse_636
forall a b. a -> b
coe
      T_IsCongruent_22
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_IsBiInverse_636
MAlonzo.Code.Function.Structures.C_IsBiInverse'46'constructor_29527
      ((T_Setoid_44
 -> T_Setoid_44 -> T_BiInverse_1164 -> T_IsCongruent_22)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Setoid_44 -> T_Setoid_44 -> T_BiInverse_1164 -> T_IsCongruent_22
du_f'45'isCongruent_1198 (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v0) (T_Setoid_44 -> AgdaAny
forall a b. a -> b
coe T_Setoid_44
v1) (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v2))
      ((T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1190 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v2)) ((T_BiInverse_1164 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_inverse'737'_1194 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v2))
      ((T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_1192 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v2)) ((T_BiInverse_1164 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_inverse'691'_1196 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v2))
-- Function.Bundles._.BiInverse.biEquivalence
d_biEquivalence_1202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44 ->
  T_BiInverse_1164 -> T_BiEquivalence_1138
d_biEquivalence_1202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Setoid_44
-> T_Setoid_44
-> T_BiInverse_1164
-> T_BiEquivalence_1138
d_biEquivalence_1202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~T_Setoid_44
v4 ~T_Setoid_44
v5 T_BiInverse_1164
v6
  = T_BiInverse_1164 -> T_BiEquivalence_1138
du_biEquivalence_1202 T_BiInverse_1164
v6
du_biEquivalence_1202 :: T_BiInverse_1164 -> T_BiEquivalence_1138
du_biEquivalence_1202 :: T_BiInverse_1164 -> T_BiEquivalence_1138
du_biEquivalence_1202 T_BiInverse_1164
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_BiEquivalence_1138)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_BiEquivalence_1138
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BiEquivalence_1138
C_BiEquivalence'46'constructor_28533 ((T_BiInverse_1164 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_f_1182 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v0))
      ((T_BiInverse_1164 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_g'8321'_1184 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v0)) ((T_BiInverse_1164 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny
d_g'8322'_1186 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v0))
      ((T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8321'_1188 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v0)) ((T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8322'_1190 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v0))
      ((T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_cong'8323'_1192 (T_BiInverse_1164 -> AgdaAny
forall a b. a -> b
coe T_BiInverse_1164
v0))
-- Function.Bundles._⟶_
d__'10230'__1204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'10230'__1204 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'10230'__1204 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↣_
d__'8611'__1210 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8611'__1210 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8611'__1210 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↠_
d__'8608'__1216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8608'__1216 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8608'__1216 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._⤖_
d__'10518'__1222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'10518'__1222 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'10518'__1222 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._⇔_
d__'8660'__1228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8660'__1228 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8660'__1228 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↩_
d__'8617'__1234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8617'__1234 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8617'__1234 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↪_
d__'8618'__1240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8618'__1240 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8618'__1240 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↩↪_
d__'8617''8618'__1246 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8617''8618'__1246 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8617''8618'__1246 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._↔_
d__'8596'__1252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> () -> () -> ()
d__'8596'__1252 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
d__'8596'__1252 = T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Bijective
d_Bijective_1272 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> () -> (AgdaAny -> AgdaAny) -> ()
d_Bijective_1272 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Bijective_1272 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Injective
d_Injective_1276 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> () -> (AgdaAny -> AgdaAny) -> ()
d_Injective_1276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Injective_1276 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Inverseʳ
d_Inverse'691'_1278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Inverse'691'_1278 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse'691'_1278 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Inverseˡ
d_Inverse'737'_1280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Inverse'737'_1280 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse'737'_1280 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Inverseᵇ
d_Inverse'7495'_1282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> () -> (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> ()
d_Inverse'7495'_1282 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Inverse'7495'_1282 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._._.Surjective
d_Surjective_1284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> (AgdaAny -> AgdaAny) -> ()
d_Surjective_1284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
d_Surjective_1284 = T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Function.Bundles._.mk⟶
d_mk'10230'_1286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () -> () -> (AgdaAny -> AgdaAny) -> T_Func_642
d_mk'10230'_1286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Func_642
d_mk'10230'_1286 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 = (AgdaAny -> AgdaAny) -> T_Func_642
du_mk'10230'_1286 AgdaAny -> AgdaAny
v4
du_mk'10230'_1286 :: (AgdaAny -> AgdaAny) -> T_Func_642
du_mk'10230'_1286 :: (AgdaAny -> AgdaAny) -> T_Func_642
du_mk'10230'_1286 AgdaAny -> AgdaAny
v0
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_642)
-> AgdaAny -> AgdaAny -> T_Func_642
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_Func_642
C_Func'46'constructor_5949 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased
-- Function.Bundles._.mk↣
d_mk'8611'_1292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Injection_704
d_mk'8611'_1292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_704
d_mk'8611'_1292 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v5 = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_704
du_mk'8611'_1292 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v5
du_mk'8611'_1292 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny ->
   AgdaAny ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 ->
   MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Injection_704
du_mk'8611'_1292 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12)
-> T_Injection_704
du_mk'8611'_1292 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Injection_704)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Injection_704
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Injection_704
C_Injection'46'constructor_8015 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased ((AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T__'8801'__12 -> T__'8801'__12
v1)
-- Function.Bundles._.mk↠
d_mk'8608'_1300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_774
d_mk'8608'_1300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_774
d_mk'8608'_1300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5 = (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_774
du_mk'8608'_1300 AgdaAny -> AgdaAny
v4 AgdaAny -> T_Σ_14
v5
du_mk'8608'_1300 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14) ->
  T_Surjection_774
du_mk'8608'_1300 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> T_Σ_14) -> T_Surjection_774
du_mk'8608'_1300 AgdaAny -> AgdaAny
v0 AgdaAny -> T_Σ_14
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> T_Σ_14)
 -> T_Surjection_774)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Surjection_774
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> T_Σ_14)
-> T_Surjection_774
C_Surjection'46'constructor_10327 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased ((AgdaAny -> T_Σ_14) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T_Σ_14
v1)
-- Function.Bundles._.mk⤖
d_mk'10518'_1308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Bijection_842
d_mk'10518'_1308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Bijection_842
d_mk'10518'_1308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 T_Σ_14
v5 = (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Bijection_842
du_mk'10518'_1308 AgdaAny -> AgdaAny
v4 T_Σ_14
v5
du_mk'10518'_1308 ::
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Bijection_842
du_mk'10518'_1308 :: (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Bijection_842
du_mk'10518'_1308 AgdaAny -> AgdaAny
v0 T_Σ_14
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Bijection_842)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Bijection_842
forall a b. a -> b
coe (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Bijection_842
C_Bijection'46'constructor_12595 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) AgdaAny
forall a. a
erased (T_Σ_14 -> AgdaAny
forall a b. a -> b
coe T_Σ_14
v1)
-- Function.Bundles._.mk⇔
d_mk'8660'_1318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_924
d_mk'8660'_1318 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Equivalence_924
d_mk'8660'_1318 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 = (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_924
du_mk'8660'_1318 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5
du_mk'8660'_1318 ::
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_924
du_mk'8660'_1318 :: (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny) -> T_Equivalence_924
du_mk'8660'_1318 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Equivalence_924)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Equivalence_924
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Equivalence_924
C_Equivalence'46'constructor_16599 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
-- Function.Bundles._.mk↩
d_mk'8617'_1328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_LeftInverse_942
d_mk'8617'_1328 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> T_LeftInverse_942
d_mk'8617'_1328 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> T__'8801'__12
v6
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> T_LeftInverse_942
du_mk'8617'_1328 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> T__'8801'__12
v6
du_mk'8617'_1328 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_LeftInverse_942
du_mk'8617'_1328 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> T_LeftInverse_942
du_mk'8617'_1328 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> T__'8801'__12
v2
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_LeftInverse_942)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_LeftInverse_942
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_LeftInverse_942
C_LeftInverse'46'constructor_17795 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
      ((AgdaAny -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T__'8801'__12
v2)
-- Function.Bundles._.mk↪
d_mk'8618'_1340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_RightInverse_1020
d_mk'8618'_1340 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> T_RightInverse_1020
d_mk'8618'_1340 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> T__'8801'__12
v6
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> T_RightInverse_1020
du_mk'8618'_1340 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> T__'8801'__12
v6
du_mk'8618'_1340 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_RightInverse_1020
du_mk'8618'_1340 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> T_RightInverse_1020
du_mk'8618'_1340 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> T__'8801'__12
v2
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_RightInverse_1020)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_RightInverse_1020
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_RightInverse_1020
C_RightInverse'46'constructor_21353 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
      ((AgdaAny -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T__'8801'__12
v2)
-- Function.Bundles._.mk↩↪
d_mk'8617''8618'_1354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_BiInverse_1164
d_mk'8617''8618'_1354 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> (AgdaAny -> T__'8801'__12)
-> T_BiInverse_1164
d_mk'8617''8618'_1354 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> T__'8801'__12
v7 AgdaAny -> T__'8801'__12
v8
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> (AgdaAny -> T__'8801'__12)
-> T_BiInverse_1164
du_mk'8617''8618'_1354 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny -> T__'8801'__12
v7 AgdaAny -> T__'8801'__12
v8
du_mk'8617''8618'_1354 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_BiInverse_1164
du_mk'8617''8618'_1354 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> (AgdaAny -> T__'8801'__12)
-> T_BiInverse_1164
du_mk'8617''8618'_1354 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> T__'8801'__12
v3 AgdaAny -> T__'8801'__12
v4
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> T_BiInverse_1164)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_BiInverse_1164
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_BiInverse_1164
C_BiInverse'46'constructor_30623 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2) AgdaAny
forall a. a
erased
      AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased ((AgdaAny -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T__'8801'__12
v3) ((AgdaAny -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T__'8801'__12
v4)
-- Function.Bundles._.mk↔
d_mk'8596'_1370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Inverse_1048
d_mk'8596'_1370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Inverse_1048
d_mk'8596'_1370 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_Σ_14
v6
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1048
du_mk'8596'_1370 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_Σ_14
v6
du_mk'8596'_1370 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> T_Inverse_1048
du_mk'8596'_1370 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1048
du_mk'8596'_1370 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 T_Σ_14
v2
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Inverse_1048)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_Inverse_1048
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Inverse_1048
C_Inverse'46'constructor_23693 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1) AgdaAny
forall a. a
erased AgdaAny
forall a. a
erased
      (T_Σ_14 -> AgdaAny
forall a b. a -> b
coe T_Σ_14
v2)
-- Function.Bundles._.mk↔′
d_mk'8596''8242'_1382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  () ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Inverse_1048
d_mk'8596''8242'_1382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> (AgdaAny -> T__'8801'__12)
-> T_Inverse_1048
d_mk'8596''8242'_1382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> T__'8801'__12
v6 AgdaAny -> T__'8801'__12
v7
  = (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> (AgdaAny -> T__'8801'__12)
-> T_Inverse_1048
du_mk'8596''8242'_1382 AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny
v5 AgdaAny -> T__'8801'__12
v6 AgdaAny -> T__'8801'__12
v7
du_mk'8596''8242'_1382 ::
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  (AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
  T_Inverse_1048
du_mk'8596''8242'_1382 :: (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> T__'8801'__12)
-> (AgdaAny -> T__'8801'__12)
-> T_Inverse_1048
du_mk'8596''8242'_1382 AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny -> T__'8801'__12
v2 AgdaAny -> T__'8801'__12
v3
  = ((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1048)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Inverse_1048
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> T_Σ_14 -> T_Inverse_1048
du_mk'8596'_1370 ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v0) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1)
      ((AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 ((AgdaAny -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T__'8801'__12
v2) ((AgdaAny -> T__'8801'__12) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> T__'8801'__12
v3))