{-# 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.Algebra.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.Algebra.Bundles.Raw
import qualified MAlonzo.Code.Algebra.Consequences.Base
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Data.Irrelevant
import qualified MAlonzo.Code.Data.Sum.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Bundles.Raw
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Bundles.SuccessorSet
d_SuccessorSet_8 :: p -> p -> ()
d_SuccessorSet_8 p
a0 p
a1 = ()
data T_SuccessorSet_8
  = C_constructor_68 (AgdaAny -> AgdaAny) AgdaAny
                     MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146
-- Algebra.Bundles.SuccessorSet.Carrier
d_Carrier_24 :: T_SuccessorSet_8 -> ()
d_Carrier_24 :: T_SuccessorSet_8 -> ()
d_Carrier_24 = T_SuccessorSet_8 -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._≈_
d__'8776'__26 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__26 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__26 = T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet.suc#
d_suc'35'_28 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 T_SuccessorSet_8
v0
  = case T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0 of
      C_constructor_68 AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsSuccessorSet_146
v5 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_SuccessorSet_8
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SuccessorSet.zero#
d_zero'35'_30 :: T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 :: T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 T_SuccessorSet_8
v0
  = case T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0 of
      C_constructor_68 AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsSuccessorSet_146
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_SuccessorSet_8
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SuccessorSet.isSuccessorSet
d_isSuccessorSet_32 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Algebra.Structures.T_IsSuccessorSet_146
d_isSuccessorSet_32 :: T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 T_SuccessorSet_8
v0
  = case T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0 of
      C_constructor_68 AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsSuccessorSet_146
v5 -> T_IsSuccessorSet_146 -> T_IsSuccessorSet_146
forall a b. a -> b
coe T_IsSuccessorSet_146
v5
      T_SuccessorSet_8
_ -> T_IsSuccessorSet_146
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SuccessorSet._.isEquivalence
d_isEquivalence_36 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_36 :: T_SuccessorSet_8 -> T_IsEquivalence_28
d_isEquivalence_36 T_SuccessorSet_8
v0
  = (T_IsSuccessorSet_146 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
      ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._.isPartialEquivalence
d_isPartialEquivalence_38 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_38 :: () -> () -> T_SuccessorSet_8 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_38 ~()
v0 ~()
v1 T_SuccessorSet_8
v2
  = T_SuccessorSet_8 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_38 T_SuccessorSet_8
v2
du_isPartialEquivalence_38 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_38 :: T_SuccessorSet_8 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_38 T_SuccessorSet_8
v0
  = let v1 :: T_IsSuccessorSet_146
v1 = T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v1)))
-- Algebra.Bundles.SuccessorSet._.refl
d_refl_40 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_refl_40 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_refl_40 T_SuccessorSet_8
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
         ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)))
-- Algebra.Bundles.SuccessorSet._.reflexive
d_reflexive_42 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_42 :: ()
-> ()
-> T_SuccessorSet_8
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_42 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_42 T_SuccessorSet_8
v2
du_reflexive_42 ::
  T_SuccessorSet_8 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_42 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_42 T_SuccessorSet_8
v0
  = let v1 :: T_IsSuccessorSet_146
v1 = T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156 (T_IsSuccessorSet_146 -> AgdaAny
forall a b. a -> b
coe T_IsSuccessorSet_146
v1))
           AgdaAny
v2)
-- Algebra.Bundles.SuccessorSet._.setoid
d_setoid_44 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_44 :: () -> () -> T_SuccessorSet_8 -> T_Setoid_46
d_setoid_44 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> T_Setoid_46
du_setoid_44 T_SuccessorSet_8
v2
du_setoid_44 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_44 :: T_SuccessorSet_8 -> T_Setoid_46
du_setoid_44 T_SuccessorSet_8
v0
  = (T_IsSuccessorSet_146 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsSuccessorSet_146 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_172
      ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._.suc#-cong
d_suc'35''45'cong_46 ::
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_46 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_suc'35''45'cong_46 T_SuccessorSet_8
v0
  = (T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSuccessorSet_146 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_suc'35''45'cong_158
      ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._.sym
d_sym_48 ::
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_48 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_48 T_SuccessorSet_8
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
         ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)))
-- Algebra.Bundles.SuccessorSet._.trans
d_trans_50 ::
  T_SuccessorSet_8 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_50 :: T_SuccessorSet_8
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_50 T_SuccessorSet_8
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsSuccessorSet_146 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSuccessorSet_146 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_156
         ((T_SuccessorSet_8 -> T_IsSuccessorSet_146) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> T_IsSuccessorSet_146
d_isSuccessorSet_32 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)))
-- Algebra.Bundles.SuccessorSet.rawSuccessorSet
d_rawSuccessorSet_52 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10
d_rawSuccessorSet_52 :: () -> () -> T_SuccessorSet_8 -> T_RawSuccessorSet_10
d_rawSuccessorSet_52 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> T_RawSuccessorSet_10
du_rawSuccessorSet_52 T_SuccessorSet_8
v2
du_rawSuccessorSet_52 ::
  T_SuccessorSet_8 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawSuccessorSet_10
du_rawSuccessorSet_52 :: T_SuccessorSet_8 -> T_RawSuccessorSet_10
du_rawSuccessorSet_52 T_SuccessorSet_8
v0
  = ((AgdaAny -> AgdaAny) -> AgdaAny -> T_RawSuccessorSet_10)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> T_RawSuccessorSet_10
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny) -> AgdaAny -> T_RawSuccessorSet_10
MAlonzo.Code.Algebra.Bundles.Raw.C_constructor_38
      (T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0)) (T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 (T_SuccessorSet_8 -> T_SuccessorSet_8
forall a b. a -> b
coe T_SuccessorSet_8
v0))
-- Algebra.Bundles.SuccessorSet._._≈_
d__'8776'__56 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__56 :: () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8776'__56 = () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._._≉_
d__'8777'__58 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8777'__58 :: () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
d__'8777'__58 = () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._.Carrier
d_Carrier_60 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_SuccessorSet_8 -> ()
d_Carrier_60 :: () -> () -> T_SuccessorSet_8 -> ()
d_Carrier_60 = () -> () -> T_SuccessorSet_8 -> ()
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._.rawSetoid
d_rawSetoid_62 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 ->
  MAlonzo.Code.Relation.Binary.Bundles.Raw.T_RawSetoid_12
d_rawSetoid_62 :: () -> () -> T_SuccessorSet_8 -> T_RawSetoid_12
d_rawSetoid_62 = () -> () -> T_SuccessorSet_8 -> T_RawSetoid_12
forall a. a
erased
-- Algebra.Bundles.SuccessorSet._.suc#
d_suc'35'_64 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_64 :: () -> () -> T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_64 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> AgdaAny -> AgdaAny
du_suc'35'_64 T_SuccessorSet_8
v2
du_suc'35'_64 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
du_suc'35'_64 :: T_SuccessorSet_8 -> AgdaAny -> AgdaAny
du_suc'35'_64 T_SuccessorSet_8
v0 = (T_SuccessorSet_8 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> AgdaAny -> AgdaAny
d_suc'35'_28 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)
-- Algebra.Bundles.SuccessorSet._.zero#
d_zero'35'_66 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SuccessorSet_8 -> AgdaAny
d_zero'35'_66 :: () -> () -> T_SuccessorSet_8 -> AgdaAny
d_zero'35'_66 ~()
v0 ~()
v1 T_SuccessorSet_8
v2 = T_SuccessorSet_8 -> AgdaAny
du_zero'35'_66 T_SuccessorSet_8
v2
du_zero'35'_66 :: T_SuccessorSet_8 -> AgdaAny
du_zero'35'_66 :: T_SuccessorSet_8 -> AgdaAny
du_zero'35'_66 T_SuccessorSet_8
v0 = (T_SuccessorSet_8 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8 -> AgdaAny
d_zero'35'_30 (T_SuccessorSet_8 -> AgdaAny
forall a b. a -> b
coe T_SuccessorSet_8
v0)
-- Algebra.Bundles.Magma
d_Magma_74 :: p -> p -> ()
d_Magma_74 p
a0 p
a1 = ()
data T_Magma_74
  = C_constructor_124 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsMagma_178
-- Algebra.Bundles.Magma.Carrier
d_Carrier_88 :: T_Magma_74 -> ()
d_Carrier_88 :: T_Magma_74 -> ()
d_Carrier_88 = T_Magma_74 -> ()
forall a. a
erased
-- Algebra.Bundles.Magma._≈_
d__'8776'__90 :: T_Magma_74 -> AgdaAny -> AgdaAny -> ()
d__'8776'__90 :: T_Magma_74 -> AgdaAny -> AgdaAny -> ()
d__'8776'__90 = T_Magma_74 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Magma._∙_
d__'8729'__92 :: T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__92 :: T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__92 T_Magma_74
v0
  = case T_Magma_74 -> T_Magma_74
forall a b. a -> b
coe T_Magma_74
v0 of
      C_constructor_124 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMagma_178
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Magma_74
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Magma.isMagma
d_isMagma_94 ::
  T_Magma_74 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_94 :: T_Magma_74 -> T_IsMagma_178
d_isMagma_94 T_Magma_74
v0
  = case T_Magma_74 -> T_Magma_74
forall a b. a -> b
coe T_Magma_74
v0 of
      C_constructor_124 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMagma_178
v4 -> T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4
      T_Magma_74
_ -> T_IsMagma_178
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Magma._.isEquivalence
d_isEquivalence_98 ::
  T_Magma_74 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_98 :: T_Magma_74 -> T_IsEquivalence_28
d_isEquivalence_98 T_Magma_74
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_Magma_74 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> AgdaAny
forall a b. a -> b
coe T_Magma_74
v0))
-- Algebra.Bundles.Magma._.isPartialEquivalence
d_isPartialEquivalence_100 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_74 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_100 :: () -> () -> T_Magma_74 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_100 ~()
v0 ~()
v1 T_Magma_74
v2
  = T_Magma_74 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_100 T_Magma_74
v2
du_isPartialEquivalence_100 ::
  T_Magma_74 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_100 :: T_Magma_74 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_100 T_Magma_74
v0
  = let v1 :: T_IsMagma_178
v1 = T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> T_Magma_74
forall a b. a -> b
coe T_Magma_74
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
         ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1)))
-- Algebra.Bundles.Magma._.refl
d_refl_102 :: T_Magma_74 -> AgdaAny -> AgdaAny
d_refl_102 :: T_Magma_74 -> AgdaAny -> AgdaAny
d_refl_102 T_Magma_74
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_Magma_74 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> AgdaAny
forall a b. a -> b
coe T_Magma_74
v0)))
-- Algebra.Bundles.Magma._.reflexive
d_reflexive_104 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_74 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_104 :: ()
-> ()
-> T_Magma_74
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_104 ~()
v0 ~()
v1 T_Magma_74
v2 = T_Magma_74 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_104 T_Magma_74
v2
du_reflexive_104 ::
  T_Magma_74 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_104 :: T_Magma_74 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_104 T_Magma_74
v0
  = let v1 :: T_IsMagma_178
v1 = T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> T_Magma_74
forall a b. a -> b
coe T_Magma_74
v0) in
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
           ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1))
           AgdaAny
v2)
-- Algebra.Bundles.Magma._.setoid
d_setoid_106 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_74 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_106 :: () -> () -> T_Magma_74 -> T_Setoid_46
d_setoid_106 ~()
v0 ~()
v1 T_Magma_74
v2 = T_Magma_74 -> T_Setoid_46
du_setoid_106 T_Magma_74
v2
du_setoid_106 ::
  T_Magma_74 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_106 :: T_Magma_74 -> T_Setoid_46
du_setoid_106 T_Magma_74
v0
  = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
      ((T_Magma_74 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> AgdaAny
forall a b. a -> b
coe T_Magma_74
v0))
-- Algebra.Bundles.Magma._.sym
d_sym_108 :: T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_108 :: T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_108 T_Magma_74
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_Magma_74 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> AgdaAny
forall a b. a -> b
coe T_Magma_74
v0)))
-- Algebra.Bundles.Magma._.trans
d_trans_110 ::
  T_Magma_74 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_110 :: T_Magma_74
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_110 T_Magma_74
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_Magma_74 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> AgdaAny
forall a b. a -> b
coe T_Magma_74
v0)))
-- Algebra.Bundles.Magma._.∙-cong
d_'8729''45'cong_112 ::
  T_Magma_74 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_112 :: T_Magma_74
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_112 T_Magma_74
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_Magma_74 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> AgdaAny
forall a b. a -> b
coe T_Magma_74
v0))
-- Algebra.Bundles.Magma._.∙-congʳ
d_'8729''45'cong'691'_114 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_114 :: ()
-> ()
-> T_Magma_74
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_114 ~()
v0 ~()
v1 T_Magma_74
v2
  = T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_114 T_Magma_74
v2
du_'8729''45'cong'691'_114 ::
  T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_114 :: T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_114 T_Magma_74
v0
  = let v1 :: T_IsMagma_178
v1 = T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> T_Magma_74
forall a b. a -> b
coe T_Magma_74
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
                = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Bundles.Magma._.∙-congˡ
d_'8729''45'cong'737'_116 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_116 :: ()
-> ()
-> T_Magma_74
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_116 ~()
v0 ~()
v1 T_Magma_74
v2
  = T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_116 T_Magma_74
v2
du_'8729''45'cong'737'_116 ::
  T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_116 :: T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_116 T_Magma_74
v0
  = let v1 :: T_IsMagma_178
v1 = T_Magma_74 -> T_IsMagma_178
d_isMagma_94 (T_Magma_74 -> T_Magma_74
forall a b. a -> b
coe T_Magma_74
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3
                = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v1) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
               ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v3)
               ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                  ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))))
-- Algebra.Bundles.Magma.rawMagma
d_rawMagma_118 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_74 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_118 :: () -> () -> T_Magma_74 -> T_RawMagma_44
d_rawMagma_118 ~()
v0 ~()
v1 T_Magma_74
v2 = T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 T_Magma_74
v2
du_rawMagma_118 ::
  T_Magma_74 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_118 :: T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 T_Magma_74
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_44)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_44
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_RawMagma_44
MAlonzo.Code.Algebra.Bundles.Raw.C_constructor_68
      (T_Magma_74 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__92 (T_Magma_74 -> T_Magma_74
forall a b. a -> b
coe T_Magma_74
v0))
-- Algebra.Bundles.Magma._._≉_
d__'8777'__122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Magma_74 -> AgdaAny -> AgdaAny -> ()
d__'8777'__122 :: () -> () -> T_Magma_74 -> AgdaAny -> AgdaAny -> ()
d__'8777'__122 = () -> () -> T_Magma_74 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma
d_SelectiveMagma_130 :: p -> p -> ()
d_SelectiveMagma_130 p
a0 p
a1 = ()
data T_SelectiveMagma_130
  = C_constructor_184 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450
-- Algebra.Bundles.SelectiveMagma.Carrier
d_Carrier_144 :: T_SelectiveMagma_130 -> ()
d_Carrier_144 :: T_SelectiveMagma_130 -> ()
d_Carrier_144 = T_SelectiveMagma_130 -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma._≈_
d__'8776'__146 :: T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> ()
d__'8776'__146 :: T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> ()
d__'8776'__146 = T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SelectiveMagma._∙_
d__'8729'__148 ::
  T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__148 :: T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__148 T_SelectiveMagma_130
v0
  = case T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0 of
      C_constructor_184 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSelectiveMagma_450
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SelectiveMagma_130
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SelectiveMagma.isSelectiveMagma
d_isSelectiveMagma_150 ::
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_450
d_isSelectiveMagma_150 :: T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 T_SelectiveMagma_130
v0
  = case T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0 of
      C_constructor_184 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSelectiveMagma_450
v4 -> T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v4
      T_SelectiveMagma_130
_ -> T_IsSelectiveMagma_450
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SelectiveMagma._.isEquivalence
d_isEquivalence_154 ::
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_154 :: T_SelectiveMagma_130 -> T_IsEquivalence_28
d_isEquivalence_154 T_SelectiveMagma_130
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458
         ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0)))
-- Algebra.Bundles.SelectiveMagma._.isMagma
d_isMagma_156 ::
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_156 :: T_SelectiveMagma_130 -> T_IsMagma_178
d_isMagma_156 T_SelectiveMagma_130
v0
  = (T_IsSelectiveMagma_450 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458
      ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0))
-- Algebra.Bundles.SelectiveMagma._.isPartialEquivalence
d_isPartialEquivalence_158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_158 :: () -> () -> T_SelectiveMagma_130 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_158 ~()
v0 ~()
v1 T_SelectiveMagma_130
v2
  = T_SelectiveMagma_130 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_158 T_SelectiveMagma_130
v2
du_isPartialEquivalence_158 ::
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_158 :: T_SelectiveMagma_130 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_158 T_SelectiveMagma_130
v0
  = let v1 :: T_IsSelectiveMagma_450
v1 = T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.SelectiveMagma._.refl
d_refl_160 :: T_SelectiveMagma_130 -> AgdaAny -> AgdaAny
d_refl_160 :: T_SelectiveMagma_130 -> AgdaAny -> AgdaAny
d_refl_160 T_SelectiveMagma_130
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458
            ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0))))
-- Algebra.Bundles.SelectiveMagma._.reflexive
d_reflexive_162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_130 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_162 :: ()
-> ()
-> T_SelectiveMagma_130
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_162 ~()
v0 ~()
v1 T_SelectiveMagma_130
v2 = T_SelectiveMagma_130
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_162 T_SelectiveMagma_130
v2
du_reflexive_162 ::
  T_SelectiveMagma_130 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_162 :: T_SelectiveMagma_130
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_162 T_SelectiveMagma_130
v0
  = let v1 :: T_IsSelectiveMagma_450
v1 = T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.SelectiveMagma._.sel
d_sel_164 ::
  T_SelectiveMagma_130 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
d_sel_164 :: T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> T__'8846'__30
d_sel_164 T_SelectiveMagma_130
v0
  = (T_IsSelectiveMagma_450 -> AgdaAny -> AgdaAny -> T__'8846'__30)
-> AgdaAny -> AgdaAny -> AgdaAny -> T__'8846'__30
forall a b. a -> b
coe
      T_IsSelectiveMagma_450 -> AgdaAny -> AgdaAny -> T__'8846'__30
MAlonzo.Code.Algebra.Structures.d_sel_460
      ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0))
-- Algebra.Bundles.SelectiveMagma._.setoid
d_setoid_166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_166 :: () -> () -> T_SelectiveMagma_130 -> T_Setoid_46
d_setoid_166 ~()
v0 ~()
v1 T_SelectiveMagma_130
v2 = T_SelectiveMagma_130 -> T_Setoid_46
du_setoid_166 T_SelectiveMagma_130
v2
du_setoid_166 ::
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_166 :: T_SelectiveMagma_130 -> T_Setoid_46
du_setoid_166 T_SelectiveMagma_130
v0
  = let v1 :: T_IsSelectiveMagma_450
v1 = T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> AgdaAny
forall a b. a -> b
coe T_IsSelectiveMagma_450
v1)))
-- Algebra.Bundles.SelectiveMagma._.sym
d_sym_168 ::
  T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 :: T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_168 T_SelectiveMagma_130
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458
            ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0))))
-- Algebra.Bundles.SelectiveMagma._.trans
d_trans_170 ::
  T_SelectiveMagma_130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 :: T_SelectiveMagma_130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_170 T_SelectiveMagma_130
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458
            ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0))))
-- Algebra.Bundles.SelectiveMagma._.∙-cong
d_'8729''45'cong_172 ::
  T_SelectiveMagma_130 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_172 :: T_SelectiveMagma_130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_172 T_SelectiveMagma_130
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSelectiveMagma_450 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458
         ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0)))
-- Algebra.Bundles.SelectiveMagma._.∙-congʳ
d_'8729''45'cong'691'_174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_174 :: ()
-> ()
-> T_SelectiveMagma_130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_174 ~()
v0 ~()
v1 T_SelectiveMagma_130
v2
  = T_SelectiveMagma_130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_174 T_SelectiveMagma_130
v2
du_'8729''45'cong'691'_174 ::
  T_SelectiveMagma_130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_174 :: T_SelectiveMagma_130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_174 T_SelectiveMagma_130
v0
  = let v1 :: T_IsSelectiveMagma_450
v1 = T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.SelectiveMagma._.∙-congˡ
d_'8729''45'cong'737'_176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_176 :: ()
-> ()
-> T_SelectiveMagma_130
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_176 ~()
v0 ~()
v1 T_SelectiveMagma_130
v2
  = T_SelectiveMagma_130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_176 T_SelectiveMagma_130
v2
du_'8729''45'cong'737'_176 ::
  T_SelectiveMagma_130 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_176 :: T_SelectiveMagma_130
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_176 T_SelectiveMagma_130
v0
  = let v1 :: T_IsSelectiveMagma_450
v1 = T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458 (T_IsSelectiveMagma_450 -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_IsSelectiveMagma_450
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.SelectiveMagma.magma
d_magma_178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_130 -> T_Magma_74
d_magma_178 :: () -> () -> T_SelectiveMagma_130 -> T_Magma_74
d_magma_178 ~()
v0 ~()
v1 T_SelectiveMagma_130
v2 = T_SelectiveMagma_130 -> T_Magma_74
du_magma_178 T_SelectiveMagma_130
v2
du_magma_178 :: T_SelectiveMagma_130 -> T_Magma_74
du_magma_178 :: T_SelectiveMagma_130 -> T_Magma_74
du_magma_178 T_SelectiveMagma_130
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_SelectiveMagma_130 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__148 (T_SelectiveMagma_130 -> T_SelectiveMagma_130
forall a b. a -> b
coe T_SelectiveMagma_130
v0))
      (T_IsSelectiveMagma_450 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_458
         ((T_SelectiveMagma_130 -> T_IsSelectiveMagma_450)
-> AgdaAny -> T_IsSelectiveMagma_450
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_IsSelectiveMagma_450
d_isSelectiveMagma_150 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0)))
-- Algebra.Bundles.SelectiveMagma._.rawMagma
d_rawMagma_182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_182 :: () -> () -> T_SelectiveMagma_130 -> T_RawMagma_44
d_rawMagma_182 ~()
v0 ~()
v1 T_SelectiveMagma_130
v2 = T_SelectiveMagma_130 -> T_RawMagma_44
du_rawMagma_182 T_SelectiveMagma_130
v2
du_rawMagma_182 ::
  T_SelectiveMagma_130 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_182 :: T_SelectiveMagma_130 -> T_RawMagma_44
du_rawMagma_182 T_SelectiveMagma_130
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_SelectiveMagma_130 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130 -> T_Magma_74
du_magma_178 (T_SelectiveMagma_130 -> AgdaAny
forall a b. a -> b
coe T_SelectiveMagma_130
v0))
-- Algebra.Bundles.CommutativeMagma
d_CommutativeMagma_190 :: p -> p -> ()
d_CommutativeMagma_190 p
a0 p
a1 = ()
data T_CommutativeMagma_190
  = C_constructor_244 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
-- Algebra.Bundles.CommutativeMagma.Carrier
d_Carrier_204 :: T_CommutativeMagma_190 -> ()
d_Carrier_204 :: T_CommutativeMagma_190 -> ()
d_Carrier_204 = T_CommutativeMagma_190 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMagma._≈_
d__'8776'__206 ::
  T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> ()
d__'8776'__206 :: T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> ()
d__'8776'__206 = T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMagma._∙_
d__'8729'__208 ::
  T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__208 :: T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__208 T_CommutativeMagma_190
v0
  = case T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0 of
      C_constructor_244 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeMagma_214
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeMagma_190
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMagma.isCommutativeMagma
d_isCommutativeMagma_210 ::
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_210 :: T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 T_CommutativeMagma_190
v0
  = case T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0 of
      C_constructor_244 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeMagma_214
v4 -> T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v4
      T_CommutativeMagma_190
_ -> T_IsCommutativeMagma_214
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMagma._.comm
d_comm_214 ::
  T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_214 :: T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_214 T_CommutativeMagma_190
v0
  = (T_IsCommutativeMagma_214 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMagma_214 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_224
      ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0))
-- Algebra.Bundles.CommutativeMagma._.isEquivalence
d_isEquivalence_216 ::
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_216 :: T_CommutativeMagma_190 -> T_IsEquivalence_28
d_isEquivalence_216 T_CommutativeMagma_190
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222
         ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0)))
-- Algebra.Bundles.CommutativeMagma._.isMagma
d_isMagma_218 ::
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_218 :: T_CommutativeMagma_190 -> T_IsMagma_178
d_isMagma_218 T_CommutativeMagma_190
v0
  = (T_IsCommutativeMagma_214 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222
      ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0))
-- Algebra.Bundles.CommutativeMagma._.isPartialEquivalence
d_isPartialEquivalence_220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_220 :: () -> () -> T_CommutativeMagma_190 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_220 ~()
v0 ~()
v1 T_CommutativeMagma_190
v2
  = T_CommutativeMagma_190 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_220 T_CommutativeMagma_190
v2
du_isPartialEquivalence_220 ::
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_220 :: T_CommutativeMagma_190 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_220 T_CommutativeMagma_190
v0
  = let v1 :: T_IsCommutativeMagma_214
v1 = T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.CommutativeMagma._.refl
d_refl_222 :: T_CommutativeMagma_190 -> AgdaAny -> AgdaAny
d_refl_222 :: T_CommutativeMagma_190 -> AgdaAny -> AgdaAny
d_refl_222 T_CommutativeMagma_190
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222
            ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0))))
-- Algebra.Bundles.CommutativeMagma._.reflexive
d_reflexive_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_190 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_224 :: ()
-> ()
-> T_CommutativeMagma_190
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_224 ~()
v0 ~()
v1 T_CommutativeMagma_190
v2 = T_CommutativeMagma_190
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_224 T_CommutativeMagma_190
v2
du_reflexive_224 ::
  T_CommutativeMagma_190 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_224 :: T_CommutativeMagma_190
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_224 T_CommutativeMagma_190
v0
  = let v1 :: T_IsCommutativeMagma_214
v1 = T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.CommutativeMagma._.setoid
d_setoid_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_226 :: () -> () -> T_CommutativeMagma_190 -> T_Setoid_46
d_setoid_226 ~()
v0 ~()
v1 T_CommutativeMagma_190
v2 = T_CommutativeMagma_190 -> T_Setoid_46
du_setoid_226 T_CommutativeMagma_190
v2
du_setoid_226 ::
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_226 :: T_CommutativeMagma_190 -> T_Setoid_46
du_setoid_226 T_CommutativeMagma_190
v0
  = let v1 :: T_IsCommutativeMagma_214
v1 = T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMagma_214
v1)))
-- Algebra.Bundles.CommutativeMagma._.sym
d_sym_228 ::
  T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_228 :: T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_228 T_CommutativeMagma_190
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222
            ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0))))
-- Algebra.Bundles.CommutativeMagma._.trans
d_trans_230 ::
  T_CommutativeMagma_190 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_230 :: T_CommutativeMagma_190
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_230 T_CommutativeMagma_190
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222
            ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0))))
-- Algebra.Bundles.CommutativeMagma._.∙-cong
d_'8729''45'cong_232 ::
  T_CommutativeMagma_190 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_232 :: T_CommutativeMagma_190
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_232 T_CommutativeMagma_190
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsCommutativeMagma_214 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222
         ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0)))
-- Algebra.Bundles.CommutativeMagma._.∙-congʳ
d_'8729''45'cong'691'_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_190 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_234 :: ()
-> ()
-> T_CommutativeMagma_190
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_234 ~()
v0 ~()
v1 T_CommutativeMagma_190
v2
  = T_CommutativeMagma_190
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_234 T_CommutativeMagma_190
v2
du_'8729''45'cong'691'_234 ::
  T_CommutativeMagma_190 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_234 :: T_CommutativeMagma_190
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_234 T_CommutativeMagma_190
v0
  = let v1 :: T_IsCommutativeMagma_214
v1 = T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.CommutativeMagma._.∙-congˡ
d_'8729''45'cong'737'_236 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_190 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_236 :: ()
-> ()
-> T_CommutativeMagma_190
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_236 ~()
v0 ~()
v1 T_CommutativeMagma_190
v2
  = T_CommutativeMagma_190
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_236 T_CommutativeMagma_190
v2
du_'8729''45'cong'737'_236 ::
  T_CommutativeMagma_190 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_236 :: T_CommutativeMagma_190
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_236 T_CommutativeMagma_190
v0
  = let v1 :: T_IsCommutativeMagma_214
v1 = T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222 (T_IsCommutativeMagma_214 -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_IsCommutativeMagma_214
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.CommutativeMagma.magma
d_magma_238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_190 -> T_Magma_74
d_magma_238 :: () -> () -> T_CommutativeMagma_190 -> T_Magma_74
d_magma_238 ~()
v0 ~()
v1 T_CommutativeMagma_190
v2 = T_CommutativeMagma_190 -> T_Magma_74
du_magma_238 T_CommutativeMagma_190
v2
du_magma_238 :: T_CommutativeMagma_190 -> T_Magma_74
du_magma_238 :: T_CommutativeMagma_190 -> T_Magma_74
du_magma_238 T_CommutativeMagma_190
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_CommutativeMagma_190 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__208 (T_CommutativeMagma_190 -> T_CommutativeMagma_190
forall a b. a -> b
coe T_CommutativeMagma_190
v0))
      (T_IsCommutativeMagma_214 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_222
         ((T_CommutativeMagma_190 -> T_IsCommutativeMagma_214)
-> AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_210 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0)))
-- Algebra.Bundles.CommutativeMagma._.rawMagma
d_rawMagma_242 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_242 :: () -> () -> T_CommutativeMagma_190 -> T_RawMagma_44
d_rawMagma_242 ~()
v0 ~()
v1 T_CommutativeMagma_190
v2 = T_CommutativeMagma_190 -> T_RawMagma_44
du_rawMagma_242 T_CommutativeMagma_190
v2
du_rawMagma_242 ::
  T_CommutativeMagma_190 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_242 :: T_CommutativeMagma_190 -> T_RawMagma_44
du_rawMagma_242 T_CommutativeMagma_190
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_CommutativeMagma_190 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190 -> T_Magma_74
du_magma_238 (T_CommutativeMagma_190 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMagma_190
v0))
-- Algebra.Bundles.IdempotentMagma
d_IdempotentMagma_250 :: p -> p -> ()
d_IdempotentMagma_250 p
a0 p
a1 = ()
data T_IdempotentMagma_250
  = C_constructor_304 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252
-- Algebra.Bundles.IdempotentMagma.Carrier
d_Carrier_264 :: T_IdempotentMagma_250 -> ()
d_Carrier_264 :: T_IdempotentMagma_250 -> ()
d_Carrier_264 = T_IdempotentMagma_250 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMagma._≈_
d__'8776'__266 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> ()
d__'8776'__266 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> ()
d__'8776'__266 = T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMagma._∙_
d__'8729'__268 ::
  T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__268 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__268 T_IdempotentMagma_250
v0
  = case T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0 of
      C_constructor_304 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsIdempotentMagma_252
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentMagma_250
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMagma.isIdempotentMagma
d_isIdempotentMagma_270 ::
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMagma_252
d_isIdempotentMagma_270 :: T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 T_IdempotentMagma_250
v0
  = case T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0 of
      C_constructor_304 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsIdempotentMagma_252
v4 -> T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v4
      T_IdempotentMagma_250
_ -> T_IsIdempotentMagma_252
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMagma._.idem
d_idem_274 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny
d_idem_274 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny
d_idem_274 T_IdempotentMagma_250
v0
  = (T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentMagma_252 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_262
      ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0))
-- Algebra.Bundles.IdempotentMagma._.isEquivalence
d_isEquivalence_276 ::
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_276 :: T_IdempotentMagma_250 -> T_IsEquivalence_28
d_isEquivalence_276 T_IdempotentMagma_250
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260
         ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0)))
-- Algebra.Bundles.IdempotentMagma._.isMagma
d_isMagma_278 ::
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_278 :: T_IdempotentMagma_250 -> T_IsMagma_178
d_isMagma_278 T_IdempotentMagma_250
v0
  = (T_IsIdempotentMagma_252 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260
      ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0))
-- Algebra.Bundles.IdempotentMagma._.isPartialEquivalence
d_isPartialEquivalence_280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_280 :: () -> () -> T_IdempotentMagma_250 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_280 ~()
v0 ~()
v1 T_IdempotentMagma_250
v2
  = T_IdempotentMagma_250 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_280 T_IdempotentMagma_250
v2
du_isPartialEquivalence_280 ::
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_280 :: T_IdempotentMagma_250 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_280 T_IdempotentMagma_250
v0
  = let v1 :: T_IsIdempotentMagma_252
v1 = T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.IdempotentMagma._.refl
d_refl_282 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny
d_refl_282 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny
d_refl_282 T_IdempotentMagma_250
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260
            ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0))))
-- Algebra.Bundles.IdempotentMagma._.reflexive
d_reflexive_284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_250 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_284 :: ()
-> ()
-> T_IdempotentMagma_250
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_284 ~()
v0 ~()
v1 T_IdempotentMagma_250
v2 = T_IdempotentMagma_250
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_284 T_IdempotentMagma_250
v2
du_reflexive_284 ::
  T_IdempotentMagma_250 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_284 :: T_IdempotentMagma_250
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_284 T_IdempotentMagma_250
v0
  = let v1 :: T_IsIdempotentMagma_252
v1 = T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.IdempotentMagma._.setoid
d_setoid_286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_286 :: () -> () -> T_IdempotentMagma_250 -> T_Setoid_46
d_setoid_286 ~()
v0 ~()
v1 T_IdempotentMagma_250
v2 = T_IdempotentMagma_250 -> T_Setoid_46
du_setoid_286 T_IdempotentMagma_250
v2
du_setoid_286 ::
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_286 :: T_IdempotentMagma_250 -> T_Setoid_46
du_setoid_286 T_IdempotentMagma_250
v0
  = let v1 :: T_IsIdempotentMagma_252
v1 = T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMagma_252
v1)))
-- Algebra.Bundles.IdempotentMagma._.sym
d_sym_288 ::
  T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_288 :: T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_288 T_IdempotentMagma_250
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260
            ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0))))
-- Algebra.Bundles.IdempotentMagma._.trans
d_trans_290 ::
  T_IdempotentMagma_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_290 :: T_IdempotentMagma_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_290 T_IdempotentMagma_250
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260
            ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0))))
-- Algebra.Bundles.IdempotentMagma._.∙-cong
d_'8729''45'cong_292 ::
  T_IdempotentMagma_250 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_292 :: T_IdempotentMagma_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_292 T_IdempotentMagma_250
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsIdempotentMagma_252 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260
         ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0)))
-- Algebra.Bundles.IdempotentMagma._.∙-congʳ
d_'8729''45'cong'691'_294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_294 :: ()
-> ()
-> T_IdempotentMagma_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_294 ~()
v0 ~()
v1 T_IdempotentMagma_250
v2
  = T_IdempotentMagma_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_294 T_IdempotentMagma_250
v2
du_'8729''45'cong'691'_294 ::
  T_IdempotentMagma_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_294 :: T_IdempotentMagma_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_294 T_IdempotentMagma_250
v0
  = let v1 :: T_IsIdempotentMagma_252
v1 = T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.IdempotentMagma._.∙-congˡ
d_'8729''45'cong'737'_296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_296 :: ()
-> ()
-> T_IdempotentMagma_250
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_296 ~()
v0 ~()
v1 T_IdempotentMagma_250
v2
  = T_IdempotentMagma_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_296 T_IdempotentMagma_250
v2
du_'8729''45'cong'737'_296 ::
  T_IdempotentMagma_250 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_296 :: T_IdempotentMagma_250
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_296 T_IdempotentMagma_250
v0
  = let v1 :: T_IsIdempotentMagma_252
v1 = T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260 (T_IsIdempotentMagma_252 -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IsIdempotentMagma_252
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.IdempotentMagma.magma
d_magma_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_250 -> T_Magma_74
d_magma_298 :: () -> () -> T_IdempotentMagma_250 -> T_Magma_74
d_magma_298 ~()
v0 ~()
v1 T_IdempotentMagma_250
v2 = T_IdempotentMagma_250 -> T_Magma_74
du_magma_298 T_IdempotentMagma_250
v2
du_magma_298 :: T_IdempotentMagma_250 -> T_Magma_74
du_magma_298 :: T_IdempotentMagma_250 -> T_Magma_74
du_magma_298 T_IdempotentMagma_250
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_IdempotentMagma_250 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__268 (T_IdempotentMagma_250 -> T_IdempotentMagma_250
forall a b. a -> b
coe T_IdempotentMagma_250
v0))
      (T_IsIdempotentMagma_252 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_260
         ((T_IdempotentMagma_250 -> T_IsIdempotentMagma_252)
-> AgdaAny -> T_IsIdempotentMagma_252
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_IsIdempotentMagma_252
d_isIdempotentMagma_270 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0)))
-- Algebra.Bundles.IdempotentMagma._.rawMagma
d_rawMagma_302 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_302 :: () -> () -> T_IdempotentMagma_250 -> T_RawMagma_44
d_rawMagma_302 ~()
v0 ~()
v1 T_IdempotentMagma_250
v2 = T_IdempotentMagma_250 -> T_RawMagma_44
du_rawMagma_302 T_IdempotentMagma_250
v2
du_rawMagma_302 ::
  T_IdempotentMagma_250 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_302 :: T_IdempotentMagma_250 -> T_RawMagma_44
du_rawMagma_302 T_IdempotentMagma_250
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_IdempotentMagma_250 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250 -> T_Magma_74
du_magma_298 (T_IdempotentMagma_250 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMagma_250
v0))
-- Algebra.Bundles.AlternativeMagma
d_AlternativeMagma_310 :: p -> p -> ()
d_AlternativeMagma_310 p
a0 p
a1 = ()
data T_AlternativeMagma_310
  = C_constructor_368 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290
-- Algebra.Bundles.AlternativeMagma.Carrier
d_Carrier_324 :: T_AlternativeMagma_310 -> ()
d_Carrier_324 :: T_AlternativeMagma_310 -> ()
d_Carrier_324 = T_AlternativeMagma_310 -> ()
forall a. a
erased
-- Algebra.Bundles.AlternativeMagma._≈_
d__'8776'__326 ::
  T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> ()
d__'8776'__326 :: T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> ()
d__'8776'__326 = T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AlternativeMagma._∙_
d__'8729'__328 ::
  T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__328 :: T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__328 T_AlternativeMagma_310
v0
  = case T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0 of
      C_constructor_368 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsAlternativeMagma_290
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_AlternativeMagma_310
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AlternativeMagma.isAlternativeMagma
d_isAlternativeMagma_330 ::
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Algebra.Structures.T_IsAlternativeMagma_290
d_isAlternativeMagma_330 :: T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 T_AlternativeMagma_310
v0
  = case T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0 of
      C_constructor_368 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsAlternativeMagma_290
v4 -> T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v4
      T_AlternativeMagma_310
_ -> T_IsAlternativeMagma_290
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AlternativeMagma._.alter
d_alter_334 ::
  T_AlternativeMagma_310 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_alter_334 :: T_AlternativeMagma_310 -> T_Σ_14
d_alter_334 T_AlternativeMagma_310
v0
  = (T_IsAlternativeMagma_290 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsAlternativeMagma_290 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_alter_300
      ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))
-- Algebra.Bundles.AlternativeMagma._.alternativeʳ
d_alternative'691'_336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'691'_336 :: () -> () -> T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'691'_336 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2 = T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_336 T_AlternativeMagma_310
v2
du_alternative'691'_336 ::
  T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_336 :: T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'691'_336 T_AlternativeMagma_310
v0
  = (T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_alternative'691'_326
      ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))
-- Algebra.Bundles.AlternativeMagma._.alternativeˡ
d_alternative'737'_338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'737'_338 :: () -> () -> T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
d_alternative'737'_338 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2 = T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_338 T_AlternativeMagma_310
v2
du_alternative'737'_338 ::
  T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_338 :: T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
du_alternative'737'_338 T_AlternativeMagma_310
v0
  = (T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAlternativeMagma_290 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_alternative'737'_324
      ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))
-- Algebra.Bundles.AlternativeMagma._.isEquivalence
d_isEquivalence_340 ::
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_340 :: T_AlternativeMagma_310 -> T_IsEquivalence_28
d_isEquivalence_340 T_AlternativeMagma_310
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298
         ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0)))
-- Algebra.Bundles.AlternativeMagma._.isMagma
d_isMagma_342 ::
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_342 :: T_AlternativeMagma_310 -> T_IsMagma_178
d_isMagma_342 T_AlternativeMagma_310
v0
  = (T_IsAlternativeMagma_290 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298
      ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))
-- Algebra.Bundles.AlternativeMagma._.isPartialEquivalence
d_isPartialEquivalence_344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_344 :: () -> () -> T_AlternativeMagma_310 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_344 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2
  = T_AlternativeMagma_310 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_344 T_AlternativeMagma_310
v2
du_isPartialEquivalence_344 ::
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_344 :: T_AlternativeMagma_310 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_344 T_AlternativeMagma_310
v0
  = let v1 :: T_IsAlternativeMagma_290
v1 = T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.AlternativeMagma._.refl
d_refl_346 :: T_AlternativeMagma_310 -> AgdaAny -> AgdaAny
d_refl_346 :: T_AlternativeMagma_310 -> AgdaAny -> AgdaAny
d_refl_346 T_AlternativeMagma_310
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298
            ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))))
-- Algebra.Bundles.AlternativeMagma._.reflexive
d_reflexive_348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_348 :: ()
-> ()
-> T_AlternativeMagma_310
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_348 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2 = T_AlternativeMagma_310
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_348 T_AlternativeMagma_310
v2
du_reflexive_348 ::
  T_AlternativeMagma_310 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_348 :: T_AlternativeMagma_310
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_348 T_AlternativeMagma_310
v0
  = let v1 :: T_IsAlternativeMagma_290
v1 = T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.AlternativeMagma._.setoid
d_setoid_350 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_350 :: () -> () -> T_AlternativeMagma_310 -> T_Setoid_46
d_setoid_350 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2 = T_AlternativeMagma_310 -> T_Setoid_46
du_setoid_350 T_AlternativeMagma_310
v2
du_setoid_350 ::
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_350 :: T_AlternativeMagma_310 -> T_Setoid_46
du_setoid_350 T_AlternativeMagma_310
v0
  = let v1 :: T_IsAlternativeMagma_290
v1 = T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> AgdaAny
forall a b. a -> b
coe T_IsAlternativeMagma_290
v1)))
-- Algebra.Bundles.AlternativeMagma._.sym
d_sym_352 ::
  T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_352 :: T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_352 T_AlternativeMagma_310
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298
            ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))))
-- Algebra.Bundles.AlternativeMagma._.trans
d_trans_354 ::
  T_AlternativeMagma_310 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_354 :: T_AlternativeMagma_310
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_354 T_AlternativeMagma_310
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298
            ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))))
-- Algebra.Bundles.AlternativeMagma._.∙-cong
d_'8729''45'cong_356 ::
  T_AlternativeMagma_310 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_356 :: T_AlternativeMagma_310
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_356 T_AlternativeMagma_310
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsAlternativeMagma_290 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298
         ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0)))
-- Algebra.Bundles.AlternativeMagma._.∙-congʳ
d_'8729''45'cong'691'_358 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_358 :: ()
-> ()
-> T_AlternativeMagma_310
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_358 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2
  = T_AlternativeMagma_310
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_358 T_AlternativeMagma_310
v2
du_'8729''45'cong'691'_358 ::
  T_AlternativeMagma_310 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_358 :: T_AlternativeMagma_310
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_358 T_AlternativeMagma_310
v0
  = let v1 :: T_IsAlternativeMagma_290
v1 = T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.AlternativeMagma._.∙-congˡ
d_'8729''45'cong'737'_360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_360 :: ()
-> ()
-> T_AlternativeMagma_310
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_360 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2
  = T_AlternativeMagma_310
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_360 T_AlternativeMagma_310
v2
du_'8729''45'cong'737'_360 ::
  T_AlternativeMagma_310 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_360 :: T_AlternativeMagma_310
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_360 T_AlternativeMagma_310
v0
  = let v1 :: T_IsAlternativeMagma_290
v1 = T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298 (T_IsAlternativeMagma_290 -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_IsAlternativeMagma_290
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.AlternativeMagma.magma
d_magma_362 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 -> T_Magma_74
d_magma_362 :: () -> () -> T_AlternativeMagma_310 -> T_Magma_74
d_magma_362 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2 = T_AlternativeMagma_310 -> T_Magma_74
du_magma_362 T_AlternativeMagma_310
v2
du_magma_362 :: T_AlternativeMagma_310 -> T_Magma_74
du_magma_362 :: T_AlternativeMagma_310 -> T_Magma_74
du_magma_362 T_AlternativeMagma_310
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_AlternativeMagma_310 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__328 (T_AlternativeMagma_310 -> T_AlternativeMagma_310
forall a b. a -> b
coe T_AlternativeMagma_310
v0))
      (T_IsAlternativeMagma_290 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_298
         ((T_AlternativeMagma_310 -> T_IsAlternativeMagma_290)
-> AgdaAny -> T_IsAlternativeMagma_290
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_IsAlternativeMagma_290
d_isAlternativeMagma_330 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0)))
-- Algebra.Bundles.AlternativeMagma._.rawMagma
d_rawMagma_366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_366 :: () -> () -> T_AlternativeMagma_310 -> T_RawMagma_44
d_rawMagma_366 ~()
v0 ~()
v1 T_AlternativeMagma_310
v2 = T_AlternativeMagma_310 -> T_RawMagma_44
du_rawMagma_366 T_AlternativeMagma_310
v2
du_rawMagma_366 ::
  T_AlternativeMagma_310 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_366 :: T_AlternativeMagma_310 -> T_RawMagma_44
du_rawMagma_366 T_AlternativeMagma_310
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_AlternativeMagma_310 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310 -> T_Magma_74
du_magma_362 (T_AlternativeMagma_310 -> AgdaAny
forall a b. a -> b
coe T_AlternativeMagma_310
v0))
-- Algebra.Bundles.FlexibleMagma
d_FlexibleMagma_374 :: p -> p -> ()
d_FlexibleMagma_374 p
a0 p
a1 = ()
data T_FlexibleMagma_374
  = C_constructor_428 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332
-- Algebra.Bundles.FlexibleMagma.Carrier
d_Carrier_388 :: T_FlexibleMagma_374 -> ()
d_Carrier_388 :: T_FlexibleMagma_374 -> ()
d_Carrier_388 = T_FlexibleMagma_374 -> ()
forall a. a
erased
-- Algebra.Bundles.FlexibleMagma._≈_
d__'8776'__390 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> ()
d__'8776'__390 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> ()
d__'8776'__390 = T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.FlexibleMagma._∙_
d__'8729'__392 ::
  T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__392 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__392 T_FlexibleMagma_374
v0
  = case T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0 of
      C_constructor_428 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsFlexibleMagma_332
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_FlexibleMagma_374
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.FlexibleMagma.isFlexibleMagma
d_isFlexibleMagma_394 ::
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Algebra.Structures.T_IsFlexibleMagma_332
d_isFlexibleMagma_394 :: T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 T_FlexibleMagma_374
v0
  = case T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0 of
      C_constructor_428 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsFlexibleMagma_332
v4 -> T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v4
      T_FlexibleMagma_374
_ -> T_IsFlexibleMagma_332
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.FlexibleMagma._.flex
d_flex_398 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_398 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> AgdaAny
d_flex_398 T_FlexibleMagma_374
v0
  = (T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsFlexibleMagma_332 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_flex_342
      ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0))
-- Algebra.Bundles.FlexibleMagma._.isEquivalence
d_isEquivalence_400 ::
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_400 :: T_FlexibleMagma_374 -> T_IsEquivalence_28
d_isEquivalence_400 T_FlexibleMagma_374
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340
         ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0)))
-- Algebra.Bundles.FlexibleMagma._.isMagma
d_isMagma_402 ::
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_402 :: T_FlexibleMagma_374 -> T_IsMagma_178
d_isMagma_402 T_FlexibleMagma_374
v0
  = (T_IsFlexibleMagma_332 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340
      ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0))
-- Algebra.Bundles.FlexibleMagma._.isPartialEquivalence
d_isPartialEquivalence_404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_404 :: () -> () -> T_FlexibleMagma_374 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_404 ~()
v0 ~()
v1 T_FlexibleMagma_374
v2
  = T_FlexibleMagma_374 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_404 T_FlexibleMagma_374
v2
du_isPartialEquivalence_404 ::
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_404 :: T_FlexibleMagma_374 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_404 T_FlexibleMagma_374
v0
  = let v1 :: T_IsFlexibleMagma_332
v1 = T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.FlexibleMagma._.refl
d_refl_406 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny
d_refl_406 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny
d_refl_406 T_FlexibleMagma_374
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340
            ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0))))
-- Algebra.Bundles.FlexibleMagma._.reflexive
d_reflexive_408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_374 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_408 :: ()
-> ()
-> T_FlexibleMagma_374
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_408 ~()
v0 ~()
v1 T_FlexibleMagma_374
v2 = T_FlexibleMagma_374
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_408 T_FlexibleMagma_374
v2
du_reflexive_408 ::
  T_FlexibleMagma_374 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_408 :: T_FlexibleMagma_374
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_408 T_FlexibleMagma_374
v0
  = let v1 :: T_IsFlexibleMagma_332
v1 = T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.FlexibleMagma._.setoid
d_setoid_410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_410 :: () -> () -> T_FlexibleMagma_374 -> T_Setoid_46
d_setoid_410 ~()
v0 ~()
v1 T_FlexibleMagma_374
v2 = T_FlexibleMagma_374 -> T_Setoid_46
du_setoid_410 T_FlexibleMagma_374
v2
du_setoid_410 ::
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_410 :: T_FlexibleMagma_374 -> T_Setoid_46
du_setoid_410 T_FlexibleMagma_374
v0
  = let v1 :: T_IsFlexibleMagma_332
v1 = T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> AgdaAny
forall a b. a -> b
coe T_IsFlexibleMagma_332
v1)))
-- Algebra.Bundles.FlexibleMagma._.sym
d_sym_412 ::
  T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_412 :: T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_412 T_FlexibleMagma_374
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340
            ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0))))
-- Algebra.Bundles.FlexibleMagma._.trans
d_trans_414 ::
  T_FlexibleMagma_374 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_414 :: T_FlexibleMagma_374
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_414 T_FlexibleMagma_374
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340
            ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0))))
-- Algebra.Bundles.FlexibleMagma._.∙-cong
d_'8729''45'cong_416 ::
  T_FlexibleMagma_374 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_416 :: T_FlexibleMagma_374
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_416 T_FlexibleMagma_374
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsFlexibleMagma_332 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340
         ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0)))
-- Algebra.Bundles.FlexibleMagma._.∙-congʳ
d_'8729''45'cong'691'_418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_374 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_418 :: ()
-> ()
-> T_FlexibleMagma_374
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_418 ~()
v0 ~()
v1 T_FlexibleMagma_374
v2
  = T_FlexibleMagma_374
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_418 T_FlexibleMagma_374
v2
du_'8729''45'cong'691'_418 ::
  T_FlexibleMagma_374 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_418 :: T_FlexibleMagma_374
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_418 T_FlexibleMagma_374
v0
  = let v1 :: T_IsFlexibleMagma_332
v1 = T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.FlexibleMagma._.∙-congˡ
d_'8729''45'cong'737'_420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_374 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_420 :: ()
-> ()
-> T_FlexibleMagma_374
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_420 ~()
v0 ~()
v1 T_FlexibleMagma_374
v2
  = T_FlexibleMagma_374
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_420 T_FlexibleMagma_374
v2
du_'8729''45'cong'737'_420 ::
  T_FlexibleMagma_374 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_420 :: T_FlexibleMagma_374
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_420 T_FlexibleMagma_374
v0
  = let v1 :: T_IsFlexibleMagma_332
v1 = T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340 (T_IsFlexibleMagma_332 -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_IsFlexibleMagma_332
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.FlexibleMagma.magma
d_magma_422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_374 -> T_Magma_74
d_magma_422 :: () -> () -> T_FlexibleMagma_374 -> T_Magma_74
d_magma_422 ~()
v0 ~()
v1 T_FlexibleMagma_374
v2 = T_FlexibleMagma_374 -> T_Magma_74
du_magma_422 T_FlexibleMagma_374
v2
du_magma_422 :: T_FlexibleMagma_374 -> T_Magma_74
du_magma_422 :: T_FlexibleMagma_374 -> T_Magma_74
du_magma_422 T_FlexibleMagma_374
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_FlexibleMagma_374 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__392 (T_FlexibleMagma_374 -> T_FlexibleMagma_374
forall a b. a -> b
coe T_FlexibleMagma_374
v0))
      (T_IsFlexibleMagma_332 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_340
         ((T_FlexibleMagma_374 -> T_IsFlexibleMagma_332)
-> AgdaAny -> T_IsFlexibleMagma_332
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_IsFlexibleMagma_332
d_isFlexibleMagma_394 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0)))
-- Algebra.Bundles.FlexibleMagma._.rawMagma
d_rawMagma_426 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_426 :: () -> () -> T_FlexibleMagma_374 -> T_RawMagma_44
d_rawMagma_426 ~()
v0 ~()
v1 T_FlexibleMagma_374
v2 = T_FlexibleMagma_374 -> T_RawMagma_44
du_rawMagma_426 T_FlexibleMagma_374
v2
du_rawMagma_426 ::
  T_FlexibleMagma_374 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_426 :: T_FlexibleMagma_374 -> T_RawMagma_44
du_rawMagma_426 T_FlexibleMagma_374
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_FlexibleMagma_374 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374 -> T_Magma_74
du_magma_422 (T_FlexibleMagma_374 -> AgdaAny
forall a b. a -> b
coe T_FlexibleMagma_374
v0))
-- Algebra.Bundles.MedialMagma
d_MedialMagma_434 :: p -> p -> ()
d_MedialMagma_434 p
a0 p
a1 = ()
data T_MedialMagma_434
  = C_constructor_488 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370
-- Algebra.Bundles.MedialMagma.Carrier
d_Carrier_448 :: T_MedialMagma_434 -> ()
d_Carrier_448 :: T_MedialMagma_434 -> ()
d_Carrier_448 = T_MedialMagma_434 -> ()
forall a. a
erased
-- Algebra.Bundles.MedialMagma._≈_
d__'8776'__450 :: T_MedialMagma_434 -> AgdaAny -> AgdaAny -> ()
d__'8776'__450 :: T_MedialMagma_434 -> AgdaAny -> AgdaAny -> ()
d__'8776'__450 = T_MedialMagma_434 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.MedialMagma._∙_
d__'8729'__452 ::
  T_MedialMagma_434 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__452 :: T_MedialMagma_434 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__452 T_MedialMagma_434
v0
  = case T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0 of
      C_constructor_488 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMedialMagma_370
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_MedialMagma_434
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MedialMagma.isMedialMagma
d_isMedialMagma_454 ::
  T_MedialMagma_434 ->
  MAlonzo.Code.Algebra.Structures.T_IsMedialMagma_370
d_isMedialMagma_454 :: T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 T_MedialMagma_434
v0
  = case T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0 of
      C_constructor_488 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsMedialMagma_370
v4 -> T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v4
      T_MedialMagma_434
_ -> T_IsMedialMagma_370
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.MedialMagma._.isEquivalence
d_isEquivalence_458 ::
  T_MedialMagma_434 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_458 :: T_MedialMagma_434 -> T_IsEquivalence_28
d_isEquivalence_458 T_MedialMagma_434
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378
         ((T_MedialMagma_434 -> T_IsMedialMagma_370) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0)))
-- Algebra.Bundles.MedialMagma._.isMagma
d_isMagma_460 ::
  T_MedialMagma_434 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_460 :: T_MedialMagma_434 -> T_IsMagma_178
d_isMagma_460 T_MedialMagma_434
v0
  = (T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378
      ((T_MedialMagma_434 -> T_IsMedialMagma_370) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0))
-- Algebra.Bundles.MedialMagma._.isPartialEquivalence
d_isPartialEquivalence_462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_434 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_462 :: () -> () -> T_MedialMagma_434 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_462 ~()
v0 ~()
v1 T_MedialMagma_434
v2
  = T_MedialMagma_434 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_462 T_MedialMagma_434
v2
du_isPartialEquivalence_462 ::
  T_MedialMagma_434 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_462 :: T_MedialMagma_434 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_462 T_MedialMagma_434
v0
  = let v1 :: T_IsMedialMagma_370
v1 = T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.MedialMagma._.medial
d_medial_464 ::
  T_MedialMagma_434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_464 :: T_MedialMagma_434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_medial_464 T_MedialMagma_434
v0
  = (T_IsMedialMagma_370
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMedialMagma_370
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_medial_380
      ((T_MedialMagma_434 -> T_IsMedialMagma_370) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0))
-- Algebra.Bundles.MedialMagma._.refl
d_refl_466 :: T_MedialMagma_434 -> AgdaAny -> AgdaAny
d_refl_466 :: T_MedialMagma_434 -> AgdaAny -> AgdaAny
d_refl_466 T_MedialMagma_434
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378
            ((T_MedialMagma_434 -> T_IsMedialMagma_370) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0))))
-- Algebra.Bundles.MedialMagma._.reflexive
d_reflexive_468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_434 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_468 :: ()
-> ()
-> T_MedialMagma_434
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_468 ~()
v0 ~()
v1 T_MedialMagma_434
v2 = T_MedialMagma_434 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_468 T_MedialMagma_434
v2
du_reflexive_468 ::
  T_MedialMagma_434 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_468 :: T_MedialMagma_434 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_468 T_MedialMagma_434
v0
  = let v1 :: T_IsMedialMagma_370
v1 = T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.MedialMagma._.setoid
d_setoid_470 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_434 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_470 :: () -> () -> T_MedialMagma_434 -> T_Setoid_46
d_setoid_470 ~()
v0 ~()
v1 T_MedialMagma_434
v2 = T_MedialMagma_434 -> T_Setoid_46
du_setoid_470 T_MedialMagma_434
v2
du_setoid_470 ::
  T_MedialMagma_434 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_470 :: T_MedialMagma_434 -> T_Setoid_46
du_setoid_470 T_MedialMagma_434
v0
  = let v1 :: T_IsMedialMagma_370
v1 = T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> AgdaAny
forall a b. a -> b
coe T_IsMedialMagma_370
v1)))
-- Algebra.Bundles.MedialMagma._.sym
d_sym_472 ::
  T_MedialMagma_434 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_472 :: T_MedialMagma_434 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_472 T_MedialMagma_434
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378
            ((T_MedialMagma_434 -> T_IsMedialMagma_370) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0))))
-- Algebra.Bundles.MedialMagma._.trans
d_trans_474 ::
  T_MedialMagma_434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_474 :: T_MedialMagma_434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_474 T_MedialMagma_434
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378
            ((T_MedialMagma_434 -> T_IsMedialMagma_370) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0))))
-- Algebra.Bundles.MedialMagma._.∙-cong
d_'8729''45'cong_476 ::
  T_MedialMagma_434 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_476 :: T_MedialMagma_434
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_476 T_MedialMagma_434
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsMedialMagma_370 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378
         ((T_MedialMagma_434 -> T_IsMedialMagma_370) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0)))
-- Algebra.Bundles.MedialMagma._.∙-congʳ
d_'8729''45'cong'691'_478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_478 :: ()
-> ()
-> T_MedialMagma_434
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_478 ~()
v0 ~()
v1 T_MedialMagma_434
v2
  = T_MedialMagma_434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_478 T_MedialMagma_434
v2
du_'8729''45'cong'691'_478 ::
  T_MedialMagma_434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_478 :: T_MedialMagma_434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_478 T_MedialMagma_434
v0
  = let v1 :: T_IsMedialMagma_370
v1 = T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.MedialMagma._.∙-congˡ
d_'8729''45'cong'737'_480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_480 :: ()
-> ()
-> T_MedialMagma_434
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_480 ~()
v0 ~()
v1 T_MedialMagma_434
v2
  = T_MedialMagma_434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_480 T_MedialMagma_434
v2
du_'8729''45'cong'737'_480 ::
  T_MedialMagma_434 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_480 :: T_MedialMagma_434
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_480 T_MedialMagma_434
v0
  = let v1 :: T_IsMedialMagma_370
v1 = T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378 (T_IsMedialMagma_370 -> T_IsMedialMagma_370
forall a b. a -> b
coe T_IsMedialMagma_370
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.MedialMagma.magma
d_magma_482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_434 -> T_Magma_74
d_magma_482 :: () -> () -> T_MedialMagma_434 -> T_Magma_74
d_magma_482 ~()
v0 ~()
v1 T_MedialMagma_434
v2 = T_MedialMagma_434 -> T_Magma_74
du_magma_482 T_MedialMagma_434
v2
du_magma_482 :: T_MedialMagma_434 -> T_Magma_74
du_magma_482 :: T_MedialMagma_434 -> T_Magma_74
du_magma_482 T_MedialMagma_434
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_MedialMagma_434 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__452 (T_MedialMagma_434 -> T_MedialMagma_434
forall a b. a -> b
coe T_MedialMagma_434
v0))
      (T_IsMedialMagma_370 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_378
         ((T_MedialMagma_434 -> T_IsMedialMagma_370)
-> AgdaAny -> T_IsMedialMagma_370
forall a b. a -> b
coe T_MedialMagma_434 -> T_IsMedialMagma_370
d_isMedialMagma_454 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0)))
-- Algebra.Bundles.MedialMagma._.rawMagma
d_rawMagma_486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MedialMagma_434 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_486 :: () -> () -> T_MedialMagma_434 -> T_RawMagma_44
d_rawMagma_486 ~()
v0 ~()
v1 T_MedialMagma_434
v2 = T_MedialMagma_434 -> T_RawMagma_44
du_rawMagma_486 T_MedialMagma_434
v2
du_rawMagma_486 ::
  T_MedialMagma_434 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_486 :: T_MedialMagma_434 -> T_RawMagma_44
du_rawMagma_486 T_MedialMagma_434
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_MedialMagma_434 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434 -> T_Magma_74
du_magma_482 (T_MedialMagma_434 -> AgdaAny
forall a b. a -> b
coe T_MedialMagma_434
v0))
-- Algebra.Bundles.SemimedialMagma
d_SemimedialMagma_494 :: p -> p -> ()
d_SemimedialMagma_494 p
a0 p
a1 = ()
data T_SemimedialMagma_494
  = C_constructor_552 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408
-- Algebra.Bundles.SemimedialMagma.Carrier
d_Carrier_508 :: T_SemimedialMagma_494 -> ()
d_Carrier_508 :: T_SemimedialMagma_494 -> ()
d_Carrier_508 = T_SemimedialMagma_494 -> ()
forall a. a
erased
-- Algebra.Bundles.SemimedialMagma._≈_
d__'8776'__510 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> ()
d__'8776'__510 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> ()
d__'8776'__510 = T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.SemimedialMagma._∙_
d__'8729'__512 ::
  T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__512 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__512 T_SemimedialMagma_494
v0
  = case T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0 of
      C_constructor_552 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemimedialMagma_408
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_SemimedialMagma_494
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemimedialMagma.isSemimedialMagma
d_isSemimedialMagma_514 ::
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemimedialMagma_408
d_isSemimedialMagma_514 :: T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 T_SemimedialMagma_494
v0
  = case T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0 of
      C_constructor_552 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemimedialMagma_408
v4 -> T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v4
      T_SemimedialMagma_494
_ -> T_IsSemimedialMagma_408
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.SemimedialMagma._.isEquivalence
d_isEquivalence_518 ::
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_518 :: T_SemimedialMagma_494 -> T_IsEquivalence_28
d_isEquivalence_518 T_SemimedialMagma_494
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416
         ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0)))
-- Algebra.Bundles.SemimedialMagma._.isMagma
d_isMagma_520 ::
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_520 :: T_SemimedialMagma_494 -> T_IsMagma_178
d_isMagma_520 T_SemimedialMagma_494
v0
  = (T_IsSemimedialMagma_408 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416
      ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))
-- Algebra.Bundles.SemimedialMagma._.isPartialEquivalence
d_isPartialEquivalence_522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_522 :: () -> () -> T_SemimedialMagma_494 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_522 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2
  = T_SemimedialMagma_494 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_522 T_SemimedialMagma_494
v2
du_isPartialEquivalence_522 ::
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_522 :: T_SemimedialMagma_494 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_522 T_SemimedialMagma_494
v0
  = let v1 :: T_IsSemimedialMagma_408
v1 = T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.SemimedialMagma._.refl
d_refl_524 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny
d_refl_524 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny
d_refl_524 T_SemimedialMagma_494
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416
            ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))))
-- Algebra.Bundles.SemimedialMagma._.reflexive
d_reflexive_526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_526 :: ()
-> ()
-> T_SemimedialMagma_494
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_526 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2 = T_SemimedialMagma_494
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_526 T_SemimedialMagma_494
v2
du_reflexive_526 ::
  T_SemimedialMagma_494 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_526 :: T_SemimedialMagma_494
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_526 T_SemimedialMagma_494
v0
  = let v1 :: T_IsSemimedialMagma_408
v1 = T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.SemimedialMagma._.semiMedial
d_semiMedial_528 ::
  T_SemimedialMagma_494 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_semiMedial_528 :: T_SemimedialMagma_494 -> T_Σ_14
d_semiMedial_528 T_SemimedialMagma_494
v0
  = (T_IsSemimedialMagma_408 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsSemimedialMagma_408 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_semiMedial_418
      ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))
-- Algebra.Bundles.SemimedialMagma._.semimedialʳ
d_semimedial'691'_530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'691'_530 :: ()
-> ()
-> T_SemimedialMagma_494
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'691'_530 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2 = T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_530 T_SemimedialMagma_494
v2
du_semimedial'691'_530 ::
  T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_530 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'691'_530 T_SemimedialMagma_494
v0
  = (T_IsSemimedialMagma_408
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_semimedial'691'_444
      ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))
-- Algebra.Bundles.SemimedialMagma._.semimedialˡ
d_semimedial'737'_532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_semimedial'737'_532 :: ()
-> ()
-> T_SemimedialMagma_494
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_semimedial'737'_532 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2 = T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_532 T_SemimedialMagma_494
v2
du_semimedial'737'_532 ::
  T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_532 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_semimedial'737'_532 T_SemimedialMagma_494
v0
  = (T_IsSemimedialMagma_408
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemimedialMagma_408 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_semimedial'737'_442
      ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))
-- Algebra.Bundles.SemimedialMagma._.setoid
d_setoid_534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_534 :: () -> () -> T_SemimedialMagma_494 -> T_Setoid_46
d_setoid_534 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2 = T_SemimedialMagma_494 -> T_Setoid_46
du_setoid_534 T_SemimedialMagma_494
v2
du_setoid_534 ::
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_534 :: T_SemimedialMagma_494 -> T_Setoid_46
du_setoid_534 T_SemimedialMagma_494
v0
  = let v1 :: T_IsSemimedialMagma_408
v1 = T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> AgdaAny
forall a b. a -> b
coe T_IsSemimedialMagma_408
v1)))
-- Algebra.Bundles.SemimedialMagma._.sym
d_sym_536 ::
  T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_536 :: T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_536 T_SemimedialMagma_494
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416
            ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))))
-- Algebra.Bundles.SemimedialMagma._.trans
d_trans_538 ::
  T_SemimedialMagma_494 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_538 :: T_SemimedialMagma_494
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_538 T_SemimedialMagma_494
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416
            ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))))
-- Algebra.Bundles.SemimedialMagma._.∙-cong
d_'8729''45'cong_540 ::
  T_SemimedialMagma_494 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_540 :: T_SemimedialMagma_494
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_540 T_SemimedialMagma_494
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemimedialMagma_408 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416
         ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0)))
-- Algebra.Bundles.SemimedialMagma._.∙-congʳ
d_'8729''45'cong'691'_542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_542 :: ()
-> ()
-> T_SemimedialMagma_494
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_542 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2
  = T_SemimedialMagma_494
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 T_SemimedialMagma_494
v2
du_'8729''45'cong'691'_542 ::
  T_SemimedialMagma_494 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 :: T_SemimedialMagma_494
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_542 T_SemimedialMagma_494
v0
  = let v1 :: T_IsSemimedialMagma_408
v1 = T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.SemimedialMagma._.∙-congˡ
d_'8729''45'cong'737'_544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_544 :: ()
-> ()
-> T_SemimedialMagma_494
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_544 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2
  = T_SemimedialMagma_494
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 T_SemimedialMagma_494
v2
du_'8729''45'cong'737'_544 ::
  T_SemimedialMagma_494 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 :: T_SemimedialMagma_494
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_544 T_SemimedialMagma_494
v0
  = let v1 :: T_IsSemimedialMagma_408
v1 = T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416 (T_IsSemimedialMagma_408 -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_IsSemimedialMagma_408
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.SemimedialMagma.magma
d_magma_546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 -> T_Magma_74
d_magma_546 :: () -> () -> T_SemimedialMagma_494 -> T_Magma_74
d_magma_546 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2 = T_SemimedialMagma_494 -> T_Magma_74
du_magma_546 T_SemimedialMagma_494
v2
du_magma_546 :: T_SemimedialMagma_494 -> T_Magma_74
du_magma_546 :: T_SemimedialMagma_494 -> T_Magma_74
du_magma_546 T_SemimedialMagma_494
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_SemimedialMagma_494 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__512 (T_SemimedialMagma_494 -> T_SemimedialMagma_494
forall a b. a -> b
coe T_SemimedialMagma_494
v0))
      (T_IsSemimedialMagma_408 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_416
         ((T_SemimedialMagma_494 -> T_IsSemimedialMagma_408)
-> AgdaAny -> T_IsSemimedialMagma_408
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_IsSemimedialMagma_408
d_isSemimedialMagma_514 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0)))
-- Algebra.Bundles.SemimedialMagma._.rawMagma
d_rawMagma_550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_550 :: () -> () -> T_SemimedialMagma_494 -> T_RawMagma_44
d_rawMagma_550 ~()
v0 ~()
v1 T_SemimedialMagma_494
v2 = T_SemimedialMagma_494 -> T_RawMagma_44
du_rawMagma_550 T_SemimedialMagma_494
v2
du_rawMagma_550 ::
  T_SemimedialMagma_494 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_550 :: T_SemimedialMagma_494 -> T_RawMagma_44
du_rawMagma_550 T_SemimedialMagma_494
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_SemimedialMagma_494 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494 -> T_Magma_74
du_magma_546 (T_SemimedialMagma_494 -> AgdaAny
forall a b. a -> b
coe T_SemimedialMagma_494
v0))
-- Algebra.Bundles.Semigroup
d_Semigroup_558 :: p -> p -> ()
d_Semigroup_558 p
a0 p
a1 = ()
data T_Semigroup_558
  = C_constructor_614 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
-- Algebra.Bundles.Semigroup.Carrier
d_Carrier_572 :: T_Semigroup_558 -> ()
d_Carrier_572 :: T_Semigroup_558 -> ()
d_Carrier_572 = T_Semigroup_558 -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._≈_
d__'8776'__574 :: T_Semigroup_558 -> AgdaAny -> AgdaAny -> ()
d__'8776'__574 :: T_Semigroup_558 -> AgdaAny -> AgdaAny -> ()
d__'8776'__574 = T_Semigroup_558 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._∙_
d__'8729'__576 :: T_Semigroup_558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__576 :: T_Semigroup_558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__576 T_Semigroup_558
v0
  = case T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0 of
      C_constructor_614 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemigroup_488
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Semigroup_558
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semigroup.isSemigroup
d_isSemigroup_578 ::
  T_Semigroup_558 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_578 :: T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 T_Semigroup_558
v0
  = case T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0 of
      C_constructor_614 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsSemigroup_488
v4 -> T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4
      T_Semigroup_558
_ -> T_IsSemigroup_488
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Semigroup._.assoc
d_assoc_582 ::
  T_Semigroup_558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_582 :: T_Semigroup_558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_582 T_Semigroup_558
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_Semigroup_558 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0))
-- Algebra.Bundles.Semigroup._.isEquivalence
d_isEquivalence_584 ::
  T_Semigroup_558 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_584 :: T_Semigroup_558 -> T_IsEquivalence_28
d_isEquivalence_584 T_Semigroup_558
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_Semigroup_558 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0)))
-- Algebra.Bundles.Semigroup._.isMagma
d_isMagma_586 ::
  T_Semigroup_558 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_586 :: T_Semigroup_558 -> T_IsMagma_178
d_isMagma_586 T_Semigroup_558
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_Semigroup_558 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0))
-- Algebra.Bundles.Semigroup._.isPartialEquivalence
d_isPartialEquivalence_588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_588 :: () -> () -> T_Semigroup_558 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_588 ~()
v0 ~()
v1 T_Semigroup_558
v2
  = T_Semigroup_558 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_588 T_Semigroup_558
v2
du_isPartialEquivalence_588 ::
  T_Semigroup_558 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_588 :: T_Semigroup_558 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_588 T_Semigroup_558
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.Semigroup._.refl
d_refl_590 :: T_Semigroup_558 -> AgdaAny -> AgdaAny
d_refl_590 :: T_Semigroup_558 -> AgdaAny -> AgdaAny
d_refl_590 T_Semigroup_558
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_Semigroup_558 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0))))
-- Algebra.Bundles.Semigroup._.reflexive
d_reflexive_592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_592 :: ()
-> ()
-> T_Semigroup_558
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_592 ~()
v0 ~()
v1 T_Semigroup_558
v2 = T_Semigroup_558 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_592 T_Semigroup_558
v2
du_reflexive_592 ::
  T_Semigroup_558 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_592 :: T_Semigroup_558 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_592 T_Semigroup_558
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.Semigroup._.setoid
d_setoid_594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_594 :: () -> () -> T_Semigroup_558 -> T_Setoid_46
d_setoid_594 ~()
v0 ~()
v1 T_Semigroup_558
v2 = T_Semigroup_558 -> T_Setoid_46
du_setoid_594 T_Semigroup_558
v2
du_setoid_594 ::
  T_Semigroup_558 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_594 :: T_Semigroup_558 -> T_Setoid_46
du_setoid_594 T_Semigroup_558
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v1)))
-- Algebra.Bundles.Semigroup._.sym
d_sym_596 ::
  T_Semigroup_558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_596 :: T_Semigroup_558 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_596 T_Semigroup_558
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_Semigroup_558 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0))))
-- Algebra.Bundles.Semigroup._.trans
d_trans_598 ::
  T_Semigroup_558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_598 :: T_Semigroup_558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_598 T_Semigroup_558
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_Semigroup_558 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0))))
-- Algebra.Bundles.Semigroup._.∙-cong
d_'8729''45'cong_600 ::
  T_Semigroup_558 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_600 :: T_Semigroup_558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_600 T_Semigroup_558
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_Semigroup_558 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0)))
-- Algebra.Bundles.Semigroup._.∙-congʳ
d_'8729''45'cong'691'_602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_602 :: ()
-> ()
-> T_Semigroup_558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_602 ~()
v0 ~()
v1 T_Semigroup_558
v2
  = T_Semigroup_558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_602 T_Semigroup_558
v2
du_'8729''45'cong'691'_602 ::
  T_Semigroup_558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_602 :: T_Semigroup_558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_602 T_Semigroup_558
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.Semigroup._.∙-congˡ
d_'8729''45'cong'737'_604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_604 :: ()
-> ()
-> T_Semigroup_558
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_604 ~()
v0 ~()
v1 T_Semigroup_558
v2
  = T_Semigroup_558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_604 T_Semigroup_558
v2
du_'8729''45'cong'737'_604 ::
  T_Semigroup_558 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_604 :: T_Semigroup_558
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_604 T_Semigroup_558
v0
  = let v1 :: T_IsSemigroup_488
v1 = T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.Semigroup.magma
d_magma_606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 -> T_Magma_74
d_magma_606 :: () -> () -> T_Semigroup_558 -> T_Magma_74
d_magma_606 ~()
v0 ~()
v1 T_Semigroup_558
v2 = T_Semigroup_558 -> T_Magma_74
du_magma_606 T_Semigroup_558
v2
du_magma_606 :: T_Semigroup_558 -> T_Magma_74
du_magma_606 :: T_Semigroup_558 -> T_Magma_74
du_magma_606 T_Semigroup_558
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_Semigroup_558 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__576 (T_Semigroup_558 -> T_Semigroup_558
forall a b. a -> b
coe T_Semigroup_558
v0))
      (T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_Semigroup_558 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe T_Semigroup_558 -> T_IsSemigroup_488
d_isSemigroup_578 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0)))
-- Algebra.Bundles.Semigroup._._≉_
d__'8777'__610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 -> AgdaAny -> AgdaAny -> ()
d__'8777'__610 :: () -> () -> T_Semigroup_558 -> AgdaAny -> AgdaAny -> ()
d__'8777'__610 = () -> () -> T_Semigroup_558 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Semigroup._.rawMagma
d_rawMagma_612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Semigroup_558 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_612 :: () -> () -> T_Semigroup_558 -> T_RawMagma_44
d_rawMagma_612 ~()
v0 ~()
v1 T_Semigroup_558
v2 = T_Semigroup_558 -> T_RawMagma_44
du_rawMagma_612 T_Semigroup_558
v2
du_rawMagma_612 ::
  T_Semigroup_558 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_612 :: T_Semigroup_558 -> T_RawMagma_44
du_rawMagma_612 T_Semigroup_558
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (T_Semigroup_558 -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558
v0))
-- Algebra.Bundles.Band
d_Band_620 :: p -> p -> ()
d_Band_620 p
a0 p
a1 = ()
data T_Band_620
  = C_constructor_682 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsBand_526
-- Algebra.Bundles.Band.Carrier
d_Carrier_634 :: T_Band_620 -> ()
d_Carrier_634 :: T_Band_620 -> ()
d_Carrier_634 = T_Band_620 -> ()
forall a. a
erased
-- Algebra.Bundles.Band._≈_
d__'8776'__636 :: T_Band_620 -> AgdaAny -> AgdaAny -> ()
d__'8776'__636 :: T_Band_620 -> AgdaAny -> AgdaAny -> ()
d__'8776'__636 = T_Band_620 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Band._∙_
d__'8729'__638 :: T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__638 :: T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__638 T_Band_620
v0
  = case T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0 of
      C_constructor_682 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsBand_526
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Band_620
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Band.isBand
d_isBand_640 ::
  T_Band_620 -> MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_640 :: T_Band_620 -> T_IsBand_526
d_isBand_640 T_Band_620
v0
  = case T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0 of
      C_constructor_682 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsBand_526
v4 -> T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v4
      T_Band_620
_ -> T_IsBand_526
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Band._.assoc
d_assoc_644 ::
  T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_644 :: T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_644 T_Band_620
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0)))
-- Algebra.Bundles.Band._.idem
d_idem_646 :: T_Band_620 -> AgdaAny -> AgdaAny
d_idem_646 :: T_Band_620 -> AgdaAny -> AgdaAny
d_idem_646 T_Band_620
v0
  = (T_IsBand_526 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
      ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0))
-- Algebra.Bundles.Band._.isEquivalence
d_isEquivalence_648 ::
  T_Band_620 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_648 :: T_Band_620 -> T_IsEquivalence_28
d_isEquivalence_648 T_Band_620
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0))))
-- Algebra.Bundles.Band._.isMagma
d_isMagma_650 ::
  T_Band_620 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_650 :: T_Band_620 -> T_IsMagma_178
d_isMagma_650 T_Band_620
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0)))
-- Algebra.Bundles.Band._.isPartialEquivalence
d_isPartialEquivalence_652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_652 :: () -> () -> T_Band_620 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_652 ~()
v0 ~()
v1 T_Band_620
v2
  = T_Band_620 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_652 T_Band_620
v2
du_isPartialEquivalence_652 ::
  T_Band_620 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_652 :: T_Band_620 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_652 T_Band_620
v0
  = let v1 :: T_IsBand_526
v1 = T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Bundles.Band._.isSemigroup
d_isSemigroup_654 ::
  T_Band_620 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_654 :: T_Band_620 -> T_IsSemigroup_488
d_isSemigroup_654 T_Band_620
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0))
-- Algebra.Bundles.Band._.refl
d_refl_656 :: T_Band_620 -> AgdaAny -> AgdaAny
d_refl_656 :: T_Band_620 -> AgdaAny -> AgdaAny
d_refl_656 T_Band_620
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0)))))
-- Algebra.Bundles.Band._.reflexive
d_reflexive_658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_658 :: ()
-> ()
-> T_Band_620
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_658 ~()
v0 ~()
v1 T_Band_620
v2 = T_Band_620 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_658 T_Band_620
v2
du_reflexive_658 ::
  T_Band_620 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_658 :: T_Band_620 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_658 T_Band_620
v0
  = let v1 :: T_IsBand_526
v1 = T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.Band._.setoid
d_setoid_660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_660 :: () -> () -> T_Band_620 -> T_Setoid_46
d_setoid_660 ~()
v0 ~()
v1 T_Band_620
v2 = T_Band_620 -> T_Setoid_46
du_setoid_660 T_Band_620
v2
du_setoid_660 ::
  T_Band_620 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_660 :: T_Band_620 -> T_Setoid_46
du_setoid_660 T_Band_620
v0
  = let v1 :: T_IsBand_526
v1 = T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Bundles.Band._.sym
d_sym_662 :: T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_662 :: T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_662 T_Band_620
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0)))))
-- Algebra.Bundles.Band._.trans
d_trans_664 ::
  T_Band_620 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_664 :: T_Band_620
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_664 T_Band_620
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0)))))
-- Algebra.Bundles.Band._.∙-cong
d_'8729''45'cong_666 ::
  T_Band_620 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_666 :: T_Band_620
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_666 T_Band_620
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0))))
-- Algebra.Bundles.Band._.∙-congʳ
d_'8729''45'cong'691'_668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_668 :: ()
-> ()
-> T_Band_620
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_668 ~()
v0 ~()
v1 T_Band_620
v2
  = T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_668 T_Band_620
v2
du_'8729''45'cong'691'_668 ::
  T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_668 :: T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_668 T_Band_620
v0
  = let v1 :: T_IsBand_526
v1 = T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.Band._.∙-congˡ
d_'8729''45'cong'737'_670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_670 :: ()
-> ()
-> T_Band_620
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_670 ~()
v0 ~()
v1 T_Band_620
v2
  = T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_670 T_Band_620
v2
du_'8729''45'cong'737'_670 ::
  T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_670 :: T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_670 T_Band_620
v0
  = let v1 :: T_IsBand_526
v1 = T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.Band.semigroup
d_semigroup_672 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 -> T_Semigroup_558
d_semigroup_672 :: () -> () -> T_Band_620 -> T_Semigroup_558
d_semigroup_672 ~()
v0 ~()
v1 T_Band_620
v2 = T_Band_620 -> T_Semigroup_558
du_semigroup_672 T_Band_620
v2
du_semigroup_672 :: T_Band_620 -> T_Semigroup_558
du_semigroup_672 :: T_Band_620 -> T_Semigroup_558
du_semigroup_672 T_Band_620
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_488 -> T_Semigroup_558)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> T_Semigroup_558
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488 -> T_Semigroup_558
C_constructor_614 (T_Band_620 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__638 (T_Band_620 -> T_Band_620
forall a b. a -> b
coe T_Band_620
v0))
      (T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_Band_620 -> T_IsBand_526) -> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe T_Band_620 -> T_IsBand_526
d_isBand_640 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0)))
-- Algebra.Bundles.Band._._≉_
d__'8777'__676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 -> AgdaAny -> AgdaAny -> ()
d__'8777'__676 :: () -> () -> T_Band_620 -> AgdaAny -> AgdaAny -> ()
d__'8777'__676 = () -> () -> T_Band_620 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Band._.magma
d_magma_678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> T_Band_620 -> T_Magma_74
d_magma_678 :: () -> () -> T_Band_620 -> T_Magma_74
d_magma_678 ~()
v0 ~()
v1 T_Band_620
v2 = T_Band_620 -> T_Magma_74
du_magma_678 T_Band_620
v2
du_magma_678 :: T_Band_620 -> T_Magma_74
du_magma_678 :: T_Band_620 -> T_Magma_74
du_magma_678 T_Band_620
v0 = (T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> T_Magma_74
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
du_semigroup_672 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0))
-- Algebra.Bundles.Band._.rawMagma
d_rawMagma_680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Band_620 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_680 :: () -> () -> T_Band_620 -> T_RawMagma_44
d_rawMagma_680 ~()
v0 ~()
v1 T_Band_620
v2 = T_Band_620 -> T_RawMagma_44
du_rawMagma_680 T_Band_620
v2
du_rawMagma_680 ::
  T_Band_620 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_680 :: T_Band_620 -> T_RawMagma_44
du_rawMagma_680 T_Band_620
v0
  = let v1 :: AgdaAny
v1 = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
du_semigroup_672 (T_Band_620 -> AgdaAny
forall a b. a -> b
coe T_Band_620
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.CommutativeSemigroup
d_CommutativeSemigroup_688 :: p -> p -> ()
d_CommutativeSemigroup_688 p
a0 p
a1 = ()
data T_CommutativeSemigroup_688
  = C_constructor_754 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
-- Algebra.Bundles.CommutativeSemigroup.Carrier
d_Carrier_702 :: T_CommutativeSemigroup_688 -> ()
d_Carrier_702 :: T_CommutativeSemigroup_688 -> ()
d_Carrier_702 = T_CommutativeSemigroup_688 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._≈_
d__'8776'__704 ::
  T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> ()
d__'8776'__704 :: T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> ()
d__'8776'__704 = T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._∙_
d__'8729'__706 ::
  T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__706 :: T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__706 T_CommutativeSemigroup_688
v0
  = case T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0 of
      C_constructor_754 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeSemigroup_568
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeSemigroup_688
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemigroup.isCommutativeSemigroup
d_isCommutativeSemigroup_708 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 :: T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 T_CommutativeSemigroup_688
v0
  = case T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0 of
      C_constructor_754 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeSemigroup_568
v4 -> T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v4
      T_CommutativeSemigroup_688
_ -> T_IsCommutativeSemigroup_568
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeSemigroup._.assoc
d_assoc_712 ::
  T_CommutativeSemigroup_688 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_712 :: T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_712 T_CommutativeSemigroup_688
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
         ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0)))
-- Algebra.Bundles.CommutativeSemigroup._.comm
d_comm_714 ::
  T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_714 :: T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_714 T_CommutativeSemigroup_688
v0
  = (T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_578
      ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))
-- Algebra.Bundles.CommutativeSemigroup._.isCommutativeMagma
d_isCommutativeMagma_716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_716 :: () -> () -> T_CommutativeSemigroup_688 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_716 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2 = T_CommutativeSemigroup_688 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_716 T_CommutativeSemigroup_688
v2
du_isCommutativeMagma_716 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_716 :: T_CommutativeSemigroup_688 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_716 T_CommutativeSemigroup_688
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
      ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))
-- Algebra.Bundles.CommutativeSemigroup._.isEquivalence
d_isEquivalence_718 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_718 :: T_CommutativeSemigroup_688 -> T_IsEquivalence_28
d_isEquivalence_718 T_CommutativeSemigroup_688
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
            ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))))
-- Algebra.Bundles.CommutativeSemigroup._.isMagma
d_isMagma_720 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_720 :: T_CommutativeSemigroup_688 -> T_IsMagma_178
d_isMagma_720 T_CommutativeSemigroup_688
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
         ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0)))
-- Algebra.Bundles.CommutativeSemigroup._.isPartialEquivalence
d_isPartialEquivalence_722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_722 :: () -> () -> T_CommutativeSemigroup_688 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_722 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2
  = T_CommutativeSemigroup_688 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_722 T_CommutativeSemigroup_688
v2
du_isPartialEquivalence_722 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_722 :: T_CommutativeSemigroup_688 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_722 T_CommutativeSemigroup_688
v0
  = let v1 :: T_IsCommutativeSemigroup_568
v1 = T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Bundles.CommutativeSemigroup._.isSemigroup
d_isSemigroup_724 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_724 :: T_CommutativeSemigroup_688 -> T_IsSemigroup_488
d_isSemigroup_724 T_CommutativeSemigroup_688
v0
  = (T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
      ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))
-- Algebra.Bundles.CommutativeSemigroup._.refl
d_refl_726 :: T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny
d_refl_726 :: T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny
d_refl_726 T_CommutativeSemigroup_688
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
               ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.reflexive
d_reflexive_728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_728 :: ()
-> ()
-> T_CommutativeSemigroup_688
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_728 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2 = T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_728 T_CommutativeSemigroup_688
v2
du_reflexive_728 ::
  T_CommutativeSemigroup_688 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_728 :: T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_728 T_CommutativeSemigroup_688
v0
  = let v1 :: T_IsCommutativeSemigroup_568
v1 = T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.CommutativeSemigroup._.setoid
d_setoid_730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_730 :: () -> () -> T_CommutativeSemigroup_688 -> T_Setoid_46
d_setoid_730 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2 = T_CommutativeSemigroup_688 -> T_Setoid_46
du_setoid_730 T_CommutativeSemigroup_688
v2
du_setoid_730 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_730 :: T_CommutativeSemigroup_688 -> T_Setoid_46
du_setoid_730 T_CommutativeSemigroup_688
v0
  = let v1 :: T_IsCommutativeSemigroup_568
v1 = T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Bundles.CommutativeSemigroup._.sym
d_sym_732 ::
  T_CommutativeSemigroup_688 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_732 :: T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_732 T_CommutativeSemigroup_688
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
               ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.trans
d_trans_734 ::
  T_CommutativeSemigroup_688 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_734 :: T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_734 T_CommutativeSemigroup_688
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
               ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0)))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-cong
d_'8729''45'cong_736 ::
  T_CommutativeSemigroup_688 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_736 :: T_CommutativeSemigroup_688
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_736 T_CommutativeSemigroup_688
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
            ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-congʳ
d_'8729''45'cong'691'_738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_738 :: ()
-> ()
-> T_CommutativeSemigroup_688
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_738 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2
  = T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_738 T_CommutativeSemigroup_688
v2
du_'8729''45'cong'691'_738 ::
  T_CommutativeSemigroup_688 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_738 :: T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_738 T_CommutativeSemigroup_688
v0
  = let v1 :: T_IsCommutativeSemigroup_568
v1 = T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.CommutativeSemigroup._.∙-congˡ
d_'8729''45'cong'737'_740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_740 :: ()
-> ()
-> T_CommutativeSemigroup_688
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_740 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2
  = T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_740 T_CommutativeSemigroup_688
v2
du_'8729''45'cong'737'_740 ::
  T_CommutativeSemigroup_688 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_740 :: T_CommutativeSemigroup_688
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_740 T_CommutativeSemigroup_688
v0
  = let v1 :: T_IsCommutativeSemigroup_568
v1 = T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576 (T_IsCommutativeSemigroup_568 -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_IsCommutativeSemigroup_568
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.CommutativeSemigroup.semigroup
d_semigroup_742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 -> T_Semigroup_558
d_semigroup_742 :: () -> () -> T_CommutativeSemigroup_688 -> T_Semigroup_558
d_semigroup_742 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2 = T_CommutativeSemigroup_688 -> T_Semigroup_558
du_semigroup_742 T_CommutativeSemigroup_688
v2
du_semigroup_742 :: T_CommutativeSemigroup_688 -> T_Semigroup_558
du_semigroup_742 :: T_CommutativeSemigroup_688 -> T_Semigroup_558
du_semigroup_742 T_CommutativeSemigroup_688
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_488 -> T_Semigroup_558)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> T_Semigroup_558
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488 -> T_Semigroup_558
C_constructor_614 (T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__706 (T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))
      (T_IsCommutativeSemigroup_568 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_576
         ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0)))
-- Algebra.Bundles.CommutativeSemigroup._._≉_
d__'8777'__746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> ()
d__'8777'__746 :: () -> () -> T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> ()
d__'8777'__746 = () -> () -> T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeSemigroup._.magma
d_magma_748 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 -> T_Magma_74
d_magma_748 :: () -> () -> T_CommutativeSemigroup_688 -> T_Magma_74
d_magma_748 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2 = T_CommutativeSemigroup_688 -> T_Magma_74
du_magma_748 T_CommutativeSemigroup_688
v2
du_magma_748 :: T_CommutativeSemigroup_688 -> T_Magma_74
du_magma_748 :: T_CommutativeSemigroup_688 -> T_Magma_74
du_magma_748 T_CommutativeSemigroup_688
v0 = (T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> T_Magma_74
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_CommutativeSemigroup_688 -> T_Semigroup_558)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_Semigroup_558
du_semigroup_742 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))
-- Algebra.Bundles.CommutativeSemigroup._.rawMagma
d_rawMagma_750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_750 :: () -> () -> T_CommutativeSemigroup_688 -> T_RawMagma_44
d_rawMagma_750 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2 = T_CommutativeSemigroup_688 -> T_RawMagma_44
du_rawMagma_750 T_CommutativeSemigroup_688
v2
du_rawMagma_750 ::
  T_CommutativeSemigroup_688 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_750 :: T_CommutativeSemigroup_688 -> T_RawMagma_44
du_rawMagma_750 T_CommutativeSemigroup_688
v0
  = let v1 :: AgdaAny
v1 = (T_CommutativeSemigroup_688 -> T_Semigroup_558)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_Semigroup_558
du_semigroup_742 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.CommutativeSemigroup.commutativeMagma
d_commutativeMagma_752 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
d_commutativeMagma_752 :: () -> () -> T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
d_commutativeMagma_752 ~()
v0 ~()
v1 T_CommutativeSemigroup_688
v2 = T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
du_commutativeMagma_752 T_CommutativeSemigroup_688
v2
du_commutativeMagma_752 ::
  T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
du_commutativeMagma_752 :: T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
du_commutativeMagma_752 T_CommutativeSemigroup_688
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeMagma_214 -> T_CommutativeMagma_190)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeMagma_190
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeMagma_214 -> T_CommutativeMagma_190
C_constructor_244 (T_CommutativeSemigroup_688 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__706 (T_CommutativeSemigroup_688 -> T_CommutativeSemigroup_688
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0))
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_708 (T_CommutativeSemigroup_688 -> AgdaAny
forall a b. a -> b
coe T_CommutativeSemigroup_688
v0)))
-- Algebra.Bundles.CommutativeBand
d_CommutativeBand_760 :: p -> p -> ()
d_CommutativeBand_760 p
a0 p
a1 = ()
data T_CommutativeBand_760
  = C_constructor_838 (AgdaAny -> AgdaAny -> AgdaAny)
                      MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
-- Algebra.Bundles.CommutativeBand.Carrier
d_Carrier_774 :: T_CommutativeBand_760 -> ()
d_Carrier_774 :: T_CommutativeBand_760 -> ()
d_Carrier_774 = T_CommutativeBand_760 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeBand._≈_
d__'8776'__776 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> ()
d__'8776'__776 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> ()
d__'8776'__776 = T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeBand._∙_
d__'8729'__778 ::
  T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__778 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__778 T_CommutativeBand_760
v0
  = case T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0 of
      C_constructor_838 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeBand_760
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeBand.isCommutativeBand
d_isCommutativeBand_780 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_780 :: T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 T_CommutativeBand_760
v0
  = case T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0 of
      C_constructor_838 AgdaAny -> AgdaAny -> AgdaAny
v3 T_IsCommutativeBand_612
v4 -> T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v4
      T_CommutativeBand_760
_ -> T_IsCommutativeBand_612
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeBand._.assoc
d_assoc_784 ::
  T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_784 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_784 T_CommutativeBand_760
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
            ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))))
-- Algebra.Bundles.CommutativeBand._.comm
d_comm_786 ::
  T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_786 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_786 T_CommutativeBand_760
v0
  = (T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_622
      ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))
-- Algebra.Bundles.CommutativeBand._.idem
d_idem_788 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny
d_idem_788 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny
d_idem_788 T_CommutativeBand_760
v0
  = (T_IsBand_526 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBand_526 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_536
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
         ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0)))
-- Algebra.Bundles.CommutativeBand._.isBand
d_isBand_790 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_790 :: T_CommutativeBand_760 -> T_IsBand_526
d_isBand_790 T_CommutativeBand_760
v0
  = (T_IsCommutativeBand_612 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
      ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))
-- Algebra.Bundles.CommutativeBand._.isCommutativeMagma
d_isCommutativeMagma_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_792 :: () -> () -> T_CommutativeBand_760 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_792 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_792 T_CommutativeBand_760
v2
du_isCommutativeMagma_792 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_792 :: T_CommutativeBand_760 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_792 T_CommutativeBand_760
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_654
            (T_IsCommutativeBand_612 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeBand_612
v1)))
-- Algebra.Bundles.CommutativeBand._.isCommutativeSemigroup
d_isCommutativeSemigroup_794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_794 :: () -> () -> T_CommutativeBand_760 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_794 ~()
v0 ~()
v1 T_CommutativeBand_760
v2
  = T_CommutativeBand_760 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_794 T_CommutativeBand_760
v2
du_isCommutativeSemigroup_794 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_794 :: T_CommutativeBand_760 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_794 T_CommutativeBand_760
v0
  = (T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_654
      ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))
-- Algebra.Bundles.CommutativeBand._.isEquivalence
d_isEquivalence_796 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_796 :: T_CommutativeBand_760 -> T_IsEquivalence_28
d_isEquivalence_796 T_CommutativeBand_760
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
               ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0)))))
-- Algebra.Bundles.CommutativeBand._.isMagma
d_isMagma_798 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_798 :: T_CommutativeBand_760 -> T_IsMagma_178
d_isMagma_798 T_CommutativeBand_760
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
         ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
            ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))))
-- Algebra.Bundles.CommutativeBand._.isPartialEquivalence
d_isPartialEquivalence_800 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_800 :: () -> () -> T_CommutativeBand_760 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_800 ~()
v0 ~()
v1 T_CommutativeBand_760
v2
  = T_CommutativeBand_760 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_800 T_CommutativeBand_760
v2
du_isPartialEquivalence_800 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_800 :: T_CommutativeBand_760 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_800 T_CommutativeBand_760
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Bundles.CommutativeBand._.isSemigroup
d_isSemigroup_802 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_802 :: T_CommutativeBand_760 -> T_IsSemigroup_488
d_isSemigroup_802 T_CommutativeBand_760
v0
  = (T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
      ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
         ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0)))
-- Algebra.Bundles.CommutativeBand._.refl
d_refl_804 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny
d_refl_804 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny
d_refl_804 T_CommutativeBand_760
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
                  ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))))))
-- Algebra.Bundles.CommutativeBand._.reflexive
d_reflexive_806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_806 :: ()
-> ()
-> T_CommutativeBand_760
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_806 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_806 T_CommutativeBand_760
v2
du_reflexive_806 ::
  T_CommutativeBand_760 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_806 :: T_CommutativeBand_760
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_806 T_CommutativeBand_760
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.CommutativeBand._.setoid
d_setoid_808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_808 :: () -> () -> T_CommutativeBand_760 -> T_Setoid_46
d_setoid_808 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760 -> T_Setoid_46
du_setoid_808 T_CommutativeBand_760
v2
du_setoid_808 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_808 :: T_CommutativeBand_760 -> T_Setoid_46
du_setoid_808 T_CommutativeBand_760
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Bundles.CommutativeBand._.sym
d_sym_810 ::
  T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_810 :: T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_810 T_CommutativeBand_760
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
                  ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))))))
-- Algebra.Bundles.CommutativeBand._.trans
d_trans_812 ::
  T_CommutativeBand_760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_812 :: T_CommutativeBand_760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_812 T_CommutativeBand_760
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
               ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
                  ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))))))
-- Algebra.Bundles.CommutativeBand._.∙-cong
d_'8729''45'cong_814 ::
  T_CommutativeBand_760 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_814 :: T_CommutativeBand_760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_814 T_CommutativeBand_760
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsBand_526 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534
            ((T_IsCommutativeBand_612 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
               ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0)))))
-- Algebra.Bundles.CommutativeBand._.∙-congʳ
d_'8729''45'cong'691'_816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_816 :: ()
-> ()
-> T_CommutativeBand_760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_816 ~()
v0 ~()
v1 T_CommutativeBand_760
v2
  = T_CommutativeBand_760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_816 T_CommutativeBand_760
v2
du_'8729''45'cong'691'_816 ::
  T_CommutativeBand_760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_816 :: T_CommutativeBand_760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_816 T_CommutativeBand_760
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.CommutativeBand._.∙-congˡ
d_'8729''45'cong'737'_818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_818 :: ()
-> ()
-> T_CommutativeBand_760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_818 ~()
v0 ~()
v1 T_CommutativeBand_760
v2
  = T_CommutativeBand_760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_818 T_CommutativeBand_760
v2
du_'8729''45'cong'737'_818 ::
  T_CommutativeBand_760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_818 :: T_CommutativeBand_760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_818 T_CommutativeBand_760
v0
  = let v1 :: T_IsCommutativeBand_612
v1 = T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBand_526
v2 = T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620 (T_IsCommutativeBand_612 -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_IsCommutativeBand_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsBand_526 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_534 (T_IsBand_526 -> T_IsBand_526
forall a b. a -> b
coe T_IsBand_526
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.CommutativeBand.band
d_band_820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 -> T_Band_620
d_band_820 :: () -> () -> T_CommutativeBand_760 -> T_Band_620
d_band_820 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760 -> T_Band_620
du_band_820 T_CommutativeBand_760
v2
du_band_820 :: T_CommutativeBand_760 -> T_Band_620
du_band_820 :: T_CommutativeBand_760 -> T_Band_620
du_band_820 T_CommutativeBand_760
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620
C_constructor_682 (T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__778 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0))
      (T_IsCommutativeBand_612 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.d_isBand_620
         ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0)))
-- Algebra.Bundles.CommutativeBand._._≉_
d__'8777'__824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> ()
d__'8777'__824 :: () -> () -> T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> ()
d__'8777'__824 = () -> () -> T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeBand._.magma
d_magma_826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 -> T_Magma_74
d_magma_826 :: () -> () -> T_CommutativeBand_760 -> T_Magma_74
d_magma_826 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760 -> T_Magma_74
du_magma_826 T_CommutativeBand_760
v2
du_magma_826 :: T_CommutativeBand_760 -> T_Magma_74
du_magma_826 :: T_CommutativeBand_760 -> T_Magma_74
du_magma_826 T_CommutativeBand_760
v0
  = let v1 :: AgdaAny
v1 = (T_CommutativeBand_760 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_Band_620
du_band_820 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.CommutativeBand._.rawMagma
d_rawMagma_828 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_828 :: () -> () -> T_CommutativeBand_760 -> T_RawMagma_44
d_rawMagma_828 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760 -> T_RawMagma_44
du_rawMagma_828 T_CommutativeBand_760
v2
du_rawMagma_828 ::
  T_CommutativeBand_760 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_828 :: T_CommutativeBand_760 -> T_RawMagma_44
du_rawMagma_828 T_CommutativeBand_760
v0
  = let v1 :: AgdaAny
v1 = (T_CommutativeBand_760 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_Band_620
du_band_820 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
du_semigroup_672 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.CommutativeBand._.semigroup
d_semigroup_830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 -> T_Semigroup_558
d_semigroup_830 :: () -> () -> T_CommutativeBand_760 -> T_Semigroup_558
d_semigroup_830 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760 -> T_Semigroup_558
du_semigroup_830 T_CommutativeBand_760
v2
du_semigroup_830 :: T_CommutativeBand_760 -> T_Semigroup_558
du_semigroup_830 :: T_CommutativeBand_760 -> T_Semigroup_558
du_semigroup_830 T_CommutativeBand_760
v0
  = (T_Band_620 -> T_Semigroup_558) -> AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe T_Band_620 -> T_Semigroup_558
du_semigroup_672 ((T_CommutativeBand_760 -> T_Band_620) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_Band_620
du_band_820 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))
-- Algebra.Bundles.CommutativeBand.commutativeSemigroup
d_commutativeSemigroup_832 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 -> T_CommutativeSemigroup_688
d_commutativeSemigroup_832 :: () -> () -> T_CommutativeBand_760 -> T_CommutativeSemigroup_688
d_commutativeSemigroup_832 ~()
v0 ~()
v1 T_CommutativeBand_760
v2
  = T_CommutativeBand_760 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_832 T_CommutativeBand_760
v2
du_commutativeSemigroup_832 ::
  T_CommutativeBand_760 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_832 :: T_CommutativeBand_760 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_832 T_CommutativeBand_760
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemigroup_568 -> T_CommutativeSemigroup_688)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeSemigroup_688
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568 -> T_CommutativeSemigroup_688
C_constructor_754 (T_CommutativeBand_760 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__778 (T_CommutativeBand_760 -> T_CommutativeBand_760
forall a b. a -> b
coe T_CommutativeBand_760
v0))
      ((T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeBand_612 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_654
         ((T_CommutativeBand_760 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_IsCommutativeBand_612
d_isCommutativeBand_780 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0)))
-- Algebra.Bundles.CommutativeBand._.commutativeMagma
d_commutativeMagma_836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeBand_760 -> T_CommutativeMagma_190
d_commutativeMagma_836 :: () -> () -> T_CommutativeBand_760 -> T_CommutativeMagma_190
d_commutativeMagma_836 ~()
v0 ~()
v1 T_CommutativeBand_760
v2 = T_CommutativeBand_760 -> T_CommutativeMagma_190
du_commutativeMagma_836 T_CommutativeBand_760
v2
du_commutativeMagma_836 ::
  T_CommutativeBand_760 -> T_CommutativeMagma_190
du_commutativeMagma_836 :: T_CommutativeBand_760 -> T_CommutativeMagma_190
du_commutativeMagma_836 T_CommutativeBand_760
v0
  = (T_CommutativeSemigroup_688 -> T_CommutativeMagma_190)
-> AgdaAny -> T_CommutativeMagma_190
forall a b. a -> b
coe
      T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
du_commutativeMagma_752 ((T_CommutativeBand_760 -> T_CommutativeSemigroup_688)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_832 (T_CommutativeBand_760 -> AgdaAny
forall a b. a -> b
coe T_CommutativeBand_760
v0))
-- Algebra.Bundles.UnitalMagma
d_UnitalMagma_844 :: p -> p -> ()
d_UnitalMagma_844 p
a0 p
a1 = ()
data T_UnitalMagma_844
  = C_constructor_908 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                      MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
-- Algebra.Bundles.UnitalMagma.Carrier
d_Carrier_860 :: T_UnitalMagma_844 -> ()
d_Carrier_860 :: T_UnitalMagma_844 -> ()
d_Carrier_860 = T_UnitalMagma_844 -> ()
forall a. a
erased
-- Algebra.Bundles.UnitalMagma._≈_
d__'8776'__862 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> ()
d__'8776'__862 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> ()
d__'8776'__862 = T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.UnitalMagma._∙_
d__'8729'__864 ::
  T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__864 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__864 T_UnitalMagma_844
v0
  = case T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0 of
      C_constructor_908 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsUnitalMagma_666
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_UnitalMagma_844
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.UnitalMagma.ε
d_ε_866 :: T_UnitalMagma_844 -> AgdaAny
d_ε_866 :: T_UnitalMagma_844 -> AgdaAny
d_ε_866 T_UnitalMagma_844
v0
  = case T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0 of
      C_constructor_908 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsUnitalMagma_666
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_UnitalMagma_844
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.UnitalMagma.isUnitalMagma
d_isUnitalMagma_868 ::
  T_UnitalMagma_844 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_868 :: T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 T_UnitalMagma_844
v0
  = case T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0 of
      C_constructor_908 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsUnitalMagma_666
v5 -> T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v5
      T_UnitalMagma_844
_ -> T_IsUnitalMagma_666
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.UnitalMagma._.identity
d_identity_872 ::
  T_UnitalMagma_844 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_872 :: T_UnitalMagma_844 -> T_Σ_14
d_identity_872 T_UnitalMagma_844
v0
  = (T_IsUnitalMagma_666 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsUnitalMagma_666 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_678
      ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))
-- Algebra.Bundles.UnitalMagma._.identityʳ
d_identity'691'_874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 -> AgdaAny -> AgdaAny
d_identity'691'_874 :: () -> () -> T_UnitalMagma_844 -> AgdaAny -> AgdaAny
d_identity'691'_874 ~()
v0 ~()
v1 T_UnitalMagma_844
v2 = T_UnitalMagma_844 -> AgdaAny -> AgdaAny
du_identity'691'_874 T_UnitalMagma_844
v2
du_identity'691'_874 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny
du_identity'691'_874 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny
du_identity'691'_874 T_UnitalMagma_844
v0
  = (T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_704
      ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))
-- Algebra.Bundles.UnitalMagma._.identityˡ
d_identity'737'_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 -> AgdaAny -> AgdaAny
d_identity'737'_876 :: () -> () -> T_UnitalMagma_844 -> AgdaAny -> AgdaAny
d_identity'737'_876 ~()
v0 ~()
v1 T_UnitalMagma_844
v2 = T_UnitalMagma_844 -> AgdaAny -> AgdaAny
du_identity'737'_876 T_UnitalMagma_844
v2
du_identity'737'_876 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny
du_identity'737'_876 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny
du_identity'737'_876 T_UnitalMagma_844
v0
  = (T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsUnitalMagma_666 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_702
      ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))
-- Algebra.Bundles.UnitalMagma._.isEquivalence
d_isEquivalence_878 ::
  T_UnitalMagma_844 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_878 :: T_UnitalMagma_844 -> T_IsEquivalence_28
d_isEquivalence_878 T_UnitalMagma_844
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676
         ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0)))
-- Algebra.Bundles.UnitalMagma._.isMagma
d_isMagma_880 ::
  T_UnitalMagma_844 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_880 :: T_UnitalMagma_844 -> T_IsMagma_178
d_isMagma_880 T_UnitalMagma_844
v0
  = (T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676
      ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))
-- Algebra.Bundles.UnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_882 :: () -> () -> T_UnitalMagma_844 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_882 ~()
v0 ~()
v1 T_UnitalMagma_844
v2
  = T_UnitalMagma_844 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_882 T_UnitalMagma_844
v2
du_isPartialEquivalence_882 ::
  T_UnitalMagma_844 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_882 :: T_UnitalMagma_844 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_882 T_UnitalMagma_844
v0
  = let v1 :: T_IsUnitalMagma_666
v1 = T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.UnitalMagma._.refl
d_refl_884 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny
d_refl_884 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny
d_refl_884 T_UnitalMagma_844
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676
            ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))))
-- Algebra.Bundles.UnitalMagma._.reflexive
d_reflexive_886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_886 :: ()
-> ()
-> T_UnitalMagma_844
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_886 ~()
v0 ~()
v1 T_UnitalMagma_844
v2 = T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_886 T_UnitalMagma_844
v2
du_reflexive_886 ::
  T_UnitalMagma_844 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_886 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_886 T_UnitalMagma_844
v0
  = let v1 :: T_IsUnitalMagma_666
v1 = T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.UnitalMagma._.setoid
d_setoid_888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_888 :: () -> () -> T_UnitalMagma_844 -> T_Setoid_46
d_setoid_888 ~()
v0 ~()
v1 T_UnitalMagma_844
v2 = T_UnitalMagma_844 -> T_Setoid_46
du_setoid_888 T_UnitalMagma_844
v2
du_setoid_888 ::
  T_UnitalMagma_844 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_888 :: T_UnitalMagma_844 -> T_Setoid_46
du_setoid_888 T_UnitalMagma_844
v0
  = let v1 :: T_IsUnitalMagma_666
v1 = T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> AgdaAny
forall a b. a -> b
coe T_IsUnitalMagma_666
v1)))
-- Algebra.Bundles.UnitalMagma._.sym
d_sym_890 ::
  T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_890 :: T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_890 T_UnitalMagma_844
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676
            ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))))
-- Algebra.Bundles.UnitalMagma._.trans
d_trans_892 ::
  T_UnitalMagma_844 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_892 :: T_UnitalMagma_844
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_892 T_UnitalMagma_844
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676
            ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))))
-- Algebra.Bundles.UnitalMagma._.∙-cong
d_'8729''45'cong_894 ::
  T_UnitalMagma_844 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_894 :: T_UnitalMagma_844
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_894 T_UnitalMagma_844
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsUnitalMagma_666 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676
         ((T_UnitalMagma_844 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0)))
-- Algebra.Bundles.UnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_896 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_896 :: ()
-> ()
-> T_UnitalMagma_844
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_896 ~()
v0 ~()
v1 T_UnitalMagma_844
v2
  = T_UnitalMagma_844
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_896 T_UnitalMagma_844
v2
du_'8729''45'cong'691'_896 ::
  T_UnitalMagma_844 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_896 :: T_UnitalMagma_844
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_896 T_UnitalMagma_844
v0
  = let v1 :: T_IsUnitalMagma_666
v1 = T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.UnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_898 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_898 :: ()
-> ()
-> T_UnitalMagma_844
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_898 ~()
v0 ~()
v1 T_UnitalMagma_844
v2
  = T_UnitalMagma_844
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_898 T_UnitalMagma_844
v2
du_'8729''45'cong'737'_898 ::
  T_UnitalMagma_844 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_898 :: T_UnitalMagma_844
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_898 T_UnitalMagma_844
v0
  = let v1 :: T_IsUnitalMagma_666
v1 = T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676 (T_IsUnitalMagma_666 -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_IsUnitalMagma_666
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.UnitalMagma.magma
d_magma_900 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 -> T_Magma_74
d_magma_900 :: () -> () -> T_UnitalMagma_844 -> T_Magma_74
d_magma_900 ~()
v0 ~()
v1 T_UnitalMagma_844
v2 = T_UnitalMagma_844 -> T_Magma_74
du_magma_900 T_UnitalMagma_844
v2
du_magma_900 :: T_UnitalMagma_844 -> T_Magma_74
du_magma_900 :: T_UnitalMagma_844 -> T_Magma_74
du_magma_900 T_UnitalMagma_844
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__864 (T_UnitalMagma_844 -> T_UnitalMagma_844
forall a b. a -> b
coe T_UnitalMagma_844
v0))
      (T_IsUnitalMagma_666 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_676
         ((T_UnitalMagma_844 -> T_IsUnitalMagma_666)
-> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe T_UnitalMagma_844 -> T_IsUnitalMagma_666
d_isUnitalMagma_868 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0)))
-- Algebra.Bundles.UnitalMagma._._≉_
d__'8777'__904 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> ()
d__'8777'__904 :: () -> () -> T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> ()
d__'8777'__904 = () -> () -> T_UnitalMagma_844 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.UnitalMagma._.rawMagma
d_rawMagma_906 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_UnitalMagma_844 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_906 :: () -> () -> T_UnitalMagma_844 -> T_RawMagma_44
d_rawMagma_906 ~()
v0 ~()
v1 T_UnitalMagma_844
v2 = T_UnitalMagma_844 -> T_RawMagma_44
du_rawMagma_906 T_UnitalMagma_844
v2
du_rawMagma_906 ::
  T_UnitalMagma_844 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_906 :: T_UnitalMagma_844 -> T_RawMagma_44
du_rawMagma_906 T_UnitalMagma_844
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_UnitalMagma_844 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844 -> T_Magma_74
du_magma_900 (T_UnitalMagma_844 -> AgdaAny
forall a b. a -> b
coe T_UnitalMagma_844
v0))
-- Algebra.Bundles.Monoid
d_Monoid_914 :: p -> p -> ()
d_Monoid_914 p
a0 p
a1 = ()
data T_Monoid_914
  = C_constructor_990 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                      MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
-- Algebra.Bundles.Monoid.Carrier
d_Carrier_930 :: T_Monoid_914 -> ()
d_Carrier_930 :: T_Monoid_914 -> ()
d_Carrier_930 = T_Monoid_914 -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._≈_
d__'8776'__932 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> ()
d__'8776'__932 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> ()
d__'8776'__932 = T_Monoid_914 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._∙_
d__'8729'__934 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__934 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__934 T_Monoid_914
v0
  = case T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0 of
      C_constructor_990 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_712
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Monoid_914
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid.ε
d_ε_936 :: T_Monoid_914 -> AgdaAny
d_ε_936 :: T_Monoid_914 -> AgdaAny
d_ε_936 T_Monoid_914
v0
  = case T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0 of
      C_constructor_990 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_712
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_Monoid_914
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid.isMonoid
d_isMonoid_938 ::
  T_Monoid_914 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_938 :: T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 T_Monoid_914
v0
  = case T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0 of
      C_constructor_990 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsMonoid_712
v5 -> T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v5
      T_Monoid_914
_ -> T_IsMonoid_712
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Monoid._.assoc
d_assoc_942 ::
  T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_942 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_942 T_Monoid_914
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0)))
-- Algebra.Bundles.Monoid._.identity
d_identity_944 ::
  T_Monoid_914 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_944 :: T_Monoid_914 -> T_Σ_14
d_identity_944 T_Monoid_914
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))
-- Algebra.Bundles.Monoid._.identityʳ
d_identity'691'_946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> AgdaAny -> AgdaAny
d_identity'691'_946 :: () -> () -> T_Monoid_914 -> AgdaAny -> AgdaAny
d_identity'691'_946 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> AgdaAny -> AgdaAny
du_identity'691'_946 T_Monoid_914
v2
du_identity'691'_946 :: T_Monoid_914 -> AgdaAny -> AgdaAny
du_identity'691'_946 :: T_Monoid_914 -> AgdaAny -> AgdaAny
du_identity'691'_946 T_Monoid_914
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
      ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))
-- Algebra.Bundles.Monoid._.identityˡ
d_identity'737'_948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> AgdaAny -> AgdaAny
d_identity'737'_948 :: () -> () -> T_Monoid_914 -> AgdaAny -> AgdaAny
d_identity'737'_948 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> AgdaAny -> AgdaAny
du_identity'737'_948 T_Monoid_914
v2
du_identity'737'_948 :: T_Monoid_914 -> AgdaAny -> AgdaAny
du_identity'737'_948 :: T_Monoid_914 -> AgdaAny -> AgdaAny
du_identity'737'_948 T_Monoid_914
v0
  = (T_IsMonoid_712 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
      ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))
-- Algebra.Bundles.Monoid._.isEquivalence
d_isEquivalence_950 ::
  T_Monoid_914 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_950 :: T_Monoid_914 -> T_IsEquivalence_28
d_isEquivalence_950 T_Monoid_914
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))))
-- Algebra.Bundles.Monoid._.isMagma
d_isMagma_952 ::
  T_Monoid_914 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_952 :: T_Monoid_914 -> T_IsMagma_178
d_isMagma_952 T_Monoid_914
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0)))
-- Algebra.Bundles.Monoid._.isPartialEquivalence
d_isPartialEquivalence_954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_954 :: () -> () -> T_Monoid_914 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_954 ~()
v0 ~()
v1 T_Monoid_914
v2
  = T_Monoid_914 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_954 T_Monoid_914
v2
du_isPartialEquivalence_954 ::
  T_Monoid_914 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_954 :: T_Monoid_914 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_954 T_Monoid_914
v0
  = let v1 :: T_IsMonoid_712
v1 = T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Bundles.Monoid._.isSemigroup
d_isSemigroup_956 ::
  T_Monoid_914 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_956 :: T_Monoid_914 -> T_IsSemigroup_488
d_isSemigroup_956 T_Monoid_914
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))
-- Algebra.Bundles.Monoid._.isUnitalMagma
d_isUnitalMagma_958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_958 :: () -> () -> T_Monoid_914 -> T_IsUnitalMagma_666
d_isUnitalMagma_958 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> T_IsUnitalMagma_666
du_isUnitalMagma_958 T_Monoid_914
v2
du_isUnitalMagma_958 ::
  T_Monoid_914 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_958 :: T_Monoid_914 -> T_IsUnitalMagma_666
du_isUnitalMagma_958 T_Monoid_914
v0
  = (T_IsMonoid_712 -> T_IsUnitalMagma_666)
-> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
      ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))
-- Algebra.Bundles.Monoid._.refl
d_refl_960 :: T_Monoid_914 -> AgdaAny -> AgdaAny
d_refl_960 :: T_Monoid_914 -> AgdaAny -> AgdaAny
d_refl_960 T_Monoid_914
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0)))))
-- Algebra.Bundles.Monoid._.reflexive
d_reflexive_962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_962 :: ()
-> ()
-> T_Monoid_914
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_962 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_962 T_Monoid_914
v2
du_reflexive_962 ::
  T_Monoid_914 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_962 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_962 T_Monoid_914
v0
  = let v1 :: T_IsMonoid_712
v1 = T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.Monoid._.setoid
d_setoid_964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_964 :: () -> () -> T_Monoid_914 -> T_Setoid_46
d_setoid_964 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> T_Setoid_46
du_setoid_964 T_Monoid_914
v2
du_setoid_964 ::
  T_Monoid_914 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_964 :: T_Monoid_914 -> T_Setoid_46
du_setoid_964 T_Monoid_914
v0
  = let v1 :: T_IsMonoid_712
v1 = T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v2))))
-- Algebra.Bundles.Monoid._.sym
d_sym_966 ::
  T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_966 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_966 T_Monoid_914
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0)))))
-- Algebra.Bundles.Monoid._.trans
d_trans_968 ::
  T_Monoid_914 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_968 :: T_Monoid_914
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_968 T_Monoid_914
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0)))))
-- Algebra.Bundles.Monoid._.∙-cong
d_'8729''45'cong_970 ::
  T_Monoid_914 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_970 :: T_Monoid_914
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_970 T_Monoid_914
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))))
-- Algebra.Bundles.Monoid._.∙-congʳ
d_'8729''45'cong'691'_972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_972 :: ()
-> ()
-> T_Monoid_914
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_972 ~()
v0 ~()
v1 T_Monoid_914
v2
  = T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_972 T_Monoid_914
v2
du_'8729''45'cong'691'_972 ::
  T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_972 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_972 T_Monoid_914
v0
  = let v1 :: T_IsMonoid_712
v1 = T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.Monoid._.∙-congˡ
d_'8729''45'cong'737'_974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_974 :: ()
-> ()
-> T_Monoid_914
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_974 ~()
v0 ~()
v1 T_Monoid_914
v2
  = T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_974 T_Monoid_914
v2
du_'8729''45'cong'737'_974 ::
  T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_974 :: T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_974 T_Monoid_914
v0
  = let v1 :: T_IsMonoid_712
v1 = T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsSemigroup_488
v2
             = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.Monoid.semigroup
d_semigroup_976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> T_Semigroup_558
d_semigroup_976 :: () -> () -> T_Monoid_914 -> T_Semigroup_558
d_semigroup_976 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 T_Monoid_914
v2
du_semigroup_976 :: T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 :: T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 T_Monoid_914
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_488 -> T_Semigroup_558)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
-> T_Semigroup_558
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488 -> T_Semigroup_558
C_constructor_614 (T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__934 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0))
      (T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0)))
-- Algebra.Bundles.Monoid._._≉_
d__'8777'__980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> AgdaAny -> AgdaAny -> ()
d__'8777'__980 :: () -> () -> T_Monoid_914 -> AgdaAny -> AgdaAny -> ()
d__'8777'__980 = () -> () -> T_Monoid_914 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Monoid._.magma
d_magma_982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> T_Magma_74
d_magma_982 :: () -> () -> T_Monoid_914 -> T_Magma_74
d_magma_982 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> T_Magma_74
du_magma_982 T_Monoid_914
v2
du_magma_982 :: T_Monoid_914 -> T_Magma_74
du_magma_982 :: T_Monoid_914 -> T_Magma_74
du_magma_982 T_Monoid_914
v0 = (T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> T_Magma_74
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0))
-- Algebra.Bundles.Monoid._.rawMagma
d_rawMagma_984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_984 :: () -> () -> T_Monoid_914 -> T_RawMagma_44
d_rawMagma_984 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> T_RawMagma_44
du_rawMagma_984 T_Monoid_914
v2
du_rawMagma_984 ::
  T_Monoid_914 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_984 :: T_Monoid_914 -> T_RawMagma_44
du_rawMagma_984 T_Monoid_914
v0
  = let v1 :: AgdaAny
v1 = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.Monoid.rawMonoid
d_rawMonoid_986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
d_rawMonoid_986 :: () -> () -> T_Monoid_914 -> T_RawMonoid_74
d_rawMonoid_986 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> T_RawMonoid_74
du_rawMonoid_986 T_Monoid_914
v2
du_rawMonoid_986 ::
  T_Monoid_914 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
du_rawMonoid_986 :: T_Monoid_914 -> T_RawMonoid_74
du_rawMonoid_986 T_Monoid_914
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_RawMonoid_74
MAlonzo.Code.Algebra.Bundles.Raw.C_constructor_102
      (T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__934 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0)) (T_Monoid_914 -> AgdaAny
d_ε_936 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0))
-- Algebra.Bundles.Monoid.unitalMagma
d_unitalMagma_988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Monoid_914 -> T_UnitalMagma_844
d_unitalMagma_988 :: () -> () -> T_Monoid_914 -> T_UnitalMagma_844
d_unitalMagma_988 ~()
v0 ~()
v1 T_Monoid_914
v2 = T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 T_Monoid_914
v2
du_unitalMagma_988 :: T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 :: T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 T_Monoid_914
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsUnitalMagma_666 -> T_UnitalMagma_844)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_UnitalMagma_844
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsUnitalMagma_666 -> T_UnitalMagma_844
C_constructor_908 (T_Monoid_914 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__934 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0)) (T_Monoid_914 -> AgdaAny
d_ε_936 (T_Monoid_914 -> T_Monoid_914
forall a b. a -> b
coe T_Monoid_914
v0))
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_Monoid_914 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_IsMonoid_712
d_isMonoid_938 (T_Monoid_914 -> AgdaAny
forall a b. a -> b
coe T_Monoid_914
v0)))
-- Algebra.Bundles.CommutativeMonoid
d_CommutativeMonoid_996 :: p -> p -> ()
d_CommutativeMonoid_996 p
a0 p
a1 = ()
data T_CommutativeMonoid_996
  = C_constructor_1088 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                       MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
-- Algebra.Bundles.CommutativeMonoid.Carrier
d_Carrier_1012 :: T_CommutativeMonoid_996 -> ()
d_Carrier_1012 :: T_CommutativeMonoid_996 -> ()
d_Carrier_1012 = T_CommutativeMonoid_996 -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._≈_
d__'8776'__1014 ::
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1014 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1014 = T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._∙_
d__'8729'__1016 ::
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1016 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1016 T_CommutativeMonoid_996
v0
  = case T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0 of
      C_constructor_1088 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_764
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_CommutativeMonoid_996
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid.ε
d_ε_1018 :: T_CommutativeMonoid_996 -> AgdaAny
d_ε_1018 :: T_CommutativeMonoid_996 -> AgdaAny
d_ε_1018 T_CommutativeMonoid_996
v0
  = case T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0 of
      C_constructor_1088 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_764
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_CommutativeMonoid_996
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid.isCommutativeMonoid
d_isCommutativeMonoid_1020 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 :: T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 T_CommutativeMonoid_996
v0
  = case T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0 of
      C_constructor_1088 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsCommutativeMonoid_764
v5 -> T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v5
      T_CommutativeMonoid_996
_ -> T_IsCommutativeMonoid_764
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.CommutativeMonoid._.assoc
d_assoc_1024 ::
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1024 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1024 T_CommutativeMonoid_996
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))))
-- Algebra.Bundles.CommutativeMonoid._.comm
d_comm_1026 ::
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1026 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1026 T_CommutativeMonoid_996
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
      ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
-- Algebra.Bundles.CommutativeMonoid._.identity
d_identity_1028 ::
  T_CommutativeMonoid_996 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1028 :: T_CommutativeMonoid_996 -> T_Σ_14
d_identity_1028 T_CommutativeMonoid_996
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0)))
-- Algebra.Bundles.CommutativeMonoid._.identityʳ
d_identity'691'_1030 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
d_identity'691'_1030 :: () -> () -> T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
d_identity'691'_1030 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
du_identity'691'_1030 T_CommutativeMonoid_996
v2
du_identity'691'_1030 ::
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
du_identity'691'_1030 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
du_identity'691'_1030 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Bundles.CommutativeMonoid._.identityˡ
d_identity'737'_1032 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
d_identity'737'_1032 :: () -> () -> T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
d_identity'737'_1032 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
du_identity'737'_1032 T_CommutativeMonoid_996
v2
du_identity'737'_1032 ::
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
du_identity'737'_1032 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
du_identity'737'_1032 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Bundles.CommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_1034 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1034 :: () -> () -> T_CommutativeMonoid_996 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_1034 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2
  = T_CommutativeMonoid_996 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1034 T_CommutativeMonoid_996
v2
du_isCommutativeMagma_1034 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1034 :: T_CommutativeMonoid_996 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1034 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
         ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
            (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Bundles.CommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_1036 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1036 :: () -> () -> T_CommutativeMonoid_996 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1036 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2
  = T_CommutativeMonoid_996 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1036 T_CommutativeMonoid_996
v2
du_isCommutativeSemigroup_1036 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1036 :: T_CommutativeMonoid_996 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1036 T_CommutativeMonoid_996
v0
  = (T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
      ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
-- Algebra.Bundles.CommutativeMonoid._.isEquivalence
d_isEquivalence_1038 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1038 :: T_CommutativeMonoid_996 -> T_IsEquivalence_28
d_isEquivalence_1038 T_CommutativeMonoid_996
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0)))))
-- Algebra.Bundles.CommutativeMonoid._.isMagma
d_isMagma_1040 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1040 :: T_CommutativeMonoid_996 -> T_IsMagma_178
d_isMagma_1040 T_CommutativeMonoid_996
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))))
-- Algebra.Bundles.CommutativeMonoid._.isMonoid
d_isMonoid_1042 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1042 :: T_CommutativeMonoid_996 -> T_IsMonoid_712
d_isMonoid_1042 T_CommutativeMonoid_996
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
-- Algebra.Bundles.CommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_1044 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1044 :: () -> () -> T_CommutativeMonoid_996 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1044 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2
  = T_CommutativeMonoid_996 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1044 T_CommutativeMonoid_996
v2
du_isPartialEquivalence_1044 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1044 :: T_CommutativeMonoid_996 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1044 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Bundles.CommutativeMonoid._.isSemigroup
d_isSemigroup_1046 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1046 :: T_CommutativeMonoid_996 -> T_IsSemigroup_488
d_isSemigroup_1046 T_CommutativeMonoid_996
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0)))
-- Algebra.Bundles.CommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_1048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1048 :: () -> () -> T_CommutativeMonoid_996 -> T_IsUnitalMagma_666
d_isUnitalMagma_1048 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_IsUnitalMagma_666
du_isUnitalMagma_1048 T_CommutativeMonoid_996
v2
du_isUnitalMagma_1048 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1048 :: T_CommutativeMonoid_996 -> T_IsUnitalMagma_666
du_isUnitalMagma_1048 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1)))
-- Algebra.Bundles.CommutativeMonoid._.refl
d_refl_1050 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
d_refl_1050 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny
d_refl_1050 T_CommutativeMonoid_996
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.reflexive
d_reflexive_1052 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1052 :: ()
-> ()
-> T_CommutativeMonoid_996
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1052 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1052 T_CommutativeMonoid_996
v2
du_reflexive_1052 ::
  T_CommutativeMonoid_996 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1052 :: T_CommutativeMonoid_996
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1052 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.CommutativeMonoid._.setoid
d_setoid_1054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1054 :: () -> () -> T_CommutativeMonoid_996 -> T_Setoid_46
d_setoid_1054 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_Setoid_46
du_setoid_1054 T_CommutativeMonoid_996
v2
du_setoid_1054 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1054 :: T_CommutativeMonoid_996 -> T_Setoid_46
du_setoid_1054 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Bundles.CommutativeMonoid._.sym
d_sym_1056 ::
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1056 :: T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1056 T_CommutativeMonoid_996
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.trans
d_trans_1058 ::
  T_CommutativeMonoid_996 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1058 :: T_CommutativeMonoid_996
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1058 T_CommutativeMonoid_996
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))))))
-- Algebra.Bundles.CommutativeMonoid._.∙-cong
d_'8729''45'cong_1060 ::
  T_CommutativeMonoid_996 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1060 :: T_CommutativeMonoid_996
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1060 T_CommutativeMonoid_996
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0)))))
-- Algebra.Bundles.CommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_1062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1062 :: ()
-> ()
-> T_CommutativeMonoid_996
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1062 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2
  = T_CommutativeMonoid_996
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1062 T_CommutativeMonoid_996
v2
du_'8729''45'cong'691'_1062 ::
  T_CommutativeMonoid_996 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1062 :: T_CommutativeMonoid_996
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1062 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.CommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_1064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1064 :: ()
-> ()
-> T_CommutativeMonoid_996
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1064 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2
  = T_CommutativeMonoid_996
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1064 T_CommutativeMonoid_996
v2
du_'8729''45'cong'737'_1064 ::
  T_CommutativeMonoid_996 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1064 :: T_CommutativeMonoid_996
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1064 T_CommutativeMonoid_996
v0
  = let v1 :: T_IsCommutativeMonoid_764
v1 = T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.CommutativeMonoid.monoid
d_monoid_1066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> T_Monoid_914
d_monoid_1066 :: () -> () -> T_CommutativeMonoid_996 -> T_Monoid_914
d_monoid_1066 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 T_CommutativeMonoid_996
v2
du_monoid_1066 :: T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 :: T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 T_CommutativeMonoid_996
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_712 -> T_Monoid_914)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> T_Monoid_914
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_712 -> T_Monoid_914
C_constructor_990 (T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1016 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0)) (T_CommutativeMonoid_996 -> AgdaAny
d_ε_1018 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
      (T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0)))
-- Algebra.Bundles.CommutativeMonoid._._≉_
d__'8777'__1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1070 :: () -> () -> T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1070 = () -> () -> T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.CommutativeMonoid._.magma
d_magma_1072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> T_Magma_74
d_magma_1072 :: () -> () -> T_CommutativeMonoid_996 -> T_Magma_74
d_magma_1072 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_Magma_74
du_magma_1072 T_CommutativeMonoid_996
v2
du_magma_1072 :: T_CommutativeMonoid_996 -> T_Magma_74
du_magma_1072 :: T_CommutativeMonoid_996 -> T_Magma_74
du_magma_1072 T_CommutativeMonoid_996
v0
  = let v1 :: AgdaAny
v1 = (T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.CommutativeMonoid._.rawMagma
d_rawMagma_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1074 :: () -> () -> T_CommutativeMonoid_996 -> T_RawMagma_44
d_rawMagma_1074 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_RawMagma_44
du_rawMagma_1074 T_CommutativeMonoid_996
v2
du_rawMagma_1074 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1074 :: T_CommutativeMonoid_996 -> T_RawMagma_44
du_rawMagma_1074 T_CommutativeMonoid_996
v0
  = let v1 :: AgdaAny
v1 = (T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.CommutativeMonoid._.rawMonoid
d_rawMonoid_1076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
d_rawMonoid_1076 :: () -> () -> T_CommutativeMonoid_996 -> T_RawMonoid_74
d_rawMonoid_1076 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_RawMonoid_74
du_rawMonoid_1076 T_CommutativeMonoid_996
v2
du_rawMonoid_1076 ::
  T_CommutativeMonoid_996 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
du_rawMonoid_1076 :: T_CommutativeMonoid_996 -> T_RawMonoid_74
du_rawMonoid_1076 T_CommutativeMonoid_996
v0
  = (T_Monoid_914 -> T_RawMonoid_74) -> AgdaAny -> T_RawMonoid_74
forall a b. a -> b
coe T_Monoid_914 -> T_RawMonoid_74
du_rawMonoid_986 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
-- Algebra.Bundles.CommutativeMonoid._.semigroup
d_semigroup_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> T_Semigroup_558
d_semigroup_1078 :: () -> () -> T_CommutativeMonoid_996 -> T_Semigroup_558
d_semigroup_1078 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_Semigroup_558
du_semigroup_1078 T_CommutativeMonoid_996
v2
du_semigroup_1078 :: T_CommutativeMonoid_996 -> T_Semigroup_558
du_semigroup_1078 :: T_CommutativeMonoid_996 -> T_Semigroup_558
du_semigroup_1078 T_CommutativeMonoid_996
v0
  = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
-- Algebra.Bundles.CommutativeMonoid._.unitalMagma
d_unitalMagma_1080 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> T_UnitalMagma_844
d_unitalMagma_1080 :: () -> () -> T_CommutativeMonoid_996 -> T_UnitalMagma_844
d_unitalMagma_1080 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_UnitalMagma_844
du_unitalMagma_1080 T_CommutativeMonoid_996
v2
du_unitalMagma_1080 :: T_CommutativeMonoid_996 -> T_UnitalMagma_844
du_unitalMagma_1080 :: T_CommutativeMonoid_996 -> T_UnitalMagma_844
du_unitalMagma_1080 T_CommutativeMonoid_996
v0
  = (T_Monoid_914 -> T_UnitalMagma_844) -> AgdaAny -> T_UnitalMagma_844
forall a b. a -> b
coe T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
-- Algebra.Bundles.CommutativeMonoid.commutativeSemigroup
d_commutativeSemigroup_1082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
d_commutativeSemigroup_1082 :: () -> () -> T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
d_commutativeSemigroup_1082 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2
  = T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082 T_CommutativeMonoid_996
v2
du_commutativeSemigroup_1082 ::
  T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082 :: T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082 T_CommutativeMonoid_996
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeSemigroup_568 -> T_CommutativeSemigroup_688)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeSemigroup_688
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeSemigroup_568 -> T_CommutativeSemigroup_688
C_constructor_754 (T_CommutativeMonoid_996 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1016 (T_CommutativeMonoid_996 -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1020 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0)))
-- Algebra.Bundles.CommutativeMonoid._.commutativeMagma
d_commutativeMagma_1086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_CommutativeMonoid_996 -> T_CommutativeMagma_190
d_commutativeMagma_1086 :: () -> () -> T_CommutativeMonoid_996 -> T_CommutativeMagma_190
d_commutativeMagma_1086 ~()
v0 ~()
v1 T_CommutativeMonoid_996
v2 = T_CommutativeMonoid_996 -> T_CommutativeMagma_190
du_commutativeMagma_1086 T_CommutativeMonoid_996
v2
du_commutativeMagma_1086 ::
  T_CommutativeMonoid_996 -> T_CommutativeMagma_190
du_commutativeMagma_1086 :: T_CommutativeMonoid_996 -> T_CommutativeMagma_190
du_commutativeMagma_1086 T_CommutativeMonoid_996
v0
  = (T_CommutativeSemigroup_688 -> T_CommutativeMagma_190)
-> AgdaAny -> T_CommutativeMagma_190
forall a b. a -> b
coe
      T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
du_commutativeMagma_752 ((T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082 (T_CommutativeMonoid_996 -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996
v0))
-- Algebra.Bundles.IdempotentMonoid
d_IdempotentMonoid_1094 :: p -> p -> ()
d_IdempotentMonoid_1094 p
a0 p
a1 = ()
data T_IdempotentMonoid_1094
  = C_constructor_1180 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                       MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
-- Algebra.Bundles.IdempotentMonoid.Carrier
d_Carrier_1110 :: T_IdempotentMonoid_1094 -> ()
d_Carrier_1110 :: T_IdempotentMonoid_1094 -> ()
d_Carrier_1110 = T_IdempotentMonoid_1094 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMonoid._≈_
d__'8776'__1112 ::
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1112 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1112 = T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMonoid._∙_
d__'8729'__1114 ::
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1114 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1114 T_IdempotentMonoid_1094
v0
  = case T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0 of
      C_constructor_1180 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentMonoid_826
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentMonoid_1094
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMonoid.ε
d_ε_1116 :: T_IdempotentMonoid_1094 -> AgdaAny
d_ε_1116 :: T_IdempotentMonoid_1094 -> AgdaAny
d_ε_1116 T_IdempotentMonoid_1094
v0
  = case T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0 of
      C_constructor_1180 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentMonoid_826
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_IdempotentMonoid_1094
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMonoid.isIdempotentMonoid
d_isIdempotentMonoid_1118 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 :: T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 T_IdempotentMonoid_1094
v0
  = case T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0 of
      C_constructor_1180 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentMonoid_826
v5 -> T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v5
      T_IdempotentMonoid_1094
_ -> T_IsIdempotentMonoid_826
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentMonoid._.assoc
d_assoc_1122 ::
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1122 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1122 T_IdempotentMonoid_1094
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
            ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))))
-- Algebra.Bundles.IdempotentMonoid._.idem
d_idem_1124 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_idem_1124 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_idem_1124 T_IdempotentMonoid_1094
v0
  = (T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_838
      ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
-- Algebra.Bundles.IdempotentMonoid._.identity
d_identity_1126 ::
  T_IdempotentMonoid_1094 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1126 :: T_IdempotentMonoid_1094 -> T_Σ_14
d_identity_1126 T_IdempotentMonoid_1094
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
         ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0)))
-- Algebra.Bundles.IdempotentMonoid._.identityʳ
d_identity'691'_1128 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_identity'691'_1128 :: () -> () -> T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_identity'691'_1128 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
du_identity'691'_1128 T_IdempotentMonoid_1094
v2
du_identity'691'_1128 ::
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
du_identity'691'_1128 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
du_identity'691'_1128 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
         ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1)))
-- Algebra.Bundles.IdempotentMonoid._.identityˡ
d_identity'737'_1130 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_identity'737'_1130 :: () -> () -> T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_identity'737'_1130 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
du_identity'737'_1130 T_IdempotentMonoid_1094
v2
du_identity'737'_1130 ::
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
du_identity'737'_1130 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
du_identity'737'_1130 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
         ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1)))
-- Algebra.Bundles.IdempotentMonoid._.isBand
d_isBand_1132 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1132 :: () -> () -> T_IdempotentMonoid_1094 -> T_IsBand_526
d_isBand_1132 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_IsBand_526
du_isBand_1132 T_IdempotentMonoid_1094
v2
du_isBand_1132 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_1132 :: T_IdempotentMonoid_1094 -> T_IsBand_526
du_isBand_1132 T_IdempotentMonoid_1094
v0
  = (T_IsIdempotentMonoid_826 -> T_IsBand_526)
-> AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
      ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
-- Algebra.Bundles.IdempotentMonoid._.isEquivalence
d_isEquivalence_1134 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1134 :: T_IdempotentMonoid_1094 -> T_IsEquivalence_28
d_isEquivalence_1134 T_IdempotentMonoid_1094
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
               ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0)))))
-- Algebra.Bundles.IdempotentMonoid._.isMagma
d_isMagma_1136 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1136 :: T_IdempotentMonoid_1094 -> T_IsMagma_178
d_isMagma_1136 T_IdempotentMonoid_1094
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
            ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))))
-- Algebra.Bundles.IdempotentMonoid._.isMonoid
d_isMonoid_1138 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1138 :: T_IdempotentMonoid_1094 -> T_IsMonoid_712
d_isMonoid_1138 T_IdempotentMonoid_1094
v0
  = (T_IsIdempotentMonoid_826 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
      ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
-- Algebra.Bundles.IdempotentMonoid._.isPartialEquivalence
d_isPartialEquivalence_1140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1140 :: () -> () -> T_IdempotentMonoid_1094 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1140 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2
  = T_IdempotentMonoid_1094 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1140 T_IdempotentMonoid_1094
v2
du_isPartialEquivalence_1140 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1140 :: T_IdempotentMonoid_1094 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1140 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Bundles.IdempotentMonoid._.isSemigroup
d_isSemigroup_1142 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1142 :: T_IdempotentMonoid_1094 -> T_IsSemigroup_488
d_isSemigroup_1142 T_IdempotentMonoid_1094
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
         ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0)))
-- Algebra.Bundles.IdempotentMonoid._.isUnitalMagma
d_isUnitalMagma_1144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1144 :: () -> () -> T_IdempotentMonoid_1094 -> T_IsUnitalMagma_666
d_isUnitalMagma_1144 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_IsUnitalMagma_666
du_isUnitalMagma_1144 T_IdempotentMonoid_1094
v2
du_isUnitalMagma_1144 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1144 :: T_IdempotentMonoid_1094 -> T_IsUnitalMagma_666
du_isUnitalMagma_1144 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1)))
-- Algebra.Bundles.IdempotentMonoid._.refl
d_refl_1146 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_refl_1146 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny
d_refl_1146 T_IdempotentMonoid_1094
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
                  ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))))))
-- Algebra.Bundles.IdempotentMonoid._.reflexive
d_reflexive_1148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1148 :: ()
-> ()
-> T_IdempotentMonoid_1094
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1148 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1148 T_IdempotentMonoid_1094
v2
du_reflexive_1148 ::
  T_IdempotentMonoid_1094 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1148 :: T_IdempotentMonoid_1094
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1148 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.IdempotentMonoid._.setoid
d_setoid_1150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1150 :: () -> () -> T_IdempotentMonoid_1094 -> T_Setoid_46
d_setoid_1150 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_Setoid_46
du_setoid_1150 T_IdempotentMonoid_1094
v2
du_setoid_1150 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1150 :: T_IdempotentMonoid_1094 -> T_Setoid_46
du_setoid_1150 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Bundles.IdempotentMonoid._.sym
d_sym_1152 ::
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1152 :: T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1152 T_IdempotentMonoid_1094
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
                  ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))))))
-- Algebra.Bundles.IdempotentMonoid._.trans
d_trans_1154 ::
  T_IdempotentMonoid_1094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1154 :: T_IdempotentMonoid_1094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1154 T_IdempotentMonoid_1094
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
                  ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))))))
-- Algebra.Bundles.IdempotentMonoid._.∙-cong
d_'8729''45'cong_1156 ::
  T_IdempotentMonoid_1094 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1156 :: T_IdempotentMonoid_1094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1156 T_IdempotentMonoid_1094
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsIdempotentMonoid_826 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
               ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0)))))
-- Algebra.Bundles.IdempotentMonoid._.∙-congʳ
d_'8729''45'cong'691'_1158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1158 :: ()
-> ()
-> T_IdempotentMonoid_1094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1158 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2
  = T_IdempotentMonoid_1094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1158 T_IdempotentMonoid_1094
v2
du_'8729''45'cong'691'_1158 ::
  T_IdempotentMonoid_1094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1158 :: T_IdempotentMonoid_1094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1158 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.IdempotentMonoid._.∙-congˡ
d_'8729''45'cong'737'_1160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1160 :: ()
-> ()
-> T_IdempotentMonoid_1094
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1160 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2
  = T_IdempotentMonoid_1094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1160 T_IdempotentMonoid_1094
v2
du_'8729''45'cong'737'_1160 ::
  T_IdempotentMonoid_1094 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1160 :: T_IdempotentMonoid_1094
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1160 T_IdempotentMonoid_1094
v0
  = let v1 :: T_IsIdempotentMonoid_826
v1 = T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836 (T_IsIdempotentMonoid_826 -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IsIdempotentMonoid_826
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.IdempotentMonoid.monoid
d_monoid_1162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> T_Monoid_914
d_monoid_1162 :: () -> () -> T_IdempotentMonoid_1094 -> T_Monoid_914
d_monoid_1162 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 T_IdempotentMonoid_1094
v2
du_monoid_1162 :: T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 :: T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 T_IdempotentMonoid_1094
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_712 -> T_Monoid_914)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> T_Monoid_914
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_712 -> T_Monoid_914
C_constructor_990 (T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1114 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0)) (T_IdempotentMonoid_1094 -> AgdaAny
d_ε_1116 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
      (T_IsIdempotentMonoid_826 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_836
         ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0)))
-- Algebra.Bundles.IdempotentMonoid._._≉_
d__'8777'__1166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1166 :: () -> () -> T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1166 = () -> () -> T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentMonoid._.magma
d_magma_1168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> T_Magma_74
d_magma_1168 :: () -> () -> T_IdempotentMonoid_1094 -> T_Magma_74
d_magma_1168 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_Magma_74
du_magma_1168 T_IdempotentMonoid_1094
v2
du_magma_1168 :: T_IdempotentMonoid_1094 -> T_Magma_74
du_magma_1168 :: T_IdempotentMonoid_1094 -> T_Magma_74
du_magma_1168 T_IdempotentMonoid_1094
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentMonoid_1094 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.IdempotentMonoid._.rawMagma
d_rawMagma_1170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1170 :: () -> () -> T_IdempotentMonoid_1094 -> T_RawMagma_44
d_rawMagma_1170 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_RawMagma_44
du_rawMagma_1170 T_IdempotentMonoid_1094
v2
du_rawMagma_1170 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1170 :: T_IdempotentMonoid_1094 -> T_RawMagma_44
du_rawMagma_1170 T_IdempotentMonoid_1094
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentMonoid_1094 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.IdempotentMonoid._.rawMonoid
d_rawMonoid_1172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
d_rawMonoid_1172 :: () -> () -> T_IdempotentMonoid_1094 -> T_RawMonoid_74
d_rawMonoid_1172 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_RawMonoid_74
du_rawMonoid_1172 T_IdempotentMonoid_1094
v2
du_rawMonoid_1172 ::
  T_IdempotentMonoid_1094 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
du_rawMonoid_1172 :: T_IdempotentMonoid_1094 -> T_RawMonoid_74
du_rawMonoid_1172 T_IdempotentMonoid_1094
v0
  = (T_Monoid_914 -> T_RawMonoid_74) -> AgdaAny -> T_RawMonoid_74
forall a b. a -> b
coe T_Monoid_914 -> T_RawMonoid_74
du_rawMonoid_986 ((T_IdempotentMonoid_1094 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
-- Algebra.Bundles.IdempotentMonoid._.semigroup
d_semigroup_1174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> T_Semigroup_558
d_semigroup_1174 :: () -> () -> T_IdempotentMonoid_1094 -> T_Semigroup_558
d_semigroup_1174 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_Semigroup_558
du_semigroup_1174 T_IdempotentMonoid_1094
v2
du_semigroup_1174 :: T_IdempotentMonoid_1094 -> T_Semigroup_558
du_semigroup_1174 :: T_IdempotentMonoid_1094 -> T_Semigroup_558
du_semigroup_1174 T_IdempotentMonoid_1094
v0
  = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 ((T_IdempotentMonoid_1094 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
-- Algebra.Bundles.IdempotentMonoid._.unitalMagma
d_unitalMagma_1176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> T_UnitalMagma_844
d_unitalMagma_1176 :: () -> () -> T_IdempotentMonoid_1094 -> T_UnitalMagma_844
d_unitalMagma_1176 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_UnitalMagma_844
du_unitalMagma_1176 T_IdempotentMonoid_1094
v2
du_unitalMagma_1176 :: T_IdempotentMonoid_1094 -> T_UnitalMagma_844
du_unitalMagma_1176 :: T_IdempotentMonoid_1094 -> T_UnitalMagma_844
du_unitalMagma_1176 T_IdempotentMonoid_1094
v0
  = (T_Monoid_914 -> T_UnitalMagma_844) -> AgdaAny -> T_UnitalMagma_844
forall a b. a -> b
coe T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 ((T_IdempotentMonoid_1094 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_Monoid_914
du_monoid_1162 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
-- Algebra.Bundles.IdempotentMonoid.band
d_band_1178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentMonoid_1094 -> T_Band_620
d_band_1178 :: () -> () -> T_IdempotentMonoid_1094 -> T_Band_620
d_band_1178 ~()
v0 ~()
v1 T_IdempotentMonoid_1094
v2 = T_IdempotentMonoid_1094 -> T_Band_620
du_band_1178 T_IdempotentMonoid_1094
v2
du_band_1178 :: T_IdempotentMonoid_1094 -> T_Band_620
du_band_1178 :: T_IdempotentMonoid_1094 -> T_Band_620
du_band_1178 T_IdempotentMonoid_1094
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> T_Band_620
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsBand_526 -> T_Band_620
C_constructor_682 (T_IdempotentMonoid_1094 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1114 (T_IdempotentMonoid_1094 -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0))
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
         ((T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094 -> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1118 (T_IdempotentMonoid_1094 -> AgdaAny
forall a b. a -> b
coe T_IdempotentMonoid_1094
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid
d_IdempotentCommutativeMonoid_1186 :: p -> p -> ()
d_IdempotentCommutativeMonoid_1186 p
a0 p
a1 = ()
data T_IdempotentCommutativeMonoid_1186
  = C_constructor_1296 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                       MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
-- Algebra.Bundles.IdempotentCommutativeMonoid.Carrier
d_Carrier_1202 :: T_IdempotentCommutativeMonoid_1186 -> ()
d_Carrier_1202 :: T_IdempotentCommutativeMonoid_1186 -> ()
d_Carrier_1202 = T_IdempotentCommutativeMonoid_1186 -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._≈_
d__'8776'__1204 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1204 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1204 = T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._∙_
d__'8729'__1206 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1206 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1206 T_IdempotentCommutativeMonoid_1186
v0
  = case T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0 of
      C_constructor_1296 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_IdempotentCommutativeMonoid_1186
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid.ε
d_ε_1208 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny
d_ε_1208 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny
d_ε_1208 T_IdempotentCommutativeMonoid_1186
v0
  = case T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0 of
      C_constructor_1296 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_IdempotentCommutativeMonoid_1186
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid.isIdempotentCommutativeMonoid
d_isIdempotentCommutativeMonoid_1210 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 :: T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 T_IdempotentCommutativeMonoid_1186
v0
  = case T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0 of
      C_constructor_1296 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 T_IsIdempotentCommutativeMonoid_884
v5 -> T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v5
      T_IdempotentCommutativeMonoid_1186
_ -> T_IsIdempotentCommutativeMonoid_884
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.IdempotentCommutativeMonoid._.assoc
d_assoc_1214 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1214 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1214 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.comm
d_comm_1216 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1216 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1216 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
         ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.idem
d_idem_1218 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_idem_1218 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_idem_1218 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_896
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identity
d_identity_1220 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1220 :: T_IdempotentCommutativeMonoid_1186 -> T_Σ_14
d_identity_1220 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identityʳ
d_identity'691'_1222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'691'_1222 :: ()
-> () -> T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'691'_1222 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'691'_1222 T_IdempotentCommutativeMonoid_1186
v2
du_identity'691'_1222 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'691'_1222 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'691'_1222 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.identityˡ
d_identity'737'_1224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'737'_1224 :: ()
-> () -> T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'737'_1224 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'737'_1224 T_IdempotentCommutativeMonoid_1186
v2
du_identity'737'_1224 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'737'_1224 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'737'_1224 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isBand
d_isBand_1226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1226 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_IsBand_526
d_isBand_1226 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IsBand_526
du_isBand_1226 T_IdempotentCommutativeMonoid_1186
v2
du_isBand_1226 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_1226 :: T_IdempotentCommutativeMonoid_1186 -> T_IsBand_526
du_isBand_1226 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeBand
d_isCommutativeBand_1228 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_1228 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsCommutativeBand_612
d_isCommutativeBand_1228 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeBand_612
du_isCommutativeBand_1228 T_IdempotentCommutativeMonoid_1186
v2
du_isCommutativeBand_1228 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_1228 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeBand_612
du_isCommutativeBand_1228 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMagma
d_isCommutativeMagma_1230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1230 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1230 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1230 T_IdempotentCommutativeMonoid_1186
v2
du_isCommutativeMagma_1230 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1230 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1230 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeMonoid
d_isCommutativeMonoid_1232 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1232 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1232 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isCommutativeSemigroup
d_isCommutativeSemigroup_1234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1234 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1234 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1234 T_IdempotentCommutativeMonoid_1186
v2
du_isCommutativeSemigroup_1234 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1234 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1234 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isEquivalence
d_isEquivalence_1236 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1236 :: T_IdempotentCommutativeMonoid_1186 -> T_IsEquivalence_28
d_isEquivalence_1236 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isIdempotentMonoid
d_isIdempotentMonoid_1238 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1238 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1238 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1238 T_IdempotentCommutativeMonoid_1186
v2
du_isIdempotentMonoid_1238 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1238 :: T_IdempotentCommutativeMonoid_1186 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1238 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isMagma
d_isMagma_1240 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1240 :: T_IdempotentCommutativeMonoid_1186 -> T_IsMagma_178
d_isMagma_1240 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isMonoid
d_isMonoid_1242 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1242 :: T_IdempotentCommutativeMonoid_1186 -> T_IsMonoid_712
d_isMonoid_1242 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
         ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isPartialEquivalence
d_isPartialEquivalence_1244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1244 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1244 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1244 T_IdempotentCommutativeMonoid_1186
v2
du_isPartialEquivalence_1244 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1244 :: T_IdempotentCommutativeMonoid_1186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1244 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isSemigroup
d_isSemigroup_1246 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1246 :: T_IdempotentCommutativeMonoid_1186 -> T_IsSemigroup_488
d_isSemigroup_1246 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.isUnitalMagma
d_isUnitalMagma_1248 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1248 :: ()
-> () -> T_IdempotentCommutativeMonoid_1186 -> T_IsUnitalMagma_666
d_isUnitalMagma_1248 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IsUnitalMagma_666
du_isUnitalMagma_1248 T_IdempotentCommutativeMonoid_1186
v2
du_isUnitalMagma_1248 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1248 :: T_IdempotentCommutativeMonoid_1186 -> T_IsUnitalMagma_666
du_isUnitalMagma_1248 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.refl
d_refl_1250 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_refl_1250 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_refl_1250 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.reflexive
d_reflexive_1252 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1252 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1252 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1252 T_IdempotentCommutativeMonoid_1186
v2
du_reflexive_1252 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1252 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1252 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.setoid
d_setoid_1254 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1254 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Setoid_46
d_setoid_1254 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Setoid_46
du_setoid_1254 T_IdempotentCommutativeMonoid_1186
v2
du_setoid_1254 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1254 :: T_IdempotentCommutativeMonoid_1186 -> T_Setoid_46
du_setoid_1254 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.sym
d_sym_1256 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1256 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1256 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.trans
d_trans_1258 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1258 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1258 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-cong
d_'8729''45'cong_1260 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1260 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1260 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congʳ
d_'8729''45'cong'691'_1262 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1262 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1262 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1262 T_IdempotentCommutativeMonoid_1186
v2
du_'8729''45'cong'691'_1262 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1262 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1262 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.∙-congˡ
d_'8729''45'cong'737'_1264 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1264 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1264 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1264 T_IdempotentCommutativeMonoid_1186
v2
du_'8729''45'cong'737'_1264 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1264 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1264 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Bundles.IdempotentCommutativeMonoid.commutativeMonoid
d_commutativeMonoid_1266 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
d_commutativeMonoid_1266 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeMonoid_996
d_commutativeMonoid_1266 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeMonoid_1266 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 T_IdempotentCommutativeMonoid_1186
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsCommutativeMonoid_764 -> T_CommutativeMonoid_996)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsCommutativeMonoid_764
-> T_CommutativeMonoid_996
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsCommutativeMonoid_764 -> T_CommutativeMonoid_996
C_constructor_1088 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1206 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)) (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
d_ε_1208 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
      (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
         ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid.idempotentMonoid
d_idempotentMonoid_1268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
d_idempotentMonoid_1268 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IdempotentMonoid_1094
d_idempotentMonoid_1268 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
du_idempotentMonoid_1268 T_IdempotentCommutativeMonoid_1186
v2
du_idempotentMonoid_1268 ::
  T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
du_idempotentMonoid_1268 :: T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
du_idempotentMonoid_1268 T_IdempotentCommutativeMonoid_1186
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsIdempotentMonoid_826 -> T_IdempotentMonoid_1094)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IdempotentMonoid_1094
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsIdempotentMonoid_826 -> T_IdempotentMonoid_1094
C_constructor_1180 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1206 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)) (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
d_ε_1208 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
         ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid.commutativeBand
d_commutativeBand_1270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
d_commutativeBand_1270 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeBand_760
d_commutativeBand_1270 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1270 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeBand_1270 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1270 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1270 T_IdempotentCommutativeMonoid_1186
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeBand_612 -> T_CommutativeBand_760)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_CommutativeBand_760
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeBand_612 -> T_CommutativeBand_760
C_constructor_838 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1206 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
         ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._._≉_
d__'8777'__1274 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1274 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__1274 = ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeMagma
d_commutativeMagma_1276 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
d_commutativeMagma_1276 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeMagma_190
d_commutativeMagma_1276 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
du_commutativeMagma_1276 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeMagma_1276 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
du_commutativeMagma_1276 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
du_commutativeMagma_1276 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_CommutativeMagma_190
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_688 -> T_CommutativeMagma_190)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
du_commutativeMagma_752
         ((T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.commutativeSemigroup
d_commutativeSemigroup_1278 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
d_commutativeSemigroup_1278 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeSemigroup_688
d_commutativeSemigroup_1278 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1278 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeSemigroup_1278 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1278 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1278 T_IdempotentCommutativeMonoid_1186
v0
  = (T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688)
-> AgdaAny -> T_CommutativeSemigroup_688
forall a b. a -> b
coe
      T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082
      ((T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.magma
d_magma_1280 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
d_magma_1280 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
d_magma_1280 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
du_magma_1280 T_IdempotentCommutativeMonoid_1186
v2
du_magma_1280 :: T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
du_magma_1280 :: T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
du_magma_1280 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.monoid
d_monoid_1282 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
d_monoid_1282 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
d_monoid_1282 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
du_monoid_1282 T_IdempotentCommutativeMonoid_1186
v2
du_monoid_1282 ::
  T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
du_monoid_1282 :: T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
du_monoid_1282 T_IdempotentCommutativeMonoid_1186
v0
  = (T_CommutativeMonoid_996 -> T_Monoid_914)
-> AgdaAny -> T_Monoid_914
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 ((T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMagma
d_rawMagma_1284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1284 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_RawMagma_44
d_rawMagma_1284 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_RawMagma_44
du_rawMagma_1284 T_IdempotentCommutativeMonoid_1186
v2
du_rawMagma_1284 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1284 :: T_IdempotentCommutativeMonoid_1186 -> T_RawMagma_44
du_rawMagma_1284 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.rawMonoid
d_rawMonoid_1286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
d_rawMonoid_1286 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_RawMonoid_74
d_rawMonoid_1286 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_RawMonoid_74
du_rawMonoid_1286 T_IdempotentCommutativeMonoid_1186
v2
du_rawMonoid_1286 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
du_rawMonoid_1286 :: T_IdempotentCommutativeMonoid_1186 -> T_RawMonoid_74
du_rawMonoid_1286 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_RawMonoid_74
forall a b. a -> b
coe ((T_Monoid_914 -> T_RawMonoid_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_RawMonoid_74
du_rawMonoid_986 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.semigroup
d_semigroup_1288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
d_semigroup_1288 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
d_semigroup_1288 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
du_semigroup_1288 T_IdempotentCommutativeMonoid_1186
v2
du_semigroup_1288 ::
  T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
du_semigroup_1288 :: T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
du_semigroup_1288 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.unitalMagma
d_unitalMagma_1290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
d_unitalMagma_1290 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
d_unitalMagma_1290 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
du_unitalMagma_1290 T_IdempotentCommutativeMonoid_1186
v2
du_unitalMagma_1290 ::
  T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
du_unitalMagma_1290 :: T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
du_unitalMagma_1290 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_UnitalMagma_844
forall a b. a -> b
coe ((T_Monoid_914 -> T_UnitalMagma_844) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.IdempotentCommutativeMonoid._.band
d_band_1294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Band_620
d_band_1294 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Band_620
d_band_1294 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Band_620
du_band_1294 T_IdempotentCommutativeMonoid_1186
v2
du_band_1294 :: T_IdempotentCommutativeMonoid_1186 -> T_Band_620
du_band_1294 :: T_IdempotentCommutativeMonoid_1186 -> T_Band_620
du_band_1294 T_IdempotentCommutativeMonoid_1186
v0
  = (T_CommutativeBand_760 -> T_Band_620) -> AgdaAny -> T_Band_620
forall a b. a -> b
coe T_CommutativeBand_760 -> T_Band_620
du_band_820 ((T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1270 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice
d_BoundedLattice_1298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 -> ()
d_BoundedLattice_1298 :: () -> () -> ()
d_BoundedLattice_1298 = () -> () -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice._∙_
d__'8729'__1308 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1308 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1308 T_IdempotentCommutativeMonoid_1186
v0 = (T_IdempotentCommutativeMonoid_1186
 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1206 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)
-- Algebra.Bundles.BoundedLattice._≈_
d__'8776'__1310 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1310 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1310 = T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice._≉_
d__'8777'__1312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1312 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> ()
d__'8777'__1312 = ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice.Carrier
d_Carrier_1314 :: T_IdempotentCommutativeMonoid_1186 -> ()
d_Carrier_1314 :: T_IdempotentCommutativeMonoid_1186 -> ()
d_Carrier_1314 = T_IdempotentCommutativeMonoid_1186 -> ()
forall a. a
erased
-- Algebra.Bundles.BoundedLattice.assoc
d_assoc_1316 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1316 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1316 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))
-- Algebra.Bundles.BoundedLattice.band
d_band_1318 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Band_620
d_band_1318 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Band_620
d_band_1318 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Band_620
du_band_1318 T_IdempotentCommutativeMonoid_1186
v2
du_band_1318 :: T_IdempotentCommutativeMonoid_1186 -> T_Band_620
du_band_1318 :: T_IdempotentCommutativeMonoid_1186 -> T_Band_620
du_band_1318 T_IdempotentCommutativeMonoid_1186
v0
  = (T_CommutativeBand_760 -> T_Band_620) -> AgdaAny -> T_Band_620
forall a b. a -> b
coe T_CommutativeBand_760 -> T_Band_620
du_band_820 ((T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1270 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice.comm
d_comm_1320 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1320 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1320 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
         ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))
-- Algebra.Bundles.BoundedLattice.commutativeBand
d_commutativeBand_1322 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
d_commutativeBand_1322 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeBand_760
d_commutativeBand_1322 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1322 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeBand_1322 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1322 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1322 T_IdempotentCommutativeMonoid_1186
v0 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760)
-> AgdaAny -> T_CommutativeBand_760
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeBand_760
du_commutativeBand_1270 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)
-- Algebra.Bundles.BoundedLattice.commutativeMagma
d_commutativeMagma_1324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
d_commutativeMagma_1324 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeMagma_190
d_commutativeMagma_1324 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
du_commutativeMagma_1324 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeMagma_1324 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
du_commutativeMagma_1324 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMagma_190
du_commutativeMagma_1324 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_CommutativeMagma_190
forall a b. a -> b
coe
      ((T_CommutativeSemigroup_688 -> T_CommutativeMagma_190)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_CommutativeSemigroup_688 -> T_CommutativeMagma_190
du_commutativeMagma_752
         ((T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.BoundedLattice.commutativeMonoid
d_commutativeMonoid_1326 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
d_commutativeMonoid_1326 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeMonoid_996
d_commutativeMonoid_1326 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1326 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeMonoid_1326 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1326 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1326 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> T_CommutativeMonoid_996
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)
-- Algebra.Bundles.BoundedLattice.commutativeSemigroup
d_commutativeSemigroup_1328 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
d_commutativeSemigroup_1328 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_CommutativeSemigroup_688
d_commutativeSemigroup_1328 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1328 T_IdempotentCommutativeMonoid_1186
v2
du_commutativeSemigroup_1328 ::
  T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1328 :: T_IdempotentCommutativeMonoid_1186 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1328 T_IdempotentCommutativeMonoid_1186
v0
  = (T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688)
-> AgdaAny -> T_CommutativeSemigroup_688
forall a b. a -> b
coe
      T_CommutativeMonoid_996 -> T_CommutativeSemigroup_688
du_commutativeSemigroup_1082
      ((T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice.idem
d_idem_1330 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_idem_1330 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_idem_1330 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_idem_896
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice.idempotentMonoid
d_idempotentMonoid_1332 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
d_idempotentMonoid_1332 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IdempotentMonoid_1094
d_idempotentMonoid_1332 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
du_idempotentMonoid_1332 T_IdempotentCommutativeMonoid_1186
v2
du_idempotentMonoid_1332 ::
  T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
du_idempotentMonoid_1332 :: T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
du_idempotentMonoid_1332 T_IdempotentCommutativeMonoid_1186
v0 = (T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094)
-> AgdaAny -> T_IdempotentMonoid_1094
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_IdempotentMonoid_1094
du_idempotentMonoid_1268 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)
-- Algebra.Bundles.BoundedLattice.identity
d_identity_1334 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1334 :: T_IdempotentCommutativeMonoid_1186 -> T_Σ_14
d_identity_1334 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))
-- Algebra.Bundles.BoundedLattice.identityʳ
d_identity'691'_1336 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'691'_1336 :: ()
-> () -> T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'691'_1336 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'691'_1336 T_IdempotentCommutativeMonoid_1186
v2
du_identity'691'_1336 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'691'_1336 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'691'_1336 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.BoundedLattice.identityˡ
d_identity'737'_1338 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'737'_1338 :: ()
-> () -> T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_identity'737'_1338 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'737'_1338 T_IdempotentCommutativeMonoid_1186
v2
du_identity'737'_1338 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'737'_1338 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
du_identity'737'_1338 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.BoundedLattice.isBand
d_isBand_1340 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_isBand_1340 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_IsBand_526
d_isBand_1340 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IsBand_526
du_isBand_1340 T_IdempotentCommutativeMonoid_1186
v2
du_isBand_1340 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_isBand_1340 :: T_IdempotentCommutativeMonoid_1186 -> T_IsBand_526
du_isBand_1340 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      ((T_IsIdempotentMonoid_826 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentMonoid_826 -> T_IsBand_526
MAlonzo.Code.Algebra.Structures.du_isBand_876
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Bundles.BoundedLattice.isCommutativeBand
d_isCommutativeBand_1342 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_isCommutativeBand_1342 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsCommutativeBand_612
d_isCommutativeBand_1342 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeBand_612
du_isCommutativeBand_1342 T_IdempotentCommutativeMonoid_1186
v2
du_isCommutativeBand_1342 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_isCommutativeBand_1342 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeBand_612
du_isCommutativeBand_1342 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612)
-> AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Structures.du_isCommutativeBand_948
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice.isCommutativeMagma
d_isCommutativeMagma_1344 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1344 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsCommutativeMagma_214
d_isCommutativeMagma_1344 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1344 T_IdempotentCommutativeMonoid_1186
v2
du_isCommutativeMagma_1344 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1344 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1344 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.BoundedLattice.isCommutativeMonoid
d_isCommutativeMonoid_1346 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1346 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1346 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice.isCommutativeSemigroup
d_isCommutativeSemigroup_1348 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1348 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1348 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1348 T_IdempotentCommutativeMonoid_1186
v2
du_isCommutativeSemigroup_1348 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1348 :: T_IdempotentCommutativeMonoid_1186 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1348 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            (T_IsIdempotentCommutativeMonoid_884 -> AgdaAny
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1)))
-- Algebra.Bundles.BoundedLattice.isEquivalence
d_isEquivalence_1350 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1350 :: T_IdempotentCommutativeMonoid_1186 -> T_IsEquivalence_28
d_isEquivalence_1350 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))))
-- Algebra.Bundles.BoundedLattice.isIdempotentCommutativeMonoid
d_isIdempotentCommutativeMonoid_1352 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1352 :: T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1352 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)
-- Algebra.Bundles.BoundedLattice.isIdempotentMonoid
d_isIdempotentMonoid_1354 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1354 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentMonoid_826
d_isIdempotentMonoid_1354 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1354 T_IdempotentCommutativeMonoid_1186
v2
du_isIdempotentMonoid_1354 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1354 :: T_IdempotentCommutativeMonoid_1186 -> T_IsIdempotentMonoid_826
du_isIdempotentMonoid_1354 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826)
-> AgdaAny -> T_IsIdempotentMonoid_826
forall a b. a -> b
coe
      T_IsIdempotentCommutativeMonoid_884 -> T_IsIdempotentMonoid_826
MAlonzo.Code.Algebra.Structures.du_isIdempotentMonoid_942
      ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice.isMagma
d_isMagma_1356 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1356 :: T_IdempotentCommutativeMonoid_1186 -> T_IsMagma_178
d_isMagma_1356 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
            ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
               ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))
-- Algebra.Bundles.BoundedLattice.isMonoid
d_isMonoid_1358 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1358 :: T_IdempotentCommutativeMonoid_1186 -> T_IsMonoid_712
d_isMonoid_1358 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
      ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
         ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))
-- Algebra.Bundles.BoundedLattice.isPartialEquivalence
d_isPartialEquivalence_1360 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1360 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1360 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1360 T_IdempotentCommutativeMonoid_1186
v2
du_isPartialEquivalence_1360 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1360 :: T_IdempotentCommutativeMonoid_1186 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1360 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Algebra.Bundles.BoundedLattice.isSemigroup
d_isSemigroup_1362 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1362 :: T_IdempotentCommutativeMonoid_1186 -> T_IsSemigroup_488
d_isSemigroup_1362 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
         ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
            ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))
-- Algebra.Bundles.BoundedLattice.isUnitalMagma
d_isUnitalMagma_1364 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1364 :: ()
-> () -> T_IdempotentCommutativeMonoid_1186 -> T_IsUnitalMagma_666
d_isUnitalMagma_1364 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_IsUnitalMagma_666
du_isUnitalMagma_1364 T_IdempotentCommutativeMonoid_1186
v2
du_isUnitalMagma_1364 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1364 :: T_IdempotentCommutativeMonoid_1186 -> T_IsUnitalMagma_666
du_isUnitalMagma_1364 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2))))
-- Algebra.Bundles.BoundedLattice.magma
d_magma_1366 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
d_magma_1366 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
d_magma_1366 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
du_magma_1366 T_IdempotentCommutativeMonoid_1186
v2
du_magma_1366 :: T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
du_magma_1366 :: T_IdempotentCommutativeMonoid_1186 -> T_Magma_74
du_magma_1366 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.BoundedLattice.monoid
d_monoid_1368 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
d_monoid_1368 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
d_monoid_1368 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
du_monoid_1368 T_IdempotentCommutativeMonoid_1186
v2
du_monoid_1368 ::
  T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
du_monoid_1368 :: T_IdempotentCommutativeMonoid_1186 -> T_Monoid_914
du_monoid_1368 T_IdempotentCommutativeMonoid_1186
v0
  = (T_CommutativeMonoid_996 -> T_Monoid_914)
-> AgdaAny -> T_Monoid_914
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 ((T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))
-- Algebra.Bundles.BoundedLattice.rawMagma
d_rawMagma_1370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1370 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_RawMagma_44
d_rawMagma_1370 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_RawMagma_44
du_rawMagma_1370 T_IdempotentCommutativeMonoid_1186
v2
du_rawMagma_1370 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1370 :: T_IdempotentCommutativeMonoid_1186 -> T_RawMagma_44
du_rawMagma_1370 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Bundles.BoundedLattice.rawMonoid
d_rawMonoid_1372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
d_rawMonoid_1372 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_RawMonoid_74
d_rawMonoid_1372 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_RawMonoid_74
du_rawMonoid_1372 T_IdempotentCommutativeMonoid_1186
v2
du_rawMonoid_1372 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
du_rawMonoid_1372 :: T_IdempotentCommutativeMonoid_1186 -> T_RawMonoid_74
du_rawMonoid_1372 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_RawMonoid_74
forall a b. a -> b
coe ((T_Monoid_914 -> T_RawMonoid_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_RawMonoid_74
du_rawMonoid_986 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.BoundedLattice.refl
d_refl_1374 ::
  T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_refl_1374 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny -> AgdaAny
d_refl_1374 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))))
-- Algebra.Bundles.BoundedLattice.reflexive
d_reflexive_1376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1376 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1376 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1376 T_IdempotentCommutativeMonoid_1186
v2
du_reflexive_1376 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1376 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1376 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.BoundedLattice.semigroup
d_semigroup_1378 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
d_semigroup_1378 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
d_semigroup_1378 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
du_semigroup_1378 T_IdempotentCommutativeMonoid_1186
v2
du_semigroup_1378 ::
  T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
du_semigroup_1378 :: T_IdempotentCommutativeMonoid_1186 -> T_Semigroup_558
du_semigroup_1378 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.BoundedLattice.setoid
d_setoid_1380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1380 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_Setoid_46
d_setoid_1380 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_Setoid_46
du_setoid_1380 T_IdempotentCommutativeMonoid_1186
v2
du_setoid_1380 ::
  T_IdempotentCommutativeMonoid_1186 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1380 :: T_IdempotentCommutativeMonoid_1186 -> T_Setoid_46
du_setoid_1380 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Algebra.Bundles.BoundedLattice.sym
d_sym_1382 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1382 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1382 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))))
-- Algebra.Bundles.BoundedLattice.trans
d_trans_1384 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1384 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1384 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
                  ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                     ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)))))))
-- Algebra.Bundles.BoundedLattice.unitalMagma
d_unitalMagma_1386 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
d_unitalMagma_1386 :: () -> () -> T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
d_unitalMagma_1386 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2 = T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
du_unitalMagma_1386 T_IdempotentCommutativeMonoid_1186
v2
du_unitalMagma_1386 ::
  T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
du_unitalMagma_1386 :: T_IdempotentCommutativeMonoid_1186 -> T_UnitalMagma_844
du_unitalMagma_1386 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: AgdaAny
v1 = (T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> T_CommutativeMonoid_996
du_commutativeMonoid_1266 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> T_UnitalMagma_844
forall a b. a -> b
coe ((T_Monoid_914 -> T_UnitalMagma_844) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 ((T_CommutativeMonoid_996 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_CommutativeMonoid_996 -> T_Monoid_914
du_monoid_1066 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.BoundedLattice.ε
d_ε_1388 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny
d_ε_1388 :: T_IdempotentCommutativeMonoid_1186 -> AgdaAny
d_ε_1388 T_IdempotentCommutativeMonoid_1186
v0 = (T_IdempotentCommutativeMonoid_1186 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186 -> AgdaAny
d_ε_1208 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0)
-- Algebra.Bundles.BoundedLattice.∙-cong
d_'8729''45'cong_1390 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1390 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1390 T_IdempotentCommutativeMonoid_1186
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsCommutativeMonoid_764 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774
               ((T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                  ((T_IdempotentCommutativeMonoid_1186
 -> T_IsIdempotentCommutativeMonoid_884)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186 -> AgdaAny
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0))))))
-- Algebra.Bundles.BoundedLattice.∙-congʳ
d_'8729''45'cong'691'_1392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1392 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1392 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1392 T_IdempotentCommutativeMonoid_1186
v2
du_'8729''45'cong'691'_1392 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1392 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1392 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Bundles.BoundedLattice.∙-congˡ
d_'8729''45'cong'737'_1394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1394 :: ()
-> ()
-> T_IdempotentCommutativeMonoid_1186
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1394 ~()
v0 ~()
v1 T_IdempotentCommutativeMonoid_1186
v2
  = T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1394 T_IdempotentCommutativeMonoid_1186
v2
du_'8729''45'cong'737'_1394 ::
  T_IdempotentCommutativeMonoid_1186 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1394 :: T_IdempotentCommutativeMonoid_1186
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1394 T_IdempotentCommutativeMonoid_1186
v0
  = let v1 :: T_IsIdempotentCommutativeMonoid_884
v1 = T_IdempotentCommutativeMonoid_1186
-> T_IsIdempotentCommutativeMonoid_884
d_isIdempotentCommutativeMonoid_1210 (T_IdempotentCommutativeMonoid_1186
-> T_IdempotentCommutativeMonoid_1186
forall a b. a -> b
coe T_IdempotentCommutativeMonoid_1186
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsCommutativeMonoid_764
v2
             = T_IsIdempotentCommutativeMonoid_884 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.d_isCommutativeMonoid_894
                 (T_IsIdempotentCommutativeMonoid_884
-> T_IsIdempotentCommutativeMonoid_884
forall a b. a -> b
coe T_IsIdempotentCommutativeMonoid_884
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Bundles.InvertibleMagma
d_InvertibleMagma_1400 :: p -> p -> ()
d_InvertibleMagma_1400 p
a0 p
a1 = ()
data T_InvertibleMagma_1400
  = C_constructor_1470 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                       (AgdaAny -> AgdaAny)
                       MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
-- Algebra.Bundles.InvertibleMagma.Carrier
d_Carrier_1418 :: T_InvertibleMagma_1400 -> ()
d_Carrier_1418 :: T_InvertibleMagma_1400 -> ()
d_Carrier_1418 = T_InvertibleMagma_1400 -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleMagma._≈_
d__'8776'__1420 ::
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1420 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1420 = T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleMagma._∙_
d__'8729'__1422 ::
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1422 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1422 T_InvertibleMagma_1400
v0
  = case T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0 of
      C_constructor_1470 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_958
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_InvertibleMagma_1400
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma.ε
d_ε_1424 :: T_InvertibleMagma_1400 -> AgdaAny
d_ε_1424 :: T_InvertibleMagma_1400 -> AgdaAny
d_ε_1424 T_InvertibleMagma_1400
v0
  = case T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0 of
      C_constructor_1470 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_958
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_InvertibleMagma_1400
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma._⁻¹
d__'8315''185'_1426 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d__'8315''185'_1426 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d__'8315''185'_1426 T_InvertibleMagma_1400
v0
  = case T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0 of
      C_constructor_1470 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_958
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_InvertibleMagma_1400
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma.isInvertibleMagma
d_isInvertibleMagma_1428 ::
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 :: T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 T_InvertibleMagma_1400
v0
  = case T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0 of
      C_constructor_1470 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleMagma_958
v6 -> T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v6
      T_InvertibleMagma_1400
_ -> T_IsInvertibleMagma_958
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleMagma._.inverse
d_inverse_1432 ::
  T_InvertibleMagma_1400 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1432 :: T_InvertibleMagma_1400 -> T_Σ_14
d_inverse_1432 T_InvertibleMagma_1400
v0
  = (T_IsInvertibleMagma_958 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_974
      ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))
-- Algebra.Bundles.InvertibleMagma._.inverseʳ
d_inverse'691'_1434 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d_inverse'691'_1434 :: () -> () -> T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d_inverse'691'_1434 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2 = T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
du_inverse'691'_1434 T_InvertibleMagma_1400
v2
du_inverse'691'_1434 ::
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
du_inverse'691'_1434 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
du_inverse'691'_1434 T_InvertibleMagma_1400
v0
  = (T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1002
      ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))
-- Algebra.Bundles.InvertibleMagma._.inverseˡ
d_inverse'737'_1436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d_inverse'737'_1436 :: () -> () -> T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d_inverse'737'_1436 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2 = T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
du_inverse'737'_1436 T_InvertibleMagma_1400
v2
du_inverse'737'_1436 ::
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
du_inverse'737'_1436 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
du_inverse'737'_1436 T_InvertibleMagma_1400
v0
  = (T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1000
      ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))
-- Algebra.Bundles.InvertibleMagma._.isEquivalence
d_isEquivalence_1438 ::
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1438 :: T_InvertibleMagma_1400 -> T_IsEquivalence_28
d_isEquivalence_1438 T_InvertibleMagma_1400
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
         ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0)))
-- Algebra.Bundles.InvertibleMagma._.isMagma
d_isMagma_1440 ::
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1440 :: T_InvertibleMagma_1400 -> T_IsMagma_178
d_isMagma_1440 T_InvertibleMagma_1400
v0
  = (T_IsInvertibleMagma_958 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
      ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))
-- Algebra.Bundles.InvertibleMagma._.isPartialEquivalence
d_isPartialEquivalence_1442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1442 :: () -> () -> T_InvertibleMagma_1400 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1442 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2
  = T_InvertibleMagma_1400 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1442 T_InvertibleMagma_1400
v2
du_isPartialEquivalence_1442 ::
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1442 :: T_InvertibleMagma_1400 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1442 T_InvertibleMagma_1400
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))))
-- Algebra.Bundles.InvertibleMagma._.refl
d_refl_1444 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d_refl_1444 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny
d_refl_1444 T_InvertibleMagma_1400
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
            ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))))
-- Algebra.Bundles.InvertibleMagma._.reflexive
d_reflexive_1446 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1446 :: ()
-> ()
-> T_InvertibleMagma_1400
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1446 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2 = T_InvertibleMagma_1400
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1446 T_InvertibleMagma_1400
v2
du_reflexive_1446 ::
  T_InvertibleMagma_1400 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1446 :: T_InvertibleMagma_1400
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1446 T_InvertibleMagma_1400
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2))
              AgdaAny
v3))
-- Algebra.Bundles.InvertibleMagma._.setoid
d_setoid_1448 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1448 :: () -> () -> T_InvertibleMagma_1400 -> T_Setoid_46
d_setoid_1448 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2 = T_InvertibleMagma_1400 -> T_Setoid_46
du_setoid_1448 T_InvertibleMagma_1400
v2
du_setoid_1448 ::
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1448 :: T_InvertibleMagma_1400 -> T_Setoid_46
du_setoid_1448 T_InvertibleMagma_1400
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1)))
-- Algebra.Bundles.InvertibleMagma._.sym
d_sym_1450 ::
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1450 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1450 T_InvertibleMagma_1400
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
            ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))))
-- Algebra.Bundles.InvertibleMagma._.trans
d_trans_1452 ::
  T_InvertibleMagma_1400 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1452 :: T_InvertibleMagma_1400
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1452 T_InvertibleMagma_1400
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
            ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))))
-- Algebra.Bundles.InvertibleMagma._.⁻¹-cong
d_'8315''185''45'cong_1454 ::
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1454 :: T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1454 T_InvertibleMagma_1400
v0
  = (T_IsInvertibleMagma_958
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_976
      ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))
-- Algebra.Bundles.InvertibleMagma._.∙-cong
d_'8729''45'cong_1456 ::
  T_InvertibleMagma_1400 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1456 :: T_InvertibleMagma_1400
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1456 T_InvertibleMagma_1400
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
         ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0)))
-- Algebra.Bundles.InvertibleMagma._.∙-congʳ
d_'8729''45'cong'691'_1458 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1458 :: ()
-> ()
-> T_InvertibleMagma_1400
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1458 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2
  = T_InvertibleMagma_1400
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1458 T_InvertibleMagma_1400
v2
du_'8729''45'cong'691'_1458 ::
  T_InvertibleMagma_1400 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1458 :: T_InvertibleMagma_1400
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1458 T_InvertibleMagma_1400
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.InvertibleMagma._.∙-congˡ
d_'8729''45'cong'737'_1460 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1460 :: ()
-> ()
-> T_InvertibleMagma_1400
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1460 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2
  = T_InvertibleMagma_1400
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1460 T_InvertibleMagma_1400
v2
du_'8729''45'cong'737'_1460 ::
  T_InvertibleMagma_1400 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1460 :: T_InvertibleMagma_1400
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1460 T_InvertibleMagma_1400
v0
  = let v1 :: T_IsInvertibleMagma_958
v1 = T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMagma_178
v2 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3
                = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4
                   = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v2) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                  ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v4)
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))))
-- Algebra.Bundles.InvertibleMagma.magma
d_magma_1462 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 -> T_Magma_74
d_magma_1462 :: () -> () -> T_InvertibleMagma_1400 -> T_Magma_74
d_magma_1462 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2 = T_InvertibleMagma_1400 -> T_Magma_74
du_magma_1462 T_InvertibleMagma_1400
v2
du_magma_1462 :: T_InvertibleMagma_1400 -> T_Magma_74
du_magma_1462 :: T_InvertibleMagma_1400 -> T_Magma_74
du_magma_1462 T_InvertibleMagma_1400
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsMagma_178 -> T_Magma_74
C_constructor_124 (T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1422 (T_InvertibleMagma_1400 -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))
      (T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
         ((T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958)
-> AgdaAny -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1428 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0)))
-- Algebra.Bundles.InvertibleMagma._._≉_
d__'8777'__1466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1466 :: () -> () -> T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1466 = () -> () -> T_InvertibleMagma_1400 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleMagma._.rawMagma
d_rawMagma_1468 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1468 :: () -> () -> T_InvertibleMagma_1400 -> T_RawMagma_44
d_rawMagma_1468 ~()
v0 ~()
v1 T_InvertibleMagma_1400
v2 = T_InvertibleMagma_1400 -> T_RawMagma_44
du_rawMagma_1468 T_InvertibleMagma_1400
v2
du_rawMagma_1468 ::
  T_InvertibleMagma_1400 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1468 :: T_InvertibleMagma_1400 -> T_RawMagma_44
du_rawMagma_1468 T_InvertibleMagma_1400
v0
  = (T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_InvertibleMagma_1400 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_Magma_74
du_magma_1462 (T_InvertibleMagma_1400 -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400
v0))
-- Algebra.Bundles.InvertibleUnitalMagma
d_InvertibleUnitalMagma_1476 :: p -> p -> ()
d_InvertibleUnitalMagma_1476 p
a0 p
a1 = ()
data T_InvertibleUnitalMagma_1476
  = C_constructor_1558 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                       (AgdaAny -> AgdaAny)
                       MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
-- Algebra.Bundles.InvertibleUnitalMagma.Carrier
d_Carrier_1494 :: T_InvertibleUnitalMagma_1476 -> ()
d_Carrier_1494 :: T_InvertibleUnitalMagma_1476 -> ()
d_Carrier_1494 = T_InvertibleUnitalMagma_1476 -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleUnitalMagma._≈_
d__'8776'__1496 ::
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1496 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1496 = T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleUnitalMagma._∙_
d__'8729'__1498 ::
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1498 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1498 T_InvertibleUnitalMagma_1476
v0
  = case T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0 of
      C_constructor_1558 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_1012
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_InvertibleUnitalMagma_1476
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma.ε
d_ε_1500 :: T_InvertibleUnitalMagma_1476 -> AgdaAny
d_ε_1500 :: T_InvertibleUnitalMagma_1476 -> AgdaAny
d_ε_1500 T_InvertibleUnitalMagma_1476
v0
  = case T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0 of
      C_constructor_1558 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_1012
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_InvertibleUnitalMagma_1476
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma._⁻¹
d__'8315''185'_1502 ::
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d__'8315''185'_1502 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d__'8315''185'_1502 T_InvertibleUnitalMagma_1476
v0
  = case T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0 of
      C_constructor_1558 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_1012
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_InvertibleUnitalMagma_1476
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1504 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 :: T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 T_InvertibleUnitalMagma_1476
v0
  = case T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0 of
      C_constructor_1558 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsInvertibleUnitalMagma_1012
v6 -> T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v6
      T_InvertibleUnitalMagma_1476
_ -> T_IsInvertibleUnitalMagma_1012
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.InvertibleUnitalMagma._.identity
d_identity_1508 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1508 :: T_InvertibleUnitalMagma_1476 -> T_Σ_14
d_identity_1508 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleUnitalMagma_1012 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_1012 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_1026
      ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.identityʳ
d_identity'691'_1510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_identity'691'_1510 :: () -> () -> T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_identity'691'_1510 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_identity'691'_1510 T_InvertibleUnitalMagma_1476
v2
du_identity'691'_1510 ::
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_identity'691'_1510 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_identity'691'_1510 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_1062
      ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.identityˡ
d_identity'737'_1512 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_identity'737'_1512 :: () -> () -> T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_identity'737'_1512 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_identity'737'_1512 T_InvertibleUnitalMagma_1476
v2
du_identity'737'_1512 ::
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_identity'737'_1512 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_identity'737'_1512 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_1012 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_1060
      ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.inverse
d_inverse_1514 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1514 :: T_InvertibleUnitalMagma_1476 -> T_Σ_14
d_inverse_1514 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleMagma_958 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_974
      ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
         ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._.inverseʳ
d_inverse'691'_1516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_inverse'691'_1516 :: () -> () -> T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_inverse'691'_1516 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_inverse'691'_1516 T_InvertibleUnitalMagma_1476
v2
du_inverse'691'_1516 ::
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_inverse'691'_1516 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_inverse'691'_1516 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: T_IsInvertibleUnitalMagma_1012
v1 = T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1002
         ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v1)))
-- Algebra.Bundles.InvertibleUnitalMagma._.inverseˡ
d_inverse'737'_1518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_inverse'737'_1518 :: () -> () -> T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_inverse'737'_1518 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_inverse'737'_1518 T_InvertibleUnitalMagma_1476
v2
du_inverse'737'_1518 ::
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_inverse'737'_1518 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
du_inverse'737'_1518 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: T_IsInvertibleUnitalMagma_1012
v1 = T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1000
         ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024 (T_IsInvertibleUnitalMagma_1012 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v1)))
-- Algebra.Bundles.InvertibleUnitalMagma._.isEquivalence
d_isEquivalence_1520 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1520 :: T_InvertibleUnitalMagma_1476 -> T_IsEquivalence_28
d_isEquivalence_1520 T_InvertibleUnitalMagma_1476
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
         ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
            ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))))
-- Algebra.Bundles.InvertibleUnitalMagma._.isInvertibleMagma
d_isInvertibleMagma_1522 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_1522 :: T_InvertibleUnitalMagma_1476 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1522 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
      ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.isMagma
d_isMagma_1524 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1524 :: T_InvertibleUnitalMagma_1476 -> T_IsMagma_178
d_isMagma_1524 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleMagma_958 -> T_IsMagma_178)
-> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
      ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
         ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._.isPartialEquivalence
d_isPartialEquivalence_1526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1526 :: ()
-> () -> T_InvertibleUnitalMagma_1476 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1526 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2
  = T_InvertibleUnitalMagma_1476 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1526 T_InvertibleUnitalMagma_1476
v2
du_isPartialEquivalence_1526 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1526 :: T_InvertibleUnitalMagma_1476 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1526 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: T_IsInvertibleUnitalMagma_1012
v1 = T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_958
v2
             = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
                 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.isUnitalMagma
d_isUnitalMagma_1528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1528 :: () -> () -> T_InvertibleUnitalMagma_1476 -> T_IsUnitalMagma_666
d_isUnitalMagma_1528 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> T_IsUnitalMagma_666
du_isUnitalMagma_1528 T_InvertibleUnitalMagma_1476
v2
du_isUnitalMagma_1528 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1528 :: T_InvertibleUnitalMagma_1476 -> T_IsUnitalMagma_666
du_isUnitalMagma_1528 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666)
-> AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      T_IsInvertibleUnitalMagma_1012 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_1064
      ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.refl
d_refl_1530 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_refl_1530 :: T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d_refl_1530 T_InvertibleUnitalMagma_1476
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
            ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
               ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.reflexive
d_reflexive_1532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1532 :: ()
-> ()
-> T_InvertibleUnitalMagma_1476
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1532 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1532 T_InvertibleUnitalMagma_1476
v2
du_reflexive_1532 ::
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1532 :: T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1532 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: T_IsInvertibleUnitalMagma_1012
v1 = T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_958
v2
             = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
                 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3))
                 AgdaAny
v4)))
-- Algebra.Bundles.InvertibleUnitalMagma._.setoid
d_setoid_1534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1534 :: () -> () -> T_InvertibleUnitalMagma_1476 -> T_Setoid_46
d_setoid_1534 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> T_Setoid_46
du_setoid_1534 T_InvertibleUnitalMagma_1476
v2
du_setoid_1534 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1534 :: T_InvertibleUnitalMagma_1476 -> T_Setoid_46
du_setoid_1534 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: T_IsInvertibleUnitalMagma_1012
v1 = T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_958
v2
             = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
                 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
            ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> AgdaAny
forall a b. a -> b
coe T_IsInvertibleMagma_958
v2))))
-- Algebra.Bundles.InvertibleUnitalMagma._.sym
d_sym_1536 ::
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1536 :: T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1536 T_InvertibleUnitalMagma_1476
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
            ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
               ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.trans
d_trans_1538 ::
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1538 :: T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1538 T_InvertibleUnitalMagma_1476
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
            ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
               ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)))))
-- Algebra.Bundles.InvertibleUnitalMagma._.⁻¹-cong
d_'8315''185''45'cong_1540 ::
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1540 :: T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1540 T_InvertibleUnitalMagma_1476
v0
  = (T_IsInvertibleMagma_958
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsInvertibleMagma_958 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_976
      ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
         ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._.∙-cong
d_'8729''45'cong_1542 ::
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1542 :: T_InvertibleUnitalMagma_1476
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1542 T_InvertibleUnitalMagma_1476
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsInvertibleMagma_958 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972
         ((T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
            ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))))
-- Algebra.Bundles.InvertibleUnitalMagma._.∙-congʳ
d_'8729''45'cong'691'_1544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1544 :: ()
-> ()
-> T_InvertibleUnitalMagma_1476
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1544 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2
  = T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1544 T_InvertibleUnitalMagma_1476
v2
du_'8729''45'cong'691'_1544 ::
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1544 :: T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1544 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: T_IsInvertibleUnitalMagma_1012
v1 = T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_958
v2
             = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
                 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.InvertibleUnitalMagma._.∙-congˡ
d_'8729''45'cong'737'_1546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1546 :: ()
-> ()
-> T_InvertibleUnitalMagma_1476
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1546 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2
  = T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1546 T_InvertibleUnitalMagma_1476
v2
du_'8729''45'cong'737'_1546 ::
  T_InvertibleUnitalMagma_1476 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1546 :: T_InvertibleUnitalMagma_1476
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1546 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: T_IsInvertibleUnitalMagma_1012
v1 = T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsInvertibleMagma_958
v2
             = T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
                 (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_IsInvertibleUnitalMagma_1012
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMagma_178
v3 = T_IsInvertibleMagma_958 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_972 (T_IsInvertibleMagma_958 -> T_IsInvertibleMagma_958
forall a b. a -> b
coe T_IsInvertibleMagma_958
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: AgdaAny
v4
                   = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5
                      = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v3) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                     ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v5)
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                           (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))))))
-- Algebra.Bundles.InvertibleUnitalMagma.invertibleMagma
d_invertibleMagma_1548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400
d_invertibleMagma_1548 :: () -> () -> T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400
d_invertibleMagma_1548 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400
du_invertibleMagma_1548 T_InvertibleUnitalMagma_1476
v2
du_invertibleMagma_1548 ::
  T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400
du_invertibleMagma_1548 :: T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400
du_invertibleMagma_1548 T_InvertibleUnitalMagma_1476
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsInvertibleMagma_958
 -> T_InvertibleMagma_1400)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> T_InvertibleMagma_1400
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> T_InvertibleMagma_1400
C_constructor_1470 (T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1498 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)) (T_InvertibleUnitalMagma_1476 -> AgdaAny
d_ε_1500 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
      (T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny
d__'8315''185'_1502 (T_InvertibleUnitalMagma_1476 -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
      (T_IsInvertibleUnitalMagma_1012 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.d_isInvertibleMagma_1024
         ((T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1504 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0)))
-- Algebra.Bundles.InvertibleUnitalMagma._._≉_
d__'8777'__1552 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1552 :: ()
-> () -> T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1552 = ()
-> () -> T_InvertibleUnitalMagma_1476 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.InvertibleUnitalMagma._.magma
d_magma_1554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 -> T_Magma_74
d_magma_1554 :: () -> () -> T_InvertibleUnitalMagma_1476 -> T_Magma_74
d_magma_1554 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> T_Magma_74
du_magma_1554 T_InvertibleUnitalMagma_1476
v2
du_magma_1554 :: T_InvertibleUnitalMagma_1476 -> T_Magma_74
du_magma_1554 :: T_InvertibleUnitalMagma_1476 -> T_Magma_74
du_magma_1554 T_InvertibleUnitalMagma_1476
v0
  = (T_InvertibleMagma_1400 -> T_Magma_74) -> AgdaAny -> T_Magma_74
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_Magma_74
du_magma_1462 ((T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400
du_invertibleMagma_1548 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0))
-- Algebra.Bundles.InvertibleUnitalMagma._.rawMagma
d_rawMagma_1556 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1556 :: () -> () -> T_InvertibleUnitalMagma_1476 -> T_RawMagma_44
d_rawMagma_1556 ~()
v0 ~()
v1 T_InvertibleUnitalMagma_1476
v2 = T_InvertibleUnitalMagma_1476 -> T_RawMagma_44
du_rawMagma_1556 T_InvertibleUnitalMagma_1476
v2
du_rawMagma_1556 ::
  T_InvertibleUnitalMagma_1476 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1556 :: T_InvertibleUnitalMagma_1476 -> T_RawMagma_44
du_rawMagma_1556 T_InvertibleUnitalMagma_1476
v0
  = let v1 :: AgdaAny
v1 = (T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476 -> T_InvertibleMagma_1400
du_invertibleMagma_1548 (T_InvertibleUnitalMagma_1476 -> AgdaAny
forall a b. a -> b
coe T_InvertibleUnitalMagma_1476
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_InvertibleMagma_1400 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_InvertibleMagma_1400 -> T_Magma_74
du_magma_1462 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.Group
d_Group_1564 :: p -> p -> ()
d_Group_1564 p
a0 p
a1 = ()
data T_Group_1564
  = C_constructor_1676 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                       (AgdaAny -> AgdaAny) MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
-- Algebra.Bundles.Group.Carrier
d_Carrier_1582 :: T_Group_1564 -> ()
d_Carrier_1582 :: T_Group_1564 -> ()
d_Carrier_1582 = T_Group_1564 -> ()
forall a. a
erased
-- Algebra.Bundles.Group._≈_
d__'8776'__1584 :: T_Group_1564 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1584 :: T_Group_1564 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1584 = T_Group_1564 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Group._∙_
d__'8729'__1586 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 T_Group_1564
v0
  = case T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0 of
      C_constructor_1676 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1074
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_Group_1564
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group.ε
d_ε_1588 :: T_Group_1564 -> AgdaAny
d_ε_1588 :: T_Group_1564 -> AgdaAny
d_ε_1588 T_Group_1564
v0
  = case T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0 of
      C_constructor_1676 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1074
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_Group_1564
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group._⁻¹
d__'8315''185'_1590 :: T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 :: T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 T_Group_1564
v0
  = case T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0 of
      C_constructor_1676 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1074
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_Group_1564
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group.isGroup
d_isGroup_1592 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_1592 :: T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 T_Group_1564
v0
  = case T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0 of
      C_constructor_1676 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsGroup_1074
v6 -> T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v6
      T_Group_1564
_ -> T_IsGroup_1074
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.Group._._-_
d__'45'__1596 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1596 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'45'__1596 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1596 T_Group_1564
v2
du__'45'__1596 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1596 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'45'__1596 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'45'__1142
      ((T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)) ((T_Group_1564 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._._//_
d__'47''47'__1598 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1598 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1598 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1598 T_Group_1564
v2
du__'47''47'__1598 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1598 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1598 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136
      ((T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)) ((T_Group_1564 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._._\\_
d__'92''92'__1600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__1600 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'92''92'__1600 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1600 T_Group_1564
v2
du__'92''92'__1600 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1600 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
du__'92''92'__1600 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'92''92'__1130
      ((T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)) ((T_Group_1564 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.assoc
d_assoc_1602 ::
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1602 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1602 T_Group_1564
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))))
-- Algebra.Bundles.Group._.identity
d_identity_1604 ::
  T_Group_1564 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1604 :: T_Group_1564 -> T_Σ_14
d_identity_1604 T_Group_1564
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)))
-- Algebra.Bundles.Group._.identityʳ
d_identity'691'_1606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny
d_identity'691'_1606 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny
d_identity'691'_1606 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny
du_identity'691'_1606 T_Group_1564
v2
du_identity'691'_1606 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_identity'691'_1606 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_identity'691'_1606 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v1)))
-- Algebra.Bundles.Group._.identityˡ
d_identity'737'_1608 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny
d_identity'737'_1608 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny
d_identity'737'_1608 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny
du_identity'737'_1608 T_Group_1564
v2
du_identity'737'_1608 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_identity'737'_1608 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_identity'737'_1608 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v1)))
-- Algebra.Bundles.Group._.inverse
d_inverse_1610 ::
  T_Group_1564 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1610 :: T_Group_1564 -> T_Σ_14
d_inverse_1610 T_Group_1564
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090
      ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.inverseʳ
d_inverse'691'_1612 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny
d_inverse'691'_1612 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny
d_inverse'691'_1612 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny
du_inverse'691'_1612 T_Group_1564
v2
du_inverse'691'_1612 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_inverse'691'_1612 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_inverse'691'_1612 T_Group_1564
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1074 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1146
      ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.inverseˡ
d_inverse'737'_1614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny
d_inverse'737'_1614 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny
d_inverse'737'_1614 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny
du_inverse'737'_1614 T_Group_1564
v2
du_inverse'737'_1614 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_inverse'737'_1614 :: T_Group_1564 -> AgdaAny -> AgdaAny
du_inverse'737'_1614 T_Group_1564
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1074 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1144
      ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.isEquivalence
d_isEquivalence_1616 ::
  T_Group_1564 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1616 :: T_Group_1564 -> T_IsEquivalence_28
d_isEquivalence_1616 T_Group_1564
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)))))
-- Algebra.Bundles.Group._.isInvertibleMagma
d_isInvertibleMagma_1618 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_1618 :: () -> () -> T_Group_1564 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1618 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1618 T_Group_1564
v2
du_isInvertibleMagma_1618 ::
  T_Group_1564 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
du_isInvertibleMagma_1618 :: T_Group_1564 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1618 T_Group_1564
v0
  = (T_IsGroup_1074 -> T_IsInvertibleMagma_958)
-> AgdaAny -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
      ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1620 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1620 :: () -> () -> T_Group_1564 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1620 ~()
v0 ~()
v1 T_Group_1564
v2
  = T_Group_1564 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1620 T_Group_1564
v2
du_isInvertibleUnitalMagma_1620 ::
  T_Group_1564 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1620 :: T_Group_1564 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1620 T_Group_1564
v0
  = (T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
      ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.isMagma
d_isMagma_1622 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1622 :: T_Group_1564 -> T_IsMagma_178
d_isMagma_1622 T_Group_1564
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))))
-- Algebra.Bundles.Group._.isMonoid
d_isMonoid_1624 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1624 :: T_Group_1564 -> T_IsMonoid_712
d_isMonoid_1624 T_Group_1564
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
      ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.isPartialEquivalence
d_isPartialEquivalence_1626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1626 :: () -> () -> T_Group_1564 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1626 ~()
v0 ~()
v1 T_Group_1564
v2
  = T_Group_1564 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1626 T_Group_1564
v2
du_isPartialEquivalence_1626 ::
  T_Group_1564 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1626 :: T_Group_1564 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1626 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))))))
-- Algebra.Bundles.Group._.isSemigroup
d_isSemigroup_1628 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1628 :: T_Group_1564 -> T_IsSemigroup_488
d_isSemigroup_1628 T_Group_1564
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)))
-- Algebra.Bundles.Group._.isUnitalMagma
d_isUnitalMagma_1630 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1630 :: () -> () -> T_Group_1564 -> T_IsUnitalMagma_666
d_isUnitalMagma_1630 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_IsUnitalMagma_666
du_isUnitalMagma_1630 T_Group_1564
v2
du_isUnitalMagma_1630 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1630 :: T_Group_1564 -> T_IsUnitalMagma_666
du_isUnitalMagma_1630 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v1)))
-- Algebra.Bundles.Group._.refl
d_refl_1632 :: T_Group_1564 -> AgdaAny -> AgdaAny
d_refl_1632 :: T_Group_1564 -> AgdaAny -> AgdaAny
d_refl_1632 T_Group_1564
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
                  ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))))))
-- Algebra.Bundles.Group._.reflexive
d_reflexive_1634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1634 :: ()
-> ()
-> T_Group_1564
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1634 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1634 T_Group_1564
v2
du_reflexive_1634 ::
  T_Group_1564 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1634 :: T_Group_1564 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1634 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4))
                    AgdaAny
v5))))
-- Algebra.Bundles.Group._.setoid
d_setoid_1636 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1636 :: () -> () -> T_Group_1564 -> T_Setoid_46
d_setoid_1636 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_Setoid_46
du_setoid_1636 T_Group_1564
v2
du_setoid_1636 ::
  T_Group_1564 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1636 :: T_Group_1564 -> T_Setoid_46
du_setoid_1636 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
               ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v3)))))
-- Algebra.Bundles.Group._.sym
d_sym_1638 ::
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1638 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1638 T_Group_1564
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
                  ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))))))
-- Algebra.Bundles.Group._.trans
d_trans_1640 ::
  T_Group_1564 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1640 :: T_Group_1564
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1640 T_Group_1564
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
                  ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))))))
-- Algebra.Bundles.Group._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1642 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1642 :: ()
-> () -> T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1642 ~()
v0 ~()
v1 T_Group_1564
v2
  = T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1642 T_Group_1564
v2
du_unique'691''45''8315''185'_1642 ::
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1642 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1642 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1074
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1158
      ((T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)) ((T_Group_1564 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny
d_ε_1588 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
      ((T_Group_1564 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)) ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1644 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1644 :: ()
-> () -> T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1644 ~()
v0 ~()
v1 T_Group_1564
v2
  = T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1644 T_Group_1564
v2
du_unique'737''45''8315''185'_1644 ::
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1644 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1644 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1074
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1152
      ((T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)) ((T_Group_1564 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny
d_ε_1588 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
      ((T_Group_1564 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)) ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.⁻¹-cong
d_'8315''185''45'cong_1646 ::
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1646 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1646 T_Group_1564
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1092
      ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.∙-cong
d_'8729''45'cong_1648 ::
  T_Group_1564 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1648 :: T_Group_1564
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1648 T_Group_1564
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)))))
-- Algebra.Bundles.Group._.∙-congʳ
d_'8729''45'cong'691'_1650 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1650 :: ()
-> ()
-> T_Group_1564
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1650 ~()
v0 ~()
v1 T_Group_1564
v2
  = T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1650 T_Group_1564
v2
du_'8729''45'cong'691'_1650 ::
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1650 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1650 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.Group._.∙-congˡ
d_'8729''45'cong'737'_1652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1652 :: ()
-> ()
-> T_Group_1564
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1652 ~()
v0 ~()
v1 T_Group_1564
v2
  = T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1652 T_Group_1564
v2
du_'8729''45'cong'737'_1652 ::
  T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1652 :: T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1652 T_Group_1564
v0
  = let v1 :: T_IsGroup_1074
v1 = T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMonoid_712
v2
             = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsSemigroup_488
v3
                = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsMagma_178
v4 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: AgdaAny
v5
                      = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6
                         = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v4) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                        ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v6)
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)))))))))
-- Algebra.Bundles.Group.rawGroup
d_rawGroup_1654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108
d_rawGroup_1654 :: () -> () -> T_Group_1564 -> T_RawGroup_108
d_rawGroup_1654 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_RawGroup_108
du_rawGroup_1654 T_Group_1564
v2
du_rawGroup_1654 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108
du_rawGroup_1654 :: T_Group_1564 -> T_RawGroup_108
du_rawGroup_1654 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_108)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_RawGroup_108
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> (AgdaAny -> AgdaAny) -> T_RawGroup_108
MAlonzo.Code.Algebra.Bundles.Raw.C_constructor_142
      (T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0)) (T_Group_1564 -> AgdaAny
d_ε_1588 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0))
      (T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group.monoid
d_monoid_1656 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> T_Monoid_914
d_monoid_1656 :: () -> () -> T_Group_1564 -> T_Monoid_914
d_monoid_1656 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_Monoid_914
du_monoid_1656 T_Group_1564
v2
du_monoid_1656 :: T_Group_1564 -> T_Monoid_914
du_monoid_1656 :: T_Group_1564 -> T_Monoid_914
du_monoid_1656 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> T_IsMonoid_712 -> T_Monoid_914)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsMonoid_712
-> T_Monoid_914
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> T_IsMonoid_712 -> T_Monoid_914
C_constructor_990 (T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0)) (T_Group_1564 -> AgdaAny
d_ε_1588 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0))
      (T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> T_IsGroup_1074
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)))
-- Algebra.Bundles.Group._._≉_
d__'8777'__1660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1660 :: () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1660 = () -> () -> T_Group_1564 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.Group._.magma
d_magma_1662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> T_Magma_74
d_magma_1662 :: () -> () -> T_Group_1564 -> T_Magma_74
d_magma_1662 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_Magma_74
du_magma_1662 T_Group_1564
v2
du_magma_1662 :: T_Group_1564 -> T_Magma_74
du_magma_1662 :: T_Group_1564 -> T_Magma_74
du_magma_1662 T_Group_1564
v0
  = let v1 :: AgdaAny
v1 = (T_Group_1564 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Bundles.Group._.rawMagma
d_rawMagma_1664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1664 :: () -> () -> T_Group_1564 -> T_RawMagma_44
d_rawMagma_1664 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_RawMagma_44
du_rawMagma_1664 T_Group_1564
v2
du_rawMagma_1664 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1664 :: T_Group_1564 -> T_RawMagma_44
du_rawMagma_1664 T_Group_1564
v0
  = let v1 :: AgdaAny
v1 = (T_Group_1564 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.Group._.rawMonoid
d_rawMonoid_1666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
d_rawMonoid_1666 :: () -> () -> T_Group_1564 -> T_RawMonoid_74
d_rawMonoid_1666 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_RawMonoid_74
du_rawMonoid_1666 T_Group_1564
v2
du_rawMonoid_1666 ::
  T_Group_1564 -> MAlonzo.Code.Algebra.Bundles.Raw.T_RawMonoid_74
du_rawMonoid_1666 :: T_Group_1564 -> T_RawMonoid_74
du_rawMonoid_1666 T_Group_1564
v0
  = (T_Monoid_914 -> T_RawMonoid_74) -> AgdaAny -> T_RawMonoid_74
forall a b. a -> b
coe T_Monoid_914 -> T_RawMonoid_74
du_rawMonoid_986 ((T_Group_1564 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.semigroup
d_semigroup_1668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> T_Semigroup_558
d_semigroup_1668 :: () -> () -> T_Group_1564 -> T_Semigroup_558
d_semigroup_1668 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_Semigroup_558
du_semigroup_1668 T_Group_1564
v2
du_semigroup_1668 :: T_Group_1564 -> T_Semigroup_558
du_semigroup_1668 :: T_Group_1564 -> T_Semigroup_558
du_semigroup_1668 T_Group_1564
v0
  = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> T_Semigroup_558
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 ((T_Group_1564 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group._.unitalMagma
d_unitalMagma_1670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> T_UnitalMagma_844
d_unitalMagma_1670 :: () -> () -> T_Group_1564 -> T_UnitalMagma_844
d_unitalMagma_1670 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_UnitalMagma_844
du_unitalMagma_1670 T_Group_1564
v2
du_unitalMagma_1670 :: T_Group_1564 -> T_UnitalMagma_844
du_unitalMagma_1670 :: T_Group_1564 -> T_UnitalMagma_844
du_unitalMagma_1670 T_Group_1564
v0
  = (T_Monoid_914 -> T_UnitalMagma_844) -> AgdaAny -> T_UnitalMagma_844
forall a b. a -> b
coe T_Monoid_914 -> T_UnitalMagma_844
du_unitalMagma_988 ((T_Group_1564 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0))
-- Algebra.Bundles.Group.invertibleMagma
d_invertibleMagma_1672 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> T_InvertibleMagma_1400
d_invertibleMagma_1672 :: () -> () -> T_Group_1564 -> T_InvertibleMagma_1400
d_invertibleMagma_1672 ~()
v0 ~()
v1 T_Group_1564
v2 = T_Group_1564 -> T_InvertibleMagma_1400
du_invertibleMagma_1672 T_Group_1564
v2
du_invertibleMagma_1672 :: T_Group_1564 -> T_InvertibleMagma_1400
du_invertibleMagma_1672 :: T_Group_1564 -> T_InvertibleMagma_1400
du_invertibleMagma_1672 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsInvertibleMagma_958
 -> T_InvertibleMagma_1400)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_InvertibleMagma_1400
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleMagma_958
-> T_InvertibleMagma_1400
C_constructor_1470 (T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0)) (T_Group_1564 -> AgdaAny
d_ε_1588 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0))
      (T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0))
      ((T_IsGroup_1074 -> T_IsInvertibleMagma_958) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
         ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)))
-- Algebra.Bundles.Group.invertibleUnitalMagma
d_invertibleUnitalMagma_1674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Group_1564 -> T_InvertibleUnitalMagma_1476
d_invertibleUnitalMagma_1674 :: () -> () -> T_Group_1564 -> T_InvertibleUnitalMagma_1476
d_invertibleUnitalMagma_1674 ~()
v0 ~()
v1 T_Group_1564
v2
  = T_Group_1564 -> T_InvertibleUnitalMagma_1476
du_invertibleUnitalMagma_1674 T_Group_1564
v2
du_invertibleUnitalMagma_1674 ::
  T_Group_1564 -> T_InvertibleUnitalMagma_1476
du_invertibleUnitalMagma_1674 :: T_Group_1564 -> T_InvertibleUnitalMagma_1476
du_invertibleUnitalMagma_1674 T_Group_1564
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsInvertibleUnitalMagma_1012
 -> T_InvertibleUnitalMagma_1476)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsInvertibleUnitalMagma_1012
-> T_InvertibleUnitalMagma_1476
C_constructor_1558 (T_Group_1564 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1586 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0)) (T_Group_1564 -> AgdaAny
d_ε_1588 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0))
      (T_Group_1564 -> AgdaAny -> AgdaAny
d__'8315''185'_1590 (T_Group_1564 -> T_Group_1564
forall a b. a -> b
coe T_Group_1564
v0))
      ((T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
         ((T_Group_1564 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_IsGroup_1074
d_isGroup_1592 (T_Group_1564 -> AgdaAny
forall a b. a -> b
coe T_Group_1564
v0)))
-- Algebra.Bundles.AbelianGroup
d_AbelianGroup_1682 :: p -> p -> ()
d_AbelianGroup_1682 p
a0 p
a1 = ()
data T_AbelianGroup_1682
  = C_constructor_1808 (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny
                       (AgdaAny -> AgdaAny)
                       MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
-- Algebra.Bundles.AbelianGroup.Carrier
d_Carrier_1700 :: T_AbelianGroup_1682 -> ()
d_Carrier_1700 :: T_AbelianGroup_1682 -> ()
d_Carrier_1700 = T_AbelianGroup_1682 -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._≈_
d__'8776'__1702 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1702 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1702 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._∙_
d__'8729'__1704 ::
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1704 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1704 T_AbelianGroup_1682
v0
  = case T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0 of
      C_constructor_1808 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1172
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v3
      T_AbelianGroup_1682
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup.ε
d_ε_1706 :: T_AbelianGroup_1682 -> AgdaAny
d_ε_1706 :: T_AbelianGroup_1682 -> AgdaAny
d_ε_1706 T_AbelianGroup_1682
v0
  = case T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0 of
      C_constructor_1808 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1172
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4
      T_AbelianGroup_1682
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup._⁻¹
d__'8315''185'_1708 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d__'8315''185'_1708 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d__'8315''185'_1708 T_AbelianGroup_1682
v0
  = case T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0 of
      C_constructor_1808 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1172
v6 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v5
      T_AbelianGroup_1682
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup.isAbelianGroup
d_isAbelianGroup_1710 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_isAbelianGroup_1710 :: T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 T_AbelianGroup_1682
v0
  = case T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0 of
      C_constructor_1808 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny
v4 AgdaAny -> AgdaAny
v5 T_IsAbelianGroup_1172
v6 -> T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v6
      T_AbelianGroup_1682
_ -> T_IsAbelianGroup_1172
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Algebra.Bundles.AbelianGroup._._//_
d__'47''47'__1714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1714 :: () -> () -> T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'47''47'__1714 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1714 T_AbelianGroup_1682
v2
du__'47''47'__1714 ::
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1714 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
du__'47''47'__1714 T_AbelianGroup_1682
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1704 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny -> AgdaAny
v2 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d__'8315''185'_1708 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du__'47''47'__1136 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
            ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2)))
-- Algebra.Bundles.AbelianGroup._.assoc
d_assoc_1716 ::
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1716 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_1716 T_AbelianGroup_1682
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
               ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))))
-- Algebra.Bundles.AbelianGroup._.comm
d_comm_1718 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1718 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_1718 T_AbelianGroup_1682
v0
  = (T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_1186
      ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
-- Algebra.Bundles.AbelianGroup._.identity
d_identity_1720 ::
  T_AbelianGroup_1682 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1720 :: T_AbelianGroup_1682 -> T_Σ_14
d_identity_1720 T_AbelianGroup_1682
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))))
-- Algebra.Bundles.AbelianGroup._.identityʳ
d_identity'691'_1722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_identity'691'_1722 :: () -> () -> T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_identity'691'_1722 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_identity'691'_1722 T_AbelianGroup_1682
v2
du_identity'691'_1722 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_identity'691'_1722 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_identity'691'_1722 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'691'_754
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v2))))
-- Algebra.Bundles.AbelianGroup._.identityˡ
d_identity'737'_1724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_identity'737'_1724 :: () -> () -> T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_identity'737'_1724 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_identity'737'_1724 T_AbelianGroup_1682
v2
du_identity'737'_1724 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_identity'737'_1724 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_identity'737'_1724 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_identity'737'_752
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v2))))
-- Algebra.Bundles.AbelianGroup._.inverse
d_inverse_1726 ::
  T_AbelianGroup_1682 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_1726 :: T_AbelianGroup_1682 -> T_Σ_14
d_inverse_1726 T_AbelianGroup_1682
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))
-- Algebra.Bundles.AbelianGroup._.inverseʳ
d_inverse'691'_1728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_inverse'691'_1728 :: () -> () -> T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_inverse'691'_1728 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_inverse'691'_1728 T_AbelianGroup_1682
v2
du_inverse'691'_1728 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_inverse'691'_1728 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_inverse'691'_1728 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'691'_1146
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Algebra.Bundles.AbelianGroup._.inverseˡ
d_inverse'737'_1730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_inverse'737'_1730 :: () -> () -> T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_inverse'737'_1730 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_inverse'737'_1730 T_AbelianGroup_1682
v2
du_inverse'737'_1730 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_inverse'737'_1730 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
du_inverse'737'_1730 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.du_inverse'737'_1144
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Algebra.Bundles.AbelianGroup._.isCommutativeMagma
d_isCommutativeMagma_1732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
d_isCommutativeMagma_1732 :: () -> () -> T_AbelianGroup_1682 -> T_IsCommutativeMagma_214
d_isCommutativeMagma_1732 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1732 T_AbelianGroup_1682
v2
du_isCommutativeMagma_1732 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMagma_214
du_isCommutativeMagma_1732 :: T_AbelianGroup_1682 -> T_IsCommutativeMagma_214
du_isCommutativeMagma_1732 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_IsCommutativeMagma_214
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
                 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsCommutativeSemigroup_568 -> T_IsCommutativeMagma_214
MAlonzo.Code.Algebra.Structures.du_isCommutativeMagma_606
            ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.AbelianGroup._.isCommutativeMonoid
d_isCommutativeMonoid_1734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1734 :: () -> () -> T_AbelianGroup_1682 -> T_IsCommutativeMonoid_764
d_isCommutativeMonoid_1734 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1734 T_AbelianGroup_1682
v2
du_isCommutativeMonoid_1734 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1734 :: T_AbelianGroup_1682 -> T_IsCommutativeMonoid_764
du_isCommutativeMonoid_1734 T_AbelianGroup_1682
v0
  = (T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
      ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
-- Algebra.Bundles.AbelianGroup._.isCommutativeSemigroup
d_isCommutativeSemigroup_1736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1736 :: () -> () -> T_AbelianGroup_1682 -> T_IsCommutativeSemigroup_568
d_isCommutativeSemigroup_1736 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1736 T_AbelianGroup_1682
v2
du_isCommutativeSemigroup_1736 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1736 :: T_AbelianGroup_1682 -> T_IsCommutativeSemigroup_568
du_isCommutativeSemigroup_1736 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_IsCommutativeSemigroup_568
forall a b. a -> b
coe
      ((T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764 -> T_IsCommutativeSemigroup_568
MAlonzo.Code.Algebra.Structures.du_isCommutativeSemigroup_814
         ((T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.du_isCommutativeMonoid_1244
            (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Algebra.Bundles.AbelianGroup._.isEquivalence
d_isEquivalence_1738 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1738 :: T_AbelianGroup_1682 -> T_IsEquivalence_28
d_isEquivalence_1738 T_AbelianGroup_1682
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                  ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))))))
-- Algebra.Bundles.AbelianGroup._.isGroup
d_isGroup_1740 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_1740 :: T_AbelianGroup_1682 -> T_IsGroup_1074
d_isGroup_1740 T_AbelianGroup_1682
v0
  = (T_IsAbelianGroup_1172 -> T_IsGroup_1074)
-> AgdaAny -> T_IsGroup_1074
forall a b. a -> b
coe
      T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
      ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
-- Algebra.Bundles.AbelianGroup._.isInvertibleMagma
d_isInvertibleMagma_1742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
d_isInvertibleMagma_1742 :: () -> () -> T_AbelianGroup_1682 -> T_IsInvertibleMagma_958
d_isInvertibleMagma_1742 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1742 T_AbelianGroup_1682
v2
du_isInvertibleMagma_1742 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleMagma_958
du_isInvertibleMagma_1742 :: T_AbelianGroup_1682 -> T_IsInvertibleMagma_958
du_isInvertibleMagma_1742 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_IsInvertibleMagma_958
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_IsInvertibleMagma_958) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleMagma_958
MAlonzo.Code.Algebra.Structures.du_isInvertibleMagma_1160
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Algebra.Bundles.AbelianGroup._.isInvertibleUnitalMagma
d_isInvertibleUnitalMagma_1744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1744 :: () -> () -> T_AbelianGroup_1682 -> T_IsInvertibleUnitalMagma_1012
d_isInvertibleUnitalMagma_1744 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1744 T_AbelianGroup_1682
v2
du_isInvertibleUnitalMagma_1744 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1744 :: T_AbelianGroup_1682 -> T_IsInvertibleUnitalMagma_1012
du_isInvertibleUnitalMagma_1744 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_IsInvertibleUnitalMagma_1012
forall a b. a -> b
coe
      ((T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsInvertibleUnitalMagma_1012
MAlonzo.Code.Algebra.Structures.du_isInvertibleUnitalMagma_1162
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1)))
-- Algebra.Bundles.AbelianGroup._.isMagma
d_isMagma_1746 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_1746 :: T_AbelianGroup_1682 -> T_IsMagma_178
d_isMagma_1746 T_AbelianGroup_1682
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
      ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
         ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
            ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
               ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))))
-- Algebra.Bundles.AbelianGroup._.isMonoid
d_isMonoid_1748 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1748 :: T_AbelianGroup_1682 -> T_IsMonoid_712
d_isMonoid_1748 T_AbelianGroup_1682
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))
-- Algebra.Bundles.AbelianGroup._.isPartialEquivalence
d_isPartialEquivalence_1750 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1750 :: () -> () -> T_AbelianGroup_1682 -> T_IsPartialEquivalence_16
d_isPartialEquivalence_1750 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1750 T_AbelianGroup_1682
v2
du_isPartialEquivalence_1750 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1750 :: T_AbelianGroup_1682 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1750 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5)))))))
-- Algebra.Bundles.AbelianGroup._.isSemigroup
d_isSemigroup_1752 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1752 :: T_AbelianGroup_1682 -> T_IsSemigroup_488
d_isSemigroup_1752 T_AbelianGroup_1682
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
      ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
         ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
            ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))))
-- Algebra.Bundles.AbelianGroup._.isUnitalMagma
d_isUnitalMagma_1754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
d_isUnitalMagma_1754 :: () -> () -> T_AbelianGroup_1682 -> T_IsUnitalMagma_666
d_isUnitalMagma_1754 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_IsUnitalMagma_666
du_isUnitalMagma_1754 T_AbelianGroup_1682
v2
du_isUnitalMagma_1754 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Structures.T_IsUnitalMagma_666
du_isUnitalMagma_1754 :: T_AbelianGroup_1682 -> T_IsUnitalMagma_666
du_isUnitalMagma_1754 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_IsUnitalMagma_666
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMonoid_712 -> T_IsUnitalMagma_666) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsUnitalMagma_666
MAlonzo.Code.Algebra.Structures.du_isUnitalMagma_756
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v2))))
-- Algebra.Bundles.AbelianGroup._.refl
d_refl_1756 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_refl_1756 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d_refl_1756 T_AbelianGroup_1682
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
                  ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                     ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))))))
-- Algebra.Bundles.AbelianGroup._.reflexive
d_reflexive_1758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1758 :: ()
-> ()
-> T_AbelianGroup_1682
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1758 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1758 T_AbelianGroup_1682
v2
du_reflexive_1758 ::
  T_AbelianGroup_1682 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1758 :: T_AbelianGroup_1682
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1758 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5))
                       AgdaAny
v6)))))
-- Algebra.Bundles.AbelianGroup._.setoid
d_setoid_1760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
d_setoid_1760 :: () -> () -> T_AbelianGroup_1682 -> T_Setoid_46
d_setoid_1760 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_Setoid_46
du_setoid_1760 T_AbelianGroup_1682
v2
du_setoid_1760 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_46
du_setoid_1760 :: T_AbelianGroup_1682 -> T_Setoid_46
du_setoid_1760 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_Setoid_46
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202
                  ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v4))))))
-- Algebra.Bundles.AbelianGroup._.sym
d_sym_1762 ::
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1762 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1762 T_AbelianGroup_1682
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
                  ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                     ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))))))
-- Algebra.Bundles.AbelianGroup._.trans
d_trans_1764 ::
  T_AbelianGroup_1682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1764 :: T_AbelianGroup_1682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1764 T_AbelianGroup_1682
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsMagma_178 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186
         ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
            ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
               ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
                  ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                     ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))))))
-- Algebra.Bundles.AbelianGroup._.uniqueʳ-⁻¹
d_unique'691''45''8315''185'_1766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'691''45''8315''185'_1766 :: ()
-> ()
-> T_AbelianGroup_1682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'691''45''8315''185'_1766 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1766 T_AbelianGroup_1682
v2
du_unique'691''45''8315''185'_1766 ::
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1766 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'691''45''8315''185'_1766 T_AbelianGroup_1682
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1704 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = T_AbelianGroup_1682 -> AgdaAny
d_ε_1706 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d__'8315''185'_1708 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1172
v4 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1074
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'691''45''8315''185'_1158
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3)
                  ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v4))))))
-- Algebra.Bundles.AbelianGroup._.uniqueˡ-⁻¹
d_unique'737''45''8315''185'_1768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_unique'737''45''8315''185'_1768 :: ()
-> ()
-> T_AbelianGroup_1682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_unique'737''45''8315''185'_1768 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1768 T_AbelianGroup_1682
v2
du_unique'737''45''8315''185'_1768 ::
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1768 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_unique'737''45''8315''185'_1768 T_AbelianGroup_1682
v0
  = let v1 :: AgdaAny -> AgdaAny -> AgdaAny
v1 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1704 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = T_AbelianGroup_1682 -> AgdaAny
d_ε_1706 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny -> AgdaAny
v3 = T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d__'8315''185'_1708 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsAbelianGroup_1172
v4 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1074
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.du_unique'737''45''8315''185'_1152
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) ((AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3)
                  ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v4))))))
-- Algebra.Bundles.AbelianGroup._.⁻¹-cong
d_'8315''185''45'cong_1770 ::
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1770 :: T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1770 T_AbelianGroup_1682
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1092
      ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))
-- Algebra.Bundles.AbelianGroup._.∙-cong
d_'8729''45'cong_1772 ::
  T_AbelianGroup_1682 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1772 :: T_AbelianGroup_1682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1772 T_AbelianGroup_1682
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188
      ((T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496
         ((T_IsMonoid_712 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722
            ((T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088
               ((T_IsAbelianGroup_1172 -> T_IsGroup_1074) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
                  ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))))))
-- Algebra.Bundles.AbelianGroup._.∙-congʳ
d_'8729''45'cong'691'_1774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'691'_1774 :: ()
-> ()
-> T_AbelianGroup_1682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'691'_1774 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1774 T_AbelianGroup_1682
v2
du_'8729''45'cong'691'_1774 ::
  T_AbelianGroup_1682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1774 :: T_AbelianGroup_1682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'691'_1774 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'691'_46
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Bundles.AbelianGroup._.∙-congˡ
d_'8729''45'cong'737'_1776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong'737'_1776 :: ()
-> ()
-> T_AbelianGroup_1682
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong'737'_1776 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1776 T_AbelianGroup_1682
v2
du_'8729''45'cong'737'_1776 ::
  T_AbelianGroup_1682 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1776 :: T_AbelianGroup_1682
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8729''45'cong'737'_1776 T_AbelianGroup_1682
v0
  = let v1 :: T_IsAbelianGroup_1172
v1 = T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsGroup_1074
v2
             = T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_IsAbelianGroup_1172
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsMonoid_712
v3
                = T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> T_IsGroup_1074
forall a b. a -> b
coe T_IsGroup_1074
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsSemigroup_488
v4
                   = T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> T_IsMonoid_712
forall a b. a -> b
coe T_IsMonoid_712
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsMagma_178
v5 = T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsSemigroup_488
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: AgdaAny
v6
                         = (T_IsMagma_178 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178 -> T_Setoid_46
MAlonzo.Code.Algebra.Structures.du_setoid_202 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v5) in
                   AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (let v7 :: AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7
                            = T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> T_IsMagma_178
forall a b. a -> b
coe T_IsMagma_178
v5) in
                      AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (((AgdaAny
  -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Base.du_'8729''45'cong'737'_42
                           ((AgdaAny
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
forall a b. a -> b
coe AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v7)
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_Setoid_46 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_Setoid_46 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_62
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6))))))))))
-- Algebra.Bundles.AbelianGroup.group
d_group_1778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> T_Group_1564
d_group_1778 :: () -> () -> T_AbelianGroup_1682 -> T_Group_1564
d_group_1778 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 T_AbelianGroup_1682
v2
du_group_1778 :: T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 :: T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 T_AbelianGroup_1682
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> T_IsGroup_1074
 -> T_Group_1564)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> T_Group_1564
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> T_IsGroup_1074
-> T_Group_1564
C_constructor_1676 (T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8729'__1704 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0)) (T_AbelianGroup_1682 -> AgdaAny
d_ε_1706 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
      (T_AbelianGroup_1682 -> AgdaAny -> AgdaAny
d__'8315''185'_1708 (T_AbelianGroup_1682 -> T_AbelianGroup_1682
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
      (T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184
         ((T_AbelianGroup_1682 -> T_IsAbelianGroup_1172)
-> AgdaAny -> T_IsAbelianGroup_1172
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_IsAbelianGroup_1172
d_isAbelianGroup_1710 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0)))
-- Algebra.Bundles.AbelianGroup._._≉_
d__'8777'__1782 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1782 :: () -> () -> T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> ()
d__'8777'__1782 = () -> () -> T_AbelianGroup_1682 -> AgdaAny -> AgdaAny -> ()
forall a. a
erased
-- Algebra.Bundles.AbelianGroup._.invertibleMagma
d_invertibleMagma_1784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> T_InvertibleMagma_1400
d_invertibleMagma_1784 :: () -> () -> T_AbelianGroup_1682 -> T_InvertibleMagma_1400
d_invertibleMagma_1784 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_InvertibleMagma_1400
du_invertibleMagma_1784 T_AbelianGroup_1682
v2
du_invertibleMagma_1784 ::
  T_AbelianGroup_1682 -> T_InvertibleMagma_1400
du_invertibleMagma_1784 :: T_AbelianGroup_1682 -> T_InvertibleMagma_1400
du_invertibleMagma_1784 T_AbelianGroup_1682
v0
  = (T_Group_1564 -> T_InvertibleMagma_1400)
-> AgdaAny -> T_InvertibleMagma_1400
forall a b. a -> b
coe T_Group_1564 -> T_InvertibleMagma_1400
du_invertibleMagma_1672 ((T_AbelianGroup_1682 -> T_Group_1564) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
-- Algebra.Bundles.AbelianGroup._.invertibleUnitalMagma
d_invertibleUnitalMagma_1786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> T_InvertibleUnitalMagma_1476
d_invertibleUnitalMagma_1786 :: () -> () -> T_AbelianGroup_1682 -> T_InvertibleUnitalMagma_1476
d_invertibleUnitalMagma_1786 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2
  = T_AbelianGroup_1682 -> T_InvertibleUnitalMagma_1476
du_invertibleUnitalMagma_1786 T_AbelianGroup_1682
v2
du_invertibleUnitalMagma_1786 ::
  T_AbelianGroup_1682 -> T_InvertibleUnitalMagma_1476
du_invertibleUnitalMagma_1786 :: T_AbelianGroup_1682 -> T_InvertibleUnitalMagma_1476
du_invertibleUnitalMagma_1786 T_AbelianGroup_1682
v0
  = (T_Group_1564 -> T_InvertibleUnitalMagma_1476)
-> AgdaAny -> T_InvertibleUnitalMagma_1476
forall a b. a -> b
coe T_Group_1564 -> T_InvertibleUnitalMagma_1476
du_invertibleUnitalMagma_1674 ((T_AbelianGroup_1682 -> T_Group_1564) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
-- Algebra.Bundles.AbelianGroup._.magma
d_magma_1788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> T_Magma_74
d_magma_1788 :: () -> () -> T_AbelianGroup_1682 -> T_Magma_74
d_magma_1788 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_Magma_74
du_magma_1788 T_AbelianGroup_1682
v2
du_magma_1788 :: T_AbelianGroup_1682 -> T_Magma_74
du_magma_1788 :: T_AbelianGroup_1682 -> T_Magma_74
du_magma_1788 T_AbelianGroup_1682
v0
  = let v1 :: AgdaAny
v1 = (T_AbelianGroup_1682 -> T_Group_1564) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_Magma_74
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Group_1564 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 ((T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Bundles.AbelianGroup._.monoid
d_monoid_1790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 -> T_Monoid_914
d_monoid_1790 :: () -> () -> T_AbelianGroup_1682 -> T_Monoid_914
d_monoid_1790 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_Monoid_914
du_monoid_1790 T_AbelianGroup_1682
v2
du_monoid_1790 :: T_AbelianGroup_1682 -> T_Monoid_914
du_monoid_1790 :: T_AbelianGroup_1682 -> T_Monoid_914
du_monoid_1790 T_AbelianGroup_1682
v0 = (T_Group_1564 -> T_Monoid_914) -> AgdaAny -> T_Monoid_914
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 ((T_AbelianGroup_1682 -> T_Group_1564) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
-- Algebra.Bundles.AbelianGroup._.rawGroup
d_rawGroup_1792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108
d_rawGroup_1792 :: () -> () -> T_AbelianGroup_1682 -> T_RawGroup_108
d_rawGroup_1792 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_RawGroup_108
du_rawGroup_1792 T_AbelianGroup_1682
v2
du_rawGroup_1792 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawGroup_108
du_rawGroup_1792 :: T_AbelianGroup_1682 -> T_RawGroup_108
du_rawGroup_1792 T_AbelianGroup_1682
v0
  = (T_Group_1564 -> T_RawGroup_108) -> AgdaAny -> T_RawGroup_108
forall a b. a -> b
coe T_Group_1564 -> T_RawGroup_108
du_rawGroup_1654 ((T_AbelianGroup_1682 -> T_Group_1564) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0))
-- Algebra.Bundles.AbelianGroup._.rawMagma
d_rawMagma_1794 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
d_rawMagma_1794 :: () -> () -> T_AbelianGroup_1682 -> T_RawMagma_44
d_rawMagma_1794 ~()
v0 ~()
v1 T_AbelianGroup_1682
v2 = T_AbelianGroup_1682 -> T_RawMagma_44
du_rawMagma_1794 T_AbelianGroup_1682
v2
du_rawMagma_1794 ::
  T_AbelianGroup_1682 ->
  MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_44
du_rawMagma_1794 :: T_AbelianGroup_1682 -> T_RawMagma_44
du_rawMagma_1794 T_AbelianGroup_1682
v0
  = let v1 :: AgdaAny
v1 = (T_AbelianGroup_1682 -> T_Group_1564) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682 -> T_Group_1564
du_group_1778 (T_AbelianGroup_1682 -> AgdaAny
forall a b. a -> b
coe T_AbelianGroup_1682
v0) in
    AgdaAny -> T_RawMagma_44
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2 = (T_Group_1564 -> T_Monoid_914) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Group_1564 -> T_Monoid_914
du_monoid_1656 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: AgdaAny
v3 = (T_Monoid_914 -> T_Semigroup_558) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Monoid_914 -> T_Semigroup_558
du_semigroup_976 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Magma_74 -> T_RawMagma_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Magma_74 -> T_RawMagma_44
du_rawMagma_118 ((T_Semigroup_558 -> T_Magma_74) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Semigroup_558 -> T_Magma_74
du_magma_606 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))))
-- Algebra.Bundles.AbelianGroup._.rawMonoid
d_rawMonoid_1796 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->