{-# 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.Data.List.Relation.Binary.Pointwise.Properties 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.Bool
import qualified MAlonzo.Code.Agda.Builtin.Equality
import qualified MAlonzo.Code.Agda.Builtin.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base
import qualified MAlonzo.Code.Data.Product
import qualified MAlonzo.Code.Relation.Nullary
import qualified MAlonzo.Code.Relation.Nullary.Decidable.Core
import qualified MAlonzo.Code.Relation.Nullary.Product
d_reflexive_28 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
d_reflexive_28 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 = du_reflexive_28
du_reflexive_28 ::
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
du_reflexive_28
= coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.du_map_120
d_refl_30 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny) ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
d_refl_30 ~v0 ~v1 ~v2 ~v3 v4 v5 = du_refl_30 v4 v5
du_refl_30 ::
(AgdaAny -> AgdaAny) ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
du_refl_30 v0 v1
= case coe v1 of
[]
-> coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C_'91''93'_56
(:) v2 v3
-> coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62
(coe v0 v2) (coe du_refl_30 (coe v0) (coe v3))
_ -> MAlonzo.RTE.mazUnreachableError
d_symmetric_40 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
d_symmetric_40 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10 v11
= du_symmetric_40 v8 v9 v10 v11
du_symmetric_40 ::
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
du_symmetric_40 v0 v1 v2 v3
= case coe v3 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C_'91''93'_56
-> coe v3
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v8 v9
-> case coe v1 of
(:) v10 v11
-> case coe v2 of
(:) v12 v13
-> coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62
(coe v0 v10 v12 v8)
(coe du_symmetric_40 (coe v0) (coe v11) (coe v13) (coe v9))
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
d_transitive_50 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
d_transitive_50 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 ~v10 ~v11
v12 v13 v14 v15 v16 v17
= du_transitive_50 v12 v13 v14 v15 v16 v17
du_transitive_50 ::
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
du_transitive_50 v0 v1 v2 v3 v4 v5
= case coe v4 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C_'91''93'_56
-> coe seq (coe v5) (coe v4)
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v10 v11
-> case coe v1 of
(:) v12 v13
-> case coe v2 of
(:) v14 v15
-> case coe v5 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v20 v21
-> case coe v3 of
(:) v22 v23
-> coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62
(coe v0 v12 v14 v22 v10 v20)
(coe
du_transitive_50 (coe v0) (coe v13) (coe v15) (coe v23)
(coe v11) (coe v21))
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
d_antisymmetric_64 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
d_antisymmetric_64 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 ~v8 ~v9 v10 v11
v12 v13 v14
= du_antisymmetric_64 v10 v11 v12 v13 v14
du_antisymmetric_64 ::
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
du_antisymmetric_64 v0 v1 v2 v3 v4
= case coe v3 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C_'91''93'_56
-> coe seq (coe v4) (coe v3)
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v9 v10
-> case coe v1 of
(:) v11 v12
-> case coe v2 of
(:) v13 v14
-> case coe v4 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v19 v20
-> coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62
(coe v0 v11 v13 v9 v19)
(coe
du_antisymmetric_64 (coe v0) (coe v12) (coe v14) (coe v10)
(coe v20))
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
d_resp'691'_78 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
d_resp'691'_78 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10 v11 v12
v13
= du_resp'691'_78 v8 v9 v10 v11 v12 v13
du_resp'691'_78 ::
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
du_resp'691'_78 v0 v1 v2 v3 v4 v5
= case coe v4 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C_'91''93'_56
-> coe seq (coe v5) (coe v4)
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v10 v11
-> case coe v2 of
(:) v12 v13
-> case coe v3 of
(:) v14 v15
-> case coe v5 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v20 v21
-> case coe v1 of
(:) v22 v23
-> coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62
(coe v0 v22 v12 v14 v10 v20)
(coe
du_resp'691'_78 (coe v0) (coe v23) (coe v13) (coe v15)
(coe v11) (coe v21))
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
d_resp'737'_92 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
d_resp'737'_92 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10 v11 v12
v13
= du_resp'737'_92 v8 v9 v10 v11 v12 v13
du_resp'737'_92 ::
(AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
[AgdaAny] ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48
du_resp'737'_92 v0 v1 v2 v3 v4 v5
= case coe v4 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C_'91''93'_56
-> coe seq (coe v5) (coe v4)
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v10 v11
-> case coe v2 of
(:) v12 v13
-> case coe v3 of
(:) v14 v15
-> case coe v5 of
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62 v20 v21
-> case coe v1 of
(:) v22 v23
-> coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62
(coe v0 v22 v12 v14 v10 v20)
(coe
du_resp'737'_92 (coe v0) (coe v23) (coe v13) (coe v15)
(coe v11) (coe v21))
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
d_respects'8322'_106 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_respects'8322'_106 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
= du_respects'8322'_106 v6
du_respects'8322'_106 ::
MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_respects'8322'_106 v0
= case coe v0 of
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v1 v2
-> coe
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
(coe du_resp'691'_78 (coe v1)) (coe du_resp'737'_92 (coe v2))
_ -> MAlonzo.RTE.mazUnreachableError
d_decidable_112 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny -> AgdaAny -> MAlonzo.Code.Relation.Nullary.T_Dec_32) ->
[AgdaAny] -> [AgdaAny] -> MAlonzo.Code.Relation.Nullary.T_Dec_32
d_decidable_112 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 v8
= du_decidable_112 v6 v7 v8
du_decidable_112 ::
(AgdaAny -> AgdaAny -> MAlonzo.Code.Relation.Nullary.T_Dec_32) ->
[AgdaAny] -> [AgdaAny] -> MAlonzo.Code.Relation.Nullary.T_Dec_32
du_decidable_112 v0 v1 v2
= case coe v1 of
[]
-> case coe v2 of
[]
-> coe
MAlonzo.Code.Relation.Nullary.C__because__46
(coe MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
(coe
MAlonzo.Code.Relation.Nullary.C_of'696'_22
(coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C_'91''93'_56))
(:) v3 v4
-> coe
MAlonzo.Code.Relation.Nullary.C__because__46
(coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
(coe MAlonzo.Code.Relation.Nullary.C_of'8319'_26)
_ -> MAlonzo.RTE.mazUnreachableError
(:) v3 v4
-> case coe v2 of
[]
-> coe
MAlonzo.Code.Relation.Nullary.C__because__46
(coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
(coe MAlonzo.Code.Relation.Nullary.C_of'8319'_26)
(:) v5 v6
-> coe
MAlonzo.Code.Relation.Nullary.Decidable.Core.du_map'8242'_168
(coe
MAlonzo.Code.Data.Product.du_uncurry_264
(coe
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.C__'8759'__62))
(coe
MAlonzo.Code.Relation.Nullary.Product.du__'215''45'dec__30
(coe v0 v3 v5) (coe du_decidable_112 (coe v0) (coe v4) (coe v6)))
_ -> MAlonzo.RTE.mazUnreachableError
_ -> MAlonzo.RTE.mazUnreachableError
d_irrelevant_132 ::
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
() ->
MAlonzo.Code.Agda.Primitive.T_Level_14 ->
(AgdaAny -> AgdaAny -> ()) ->
(AgdaAny ->
AgdaAny ->
AgdaAny ->
AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
[AgdaAny] ->
[AgdaAny] ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Data.List.Relation.Binary.Pointwise.Base.T_Pointwise_48 ->
MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
d_irrelevant_132 = erased