content: {-# 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.Relation.Binary.Construct.Add.Infimum.Equality where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Equality qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality qualified
  import MAlonzo.Code.Relation.Binary.Structures qualified
  import MAlonzo.Code.Relation.Nullary.Decidable.Core qualified
  import MAlonzo.RTE (AgdaAny, add64, addInt, coe, eq64, eqInt, erased, geqInt, lt64, ltInt, mul64,
                      mulInt, quot64, quotInt, rem64, remInt, sub64, subInt, word64FromNat,
                      word64ToNat)
  import MAlonzo.RTE qualified
  
  -- Relation.Binary.Construct.Add.Infimum.Equality._._≈∙_
  d__'8776''8729'__22 a0 a1 a2 a3 a4 a5 = ()
  -- Relation.Binary.Construct.Add.Infimum.Equality._.[≈]-injective
  d_'91''8776''93''45'injective_26 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    AgdaAny
  d_'91''8776''93''45'injective_26 ~v0 ~v1 ~v2 ~v3
    = du_'91''8776''93''45'injective_26
  du_'91''8776''93''45'injective_26 ::
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    AgdaAny
  du_'91''8776''93''45'injective_26 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'91''8776''93''45'injective_34
        v2
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-dec
  d_'8776''8729''45'dec_28 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_'8776''8729''45'dec_28 ~v0 ~v1 ~v2 ~v3
    = du_'8776''8729''45'dec_28
  du_'8776''8729''45'dec_28 ::
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_'8776''8729''45'dec_28
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'8776''8729''45'dec_66
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-irrelevant
  d_'8776''8729''45'irrelevant_30 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny ->
     AgdaAny ->
     AgdaAny ->
     AgdaAny -> MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'8776''8729''45'irrelevant_30 = erased
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-isDecEquivalence
  d_'8776''8729''45'isDecEquivalence_32 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecEquivalence_44 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecEquivalence_44
  d_'8776''8729''45'isDecEquivalence_32 ~v0 ~v1 ~v2 ~v3
    = du_'8776''8729''45'isDecEquivalence_32
  du_'8776''8729''45'isDecEquivalence_32 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecEquivalence_44 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecEquivalence_44
  du_'8776''8729''45'isDecEquivalence_32
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'8776''8729''45'isDecEquivalence_128
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-isEquivalence
  d_'8776''8729''45'isEquivalence_34 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_'8776''8729''45'isEquivalence_34 ~v0 ~v1 ~v2 ~v3
    = du_'8776''8729''45'isEquivalence_34
  du_'8776''8729''45'isEquivalence_34 ::
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  du_'8776''8729''45'isEquivalence_34
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'8776''8729''45'isEquivalence_108
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-refl
  d_'8776''8729''45'refl_36 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny) ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20
  d_'8776''8729''45'refl_36 ~v0 ~v1 ~v2 ~v3
    = du_'8776''8729''45'refl_36
  du_'8776''8729''45'refl_36 ::
    (AgdaAny -> AgdaAny) ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20
  du_'8776''8729''45'refl_36
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'8776''8729''45'refl_38
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-substitutive
  d_'8776''8729''45'substitutive_38 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (Maybe AgdaAny -> ()) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    AgdaAny -> AgdaAny
  d_'8776''8729''45'substitutive_38 ~v0 ~v1 ~v2 ~v3
    = du_'8776''8729''45'substitutive_38
  du_'8776''8729''45'substitutive_38 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    ((AgdaAny -> ()) ->
     AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (Maybe AgdaAny -> ()) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    AgdaAny -> AgdaAny
  du_'8776''8729''45'substitutive_38 v0 v1 v2 v3 v4 v5
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'8776''8729''45'substitutive_96
        v1 v2 v3 v4 v5
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-sym
  d_'8776''8729''45'sym_40 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20
  d_'8776''8729''45'sym_40 ~v0 ~v1 ~v2 ~v3
    = du_'8776''8729''45'sym_40
  du_'8776''8729''45'sym_40 ::
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20
  du_'8776''8729''45'sym_40
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'8776''8729''45'sym_46
  -- Relation.Binary.Construct.Add.Infimum.Equality._.≈∙-trans
  d_'8776''8729''45'trans_42 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20
  d_'8776''8729''45'trans_42 ~v0 ~v1 ~v2 ~v3
    = du_'8776''8729''45'trans_42
  du_'8776''8729''45'trans_42 ::
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    Maybe AgdaAny ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20 ->
    MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.T__'8776''8729'__20
  du_'8776''8729''45'trans_42
    = coe
        MAlonzo.Code.Relation.Binary.Construct.Add.Point.Equality.du_'8776''8729''45'trans_54
  