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.Unary.Properties where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Bool qualified
  import MAlonzo.Code.Agda.Builtin.Equality qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Builtin.Unit qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Data.Irrelevant qualified
  import MAlonzo.Code.Data.Product.Base qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Relation.Nullary.Decidable.Core qualified
  import MAlonzo.Code.Relation.Nullary.Reflects 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.Unary.Properties.∅?
  d_'8709''63'_22 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_'8709''63'_22 ~v0 ~v1 ~v2 = du_'8709''63'_22
  du_'8709''63'_22 ::
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_'8709''63'_22
    = coe
        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
        (coe MAlonzo.Code.Agda.Builtin.Bool.C_false_8)
        (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26)
  -- Relation.Unary.Properties.∅-Empty
  d_'8709''45'Empty_24 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    AgdaAny ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8709''45'Empty_24 = erased
  -- Relation.Unary.Properties.∁∅-Universal
  d_'8705''8709''45'Universal_28 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    AgdaAny ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8705''8709''45'Universal_28 = erased
  -- Relation.Unary.Properties.U?
  d_U'63'_34 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_U'63'_34 ~v0 ~v1 ~v2 = du_U'63'_34
  du_U'63'_34 ::
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_U'63'_34
    = coe
        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
        (coe MAlonzo.Code.Agda.Builtin.Bool.C_true_10)
        (coe
           MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
           (coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8))
  -- Relation.Unary.Properties.U-Universal
  d_U'45'Universal_36 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  d_U'45'Universal_36 ~v0 ~v1 ~v2 = du_U'45'Universal_36
  du_U'45'Universal_36 :: MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  du_U'45'Universal_36 = coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
  -- Relation.Unary.Properties.∁U-Empty
  d_'8705'U'45'Empty_40 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    AgdaAny ->
    (MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6 ->
     MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8705'U'45'Empty_40 = erased
  -- Relation.Unary.Properties.∅-⊆
  d_'8709''45''8838'_48 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 -> AgdaAny
  d_'8709''45''8838'_48 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8709''45''8838'_48
  du_'8709''45''8838'_48 :: AgdaAny
  du_'8709''45''8838'_48 = MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊆-U
  d_'8838''45'U_54 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  d_'8838''45'U_54 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 = du_'8838''45'U_54
  du_'8838''45'U_54 :: MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  du_'8838''45'U_54 = coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
  -- Relation.Unary.Properties.⊆-refl
  d_'8838''45'refl_58 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''45'refl_58 ~v0 ~v1 ~v2 ~v3 ~v4 v5
    = du_'8838''45'refl_58 v5
  du_'8838''45'refl_58 :: AgdaAny -> AgdaAny
  du_'8838''45'refl_58 v0 = coe v0
  -- Relation.Unary.Properties.⊆-reflexive
  d_'8838''45'reflexive_62 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''45'reflexive_62 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7
    = du_'8838''45'reflexive_62 v6 v7
  du_'8838''45'reflexive_62 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8838''45'reflexive_62 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3 -> coe v2 v1
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊆-trans
  d_'8838''45'trans_68 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''45'trans_68 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10 v11
    = du_'8838''45'trans_68 v8 v9 v10 v11
  du_'8838''45'trans_68 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8838''45'trans_68 v0 v1 v2 v3 = coe v1 v2 (coe v0 v2 v3)
  -- Relation.Unary.Properties.⊆-antisym
  d_'8838''45'antisym_76 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8838''45'antisym_76 ~v0 ~v1 ~v2 ~v3 ~v4
    = du_'8838''45'antisym_76
  du_'8838''45'antisym_76 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8838''45'antisym_76
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
  -- Relation.Unary.Properties.⊆-min
  d_'8838''45'min_78 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 -> AgdaAny
  d_'8838''45'min_78 ~v0 ~v1 ~v2 = du_'8838''45'min_78
  du_'8838''45'min_78 ::
    (AgdaAny -> ()) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 -> AgdaAny
  du_'8838''45'min_78 v0 v1 v2 = coe du_'8709''45''8838'_48
  -- Relation.Unary.Properties.⊆-max
  d_'8838''45'max_80 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  d_'8838''45'max_80 ~v0 ~v1 ~v2 = du_'8838''45'max_80
  du_'8838''45'max_80 ::
    (AgdaAny -> ()) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  du_'8838''45'max_80 v0 v1 v2 = coe du_'8838''45'U_54
  -- Relation.Unary.Properties.⊂⇒⊆
  d_'8834''8658''8838'_82 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8834''8658''8838'_82 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8834''8658''8838'_82 v6
  du_'8834''8658''8838'_82 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8834''8658''8838'_82 v0
    = coe MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 (coe v0)
  -- Relation.Unary.Properties.⊂-trans
  d_'8834''45'trans_84 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''45'trans_84 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9
    = du_'8834''45'trans_84 v8 v9
  du_'8834''45'trans_84 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''45'trans_84 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> case coe v1 of
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v4 v5
                 -> coe
                      MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                      (coe (\ v6 v7 -> coe v4 v6 (coe v2 v6 v7)))
                      (coe (\ v6 -> coe v5 (\ v7 v8 -> coe v2 v7 (coe v6 v7 v8))))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂-⊆-trans
  d_'8834''45''8838''45'trans_100 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''45''8838''45'trans_100 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8
                                  v9
    = du_'8834''45''8838''45'trans_100 v8 v9
  du_'8834''45''8838''45'trans_100 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''45''8838''45'trans_100 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
               (coe (\ v4 v5 -> coe v1 v4 (coe v2 v4 v5)))
               (coe (\ v4 -> coe v3 (\ v5 v6 -> coe v4 v5 (coe v1 v5 v6))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊆-⊂-trans
  d_'8838''45''8834''45'trans_114 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8838''45''8834''45'trans_114 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8
                                  v9
    = du_'8838''45''8834''45'trans_114 v8 v9
  du_'8838''45''8834''45'trans_114 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8838''45''8834''45'trans_114 v0 v1
    = case coe v1 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
               (coe (\ v4 v5 -> coe v2 v4 (coe v0 v4 v5)))
               (coe (\ v4 -> coe v3 (\ v5 v6 -> coe v0 v5 (coe v4 v5 v6))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂-respʳ-≐
  d_'8834''45'resp'691''45''8784'_128 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''45'resp'691''45''8784'_128 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 v7
                                      v8
    = du_'8834''45'resp'691''45''8784'_128 v7 v8
  du_'8834''45'resp'691''45''8784'_128 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''45'resp'691''45''8784'_128 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe du_'8834''45''8838''45'trans_100 (coe v1) (coe v2)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂-respˡ-≐
  d_'8834''45'resp'737''45''8784'_134 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''45'resp'737''45''8784'_134 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 v7
                                      v8
    = du_'8834''45'resp'737''45''8784'_134 v7 v8
  du_'8834''45'resp'737''45''8784'_134 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''45'resp'737''45''8784'_134 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe du_'8838''45''8834''45'trans_114 (coe v3) (coe v1)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂-resp-≐
  d_'8834''45'resp'45''8784'_140 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''45'resp'45''8784'_140 ~v0 ~v1 ~v2
    = du_'8834''45'resp'45''8784'_140
  du_'8834''45'resp'45''8784'_140 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''45'resp'45''8784'_140
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (\ v0 v1 v2 v3 v4 ->
           coe du_'8834''45'resp'691''45''8784'_128 v3 v4)
        (\ v0 v1 v2 v3 v4 ->
           coe du_'8834''45'resp'737''45''8784'_134 v3 v4)
  -- Relation.Unary.Properties.⊂-irrefl
  d_'8834''45'irrefl_142 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8834''45'irrefl_142 = erased
  -- Relation.Unary.Properties.⊂-antisym
  d_'8834''45'antisym_148 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''45'antisym_148 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6
    = du_'8834''45'antisym_148 v5 v6
  du_'8834''45'antisym_148 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''45'antisym_148 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> case coe v1 of
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v4 v5
                 -> coe du_'8838''45'antisym_76 v2 v4
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂-asym
  d_'8834''45'asym_154 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8834''45'asym_154 = erased
  -- Relation.Unary.Properties.∅-⊆′
  d_'8709''45''8838''8242'_160 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 -> AgdaAny
  d_'8709''45''8838''8242'_160 = erased
  -- Relation.Unary.Properties.⊆′-U
  d_'8838''8242''45'U_164 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  d_'8838''8242''45'U_164 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8838''8242''45'U_164
  du_'8838''8242''45'U_164 ::
    MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  du_'8838''8242''45'U_164
    = coe MAlonzo.Code.Agda.Builtin.Unit.C_tt_8
  -- Relation.Unary.Properties.⊆′-refl
  d_'8838''8242''45'refl_166 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''8242''45'refl_166 ~v0 ~v1 ~v2 ~v3 ~v4 v5
    = du_'8838''8242''45'refl_166 v5
  du_'8838''8242''45'refl_166 :: AgdaAny -> AgdaAny
  du_'8838''8242''45'refl_166 v0 = coe v0
  -- Relation.Unary.Properties.⊆′-reflexive
  d_'8838''8242''45'reflexive_172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''8242''45'reflexive_172 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8838''8242''45'reflexive_172 v6
  du_'8838''8242''45'reflexive_172 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8838''8242''45'reflexive_172 v0
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v1 v2 -> coe v1
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊆′-trans
  d_'8838''8242''45'trans_178 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''8242''45'trans_178 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9
                              v10 v11
    = du_'8838''8242''45'trans_178 v8 v9 v10 v11
  du_'8838''8242''45'trans_178 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8838''8242''45'trans_178 v0 v1 v2 v3 = coe v1 v2 (coe v0 v2 v3)
  -- Relation.Unary.Properties.⊆′-antisym
  d_'8838''8242''45'antisym_188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8838''8242''45'antisym_188 ~v0 ~v1 ~v2 ~v3 ~v4
    = du_'8838''8242''45'antisym_188
  du_'8838''8242''45'antisym_188 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8838''8242''45'antisym_188
    = coe MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
  -- Relation.Unary.Properties.⊆′-min
  d_'8838''8242''45'min_190 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 -> AgdaAny
  d_'8838''8242''45'min_190 v0 ~v1 v2
    = du_'8838''8242''45'min_190 v0 v2
  du_'8838''8242''45'min_190 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20 -> AgdaAny
  du_'8838''8242''45'min_190 v0 v1
    = coe d_'8709''45''8838''8242'_160 v0 erased v1
  -- Relation.Unary.Properties.⊆′-max
  d_'8838''8242''45'max_192 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  d_'8838''8242''45'max_192 ~v0 ~v1 ~v2 = du_'8838''8242''45'max_192
  du_'8838''8242''45'max_192 ::
    (AgdaAny -> ()) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6
  du_'8838''8242''45'max_192 v0 v1 v2 = coe du_'8838''8242''45'U_164
  -- Relation.Unary.Properties.⊂′⇒⊆′
  d_'8834''8242''8658''8838''8242'_194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8834''8242''8658''8838''8242'_194 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8834''8242''8658''8838''8242'_194 v6
  du_'8834''8242''8658''8838''8242'_194 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8834''8242''8658''8838''8242'_194 v0
    = coe MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28 (coe v0)
  -- Relation.Unary.Properties.⊂′-trans
  d_'8834''8242''45'trans_196 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8242''45'trans_196 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9
    = du_'8834''8242''45'trans_196 v8 v9
  du_'8834''8242''45'trans_196 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8242''45'trans_196 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> case coe v1 of
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v4 v5
                 -> coe
                      MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
                      (coe du_'8838''8242''45'trans_178 (coe v2) (coe v4))
                      (coe
                         (\ v6 ->
                            coe v5 (coe du_'8838''8242''45'trans_178 (coe v6) (coe v2))))
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂′-⊆′-trans
  d_'8834''8242''45''8838''8242''45'trans_208 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8242''45''8838''8242''45'trans_208 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
                                              ~v6 ~v7 v8 v9
    = du_'8834''8242''45''8838''8242''45'trans_208 v8 v9
  du_'8834''8242''45''8838''8242''45'trans_208 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8242''45''8838''8242''45'trans_208 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
               (coe du_'8838''8242''45'trans_178 (coe v2) (coe v1))
               (coe
                  (\ v4 ->
                     coe v3 (coe du_'8838''8242''45'trans_178 (coe v1) (coe v4))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊆′-⊂′-trans
  d_'8838''8242''45''8834''8242''45'trans_218 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8838''8242''45''8834''8242''45'trans_218 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
                                              ~v6 ~v7 v8 v9
    = du_'8838''8242''45''8834''8242''45'trans_218 v8 v9
  du_'8838''8242''45''8834''8242''45'trans_218 ::
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8838''8242''45''8834''8242''45'trans_218 v0 v1
    = case coe v1 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
               (coe du_'8838''8242''45'trans_178 (coe v0) (coe v2))
               (coe
                  (\ v4 ->
                     coe v3 (coe du_'8838''8242''45'trans_178 (coe v4) (coe v0))))
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂′-respʳ-≐′
  d_'8834''8242''45'resp'691''45''8784''8242'_228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8242''45'resp'691''45''8784''8242'_228 ~v0 ~v1 ~v2 ~v3 ~v4
                                                  ~v5 ~v6 v7 v8
    = du_'8834''8242''45'resp'691''45''8784''8242'_228 v7 v8
  du_'8834''8242''45'resp'691''45''8784''8242'_228 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8242''45'resp'691''45''8784''8242'_228 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe
               du_'8834''8242''45''8838''8242''45'trans_208 (coe v1) (coe v2)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂′-respˡ-≐′
  d_'8834''8242''45'resp'737''45''8784''8242'_234 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8242''45'resp'737''45''8784''8242'_234 ~v0 ~v1 ~v2 ~v3 ~v4
                                                  ~v5 ~v6 v7 v8
    = du_'8834''8242''45'resp'737''45''8784''8242'_234 v7 v8
  du_'8834''8242''45'resp'737''45''8784''8242'_234 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8242''45'resp'737''45''8784''8242'_234 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> coe
               du_'8838''8242''45''8834''8242''45'trans_218 (coe v3) (coe v1)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊂′-resp-≐′
  d_'8834''8242''45'resp'45''8784''8242'_240 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8242''45'resp'45''8784''8242'_240 ~v0 ~v1 ~v2
    = du_'8834''8242''45'resp'45''8784''8242'_240
  du_'8834''8242''45'resp'45''8784''8242'_240 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8242''45'resp'45''8784''8242'_240
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (\ v0 v1 v2 v3 v4 ->
           coe du_'8834''8242''45'resp'691''45''8784''8242'_228 v3 v4)
        (\ v0 v1 v2 v3 v4 ->
           coe du_'8834''8242''45'resp'737''45''8784''8242'_234 v3 v4)
  -- Relation.Unary.Properties.⊂′-irrefl
  d_'8834''8242''45'irrefl_242 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8834''8242''45'irrefl_242 = erased
  -- Relation.Unary.Properties.⊂′-antisym
  d_'8834''8242''45'antisym_248 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8242''45'antisym_248 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6
    = du_'8834''8242''45'antisym_248 v5 v6
  du_'8834''8242''45'antisym_248 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8242''45'antisym_248 v0 v1
    = case coe v0 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v2 v3
          -> case coe v1 of
               MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v4 v5
                 -> coe du_'8838''8242''45'antisym_188 v2 v4
               _ -> MAlonzo.RTE.mazUnreachableError
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties.⊆⇒⊆′
  d_'8838''8658''8838''8242'_254 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''8658''8838''8242'_254 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 v8
    = du_'8838''8658''8838''8242'_254 v6 v7 v8
  du_'8838''8658''8838''8242'_254 ::
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8838''8658''8838''8242'_254 v0 v1 v2 = coe v0 v1 v2
  -- Relation.Unary.Properties.⊆′⇒⊆
  d_'8838''8242''8658''8838'_260 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8838''8242''8658''8838'_260 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 v8
    = du_'8838''8242''8658''8838'_260 v6 v7 v8
  du_'8838''8242''8658''8838'_260 ::
    (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8838''8242''8658''8838'_260 v0 v1 v2 = coe v0 v1 v2
  -- Relation.Unary.Properties.⊂⇒⊂′
  d_'8834''8658''8834''8242'_266 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8658''8834''8242'_266 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8834''8658''8834''8242'_266
  du_'8834''8658''8834''8242'_266 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8658''8834''8242'_266
    = coe
        MAlonzo.Code.Data.Product.Base.du_map_128
        (coe du_'8838''8658''8838''8242'_254)
        (coe
           (\ v0 v1 v2 ->
              coe v1 (coe du_'8838''8242''8658''8838'_260 (coe v2))))
  -- Relation.Unary.Properties.⊂′⇒⊂
  d_'8834''8242''8658''8834'_270 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8834''8242''8658''8834'_270 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8834''8242''8658''8834'_270
  du_'8834''8242''8658''8834'_270 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8834''8242''8658''8834'_270
    = coe
        MAlonzo.Code.Data.Product.Base.du_map_128
        (coe du_'8838''8242''8658''8838'_260)
        (coe
           (\ v0 v1 v2 ->
              coe v1 (coe du_'8838''8658''8838''8242'_254 (coe v2))))
  -- Relation.Unary.Properties.≐-refl
  d_'8784''45'refl_274 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''45'refl_274 ~v0 ~v1 ~v2 ~v3 = du_'8784''45'refl_274
  du_'8784''45'refl_274 :: MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''45'refl_274
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe (\ v0 v1 -> v1))
        (coe (\ v0 v1 -> v1))
  -- Relation.Unary.Properties.≐-sym
  d_'8784''45'sym_276 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''45'sym_276 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 = du_'8784''45'sym_276
  du_'8784''45'sym_276 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''45'sym_276
    = coe MAlonzo.Code.Data.Product.Base.du_swap_370
  -- Relation.Unary.Properties.≐-trans
  d_'8784''45'trans_278 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''45'trans_278 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7
    = du_'8784''45'trans_278
  du_'8784''45'trans_278 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''45'trans_278
    = coe
        MAlonzo.Code.Data.Product.Base.du_zip'8242'_312
        (coe (\ v0 v1 v2 v3 -> coe v1 v2 (coe v0 v2 v3)))
        (coe (\ v0 v1 v2 v3 -> coe v0 v2 (coe v1 v2 v3)))
  -- Relation.Unary.Properties.≐′-refl
  d_'8784''8242''45'refl_292 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''8242''45'refl_292 ~v0 ~v1 ~v2 ~v3
    = du_'8784''8242''45'refl_292
  du_'8784''8242''45'refl_292 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''8242''45'refl_292
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 (coe (\ v0 v1 -> v1))
        (coe (\ v0 v1 -> v1))
  -- Relation.Unary.Properties.≐′-sym
  d_'8784''8242''45'sym_298 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''8242''45'sym_298 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8784''8242''45'sym_298
  du_'8784''8242''45'sym_298 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''8242''45'sym_298
    = coe MAlonzo.Code.Data.Product.Base.du_swap_370
  -- Relation.Unary.Properties.≐′-trans
  d_'8784''8242''45'trans_300 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''8242''45'trans_300 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7
    = du_'8784''8242''45'trans_300
  du_'8784''8242''45'trans_300 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''8242''45'trans_300
    = coe
        MAlonzo.Code.Data.Product.Base.du_zip'8242'_312
        (coe (\ v0 v1 v2 v3 -> coe v1 v2 (coe v0 v2 v3)))
        (coe (\ v0 v1 v2 v3 -> coe v0 v2 (coe v1 v2 v3)))
  -- Relation.Unary.Properties.≐⇒≐′
  d_'8784''8658''8784''8242'_318 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''8658''8784''8242'_318 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8784''8658''8784''8242'_318
  du_'8784''8658''8784''8242'_318 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''8658''8784''8242'_318
    = coe
        MAlonzo.Code.Data.Product.Base.du_map_128
        (coe du_'8838''8658''8838''8242'_254)
        (coe (\ v0 -> coe du_'8838''8658''8838''8242'_254))
  -- Relation.Unary.Properties.≐′⇒≐
  d_'8784''8242''8658''8784'_320 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8784''8242''8658''8784'_320 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8784''8242''8658''8784'_320
  du_'8784''8242''8658''8784'_320 ::
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8784''8242''8658''8784'_320
    = coe
        MAlonzo.Code.Data.Product.Base.du_map_128
        (coe du_'8838''8242''8658''8838'_260)
        (coe (\ v0 -> coe du_'8838''8242''8658''8838'_260))
  -- Relation.Unary.Properties.∁?
  d_'8705''63'_324 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_'8705''63'_324 ~v0 ~v1 ~v2 ~v3 v4 v5 = du_'8705''63'_324 v4 v5
  du_'8705''63'_324 ::
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_'8705''63'_324 v0 v1
    = coe
        MAlonzo.Code.Relation.Nullary.Decidable.Core.du_'172''63'_70
        (coe v0 v1)
  -- Relation.Unary.Properties._∪?_
  d__'8746''63'__334 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8746''63'__334 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 v8
    = du__'8746''63'__334 v6 v7 v8
  du__'8746''63'__334 ::
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8746''63'__334 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Nullary.Decidable.Core.du__'8846''45'dec__86
        (coe v0 v2) (coe v1 v2)
  -- Relation.Unary.Properties._∩?_
  d__'8745''63'__346 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8745''63'__346 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 v8
    = du__'8745''63'__346 v6 v7 v8
  du__'8745''63'__346 ::
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8745''63'__346 v0 v1 v2
    = coe
        MAlonzo.Code.Relation.Nullary.Decidable.Core.du__'215''45'dec__76
        (coe v0 v2) (coe v1 v2)
  -- Relation.Unary.Properties._×?_
  d__'215''63'__358 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'215''63'__358 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10
    = du__'215''63'__358 v8 v9 v10
  du__'215''63'__358 ::
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'215''63'__358 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v3 v4
          -> coe
               MAlonzo.Code.Relation.Nullary.Decidable.Core.du__'215''45'dec__76
               (coe v0 v3) (coe v1 v4)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties._⊙?_
  d__'8857''63'__372 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8857''63'__372 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 ~v7 v8 v9 v10
    = du__'8857''63'__372 v8 v9 v10
  du__'8857''63'__372 ::
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8857''63'__372 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32 v3 v4
          -> coe
               MAlonzo.Code.Relation.Nullary.Decidable.Core.du__'8846''45'dec__86
               (coe v0 v3) (coe v1 v4)
        _ -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties._⊎?_
  d__'8846''63'__386 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> ()) ->
    (AgdaAny -> ()) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8846''63'__386 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 ~v6 v7 v8 v9
    = du__'8846''63'__386 v7 v8 v9
  du__'8846''63'__386 ::
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    (AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8846''63'__386 v0 v1 v2
    = case coe v2 of
        MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v3 -> coe v0 v3
        MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v3 -> coe v1 v3
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Unary.Properties._~?
  d__'126''63'_402 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 -> ()) ->
    (MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'126''63'_402 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7
    = du__'126''63'_402 v6 v7
  du__'126''63'_402 ::
    (MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'126''63'_402 v0 v1
    = coe v0 (coe MAlonzo.Code.Data.Product.Base.du_swap_370 (coe v1))
  -- Relation.Unary.Properties.U-irrelevant
  d_U'45'irrelevant_406 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6 ->
    MAlonzo.Code.Agda.Builtin.Unit.T_'8868'_6 ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_U'45'irrelevant_406 = erased
  -- Relation.Unary.Properties.∁-irrelevant
  d_'8705''45'irrelevant_414 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    (AgdaAny -> ()) ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12
  d_'8705''45'irrelevant_414 = erased
  