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.Structures where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Equality qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Data.Irrelevant qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Relation.Binary.Consequences qualified
  import MAlonzo.Code.Relation.Binary.Definitions 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.Structures.IsPartialEquivalence
  d_IsPartialEquivalence_16 a0 a1 a2 a3 = ()
  data T_IsPartialEquivalence_16
    = C_IsPartialEquivalence'46'constructor_273 (AgdaAny ->
                                                 AgdaAny -> AgdaAny -> AgdaAny)
                                                (AgdaAny ->
                                                 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
  -- Relation.Binary.Structures.IsPartialEquivalence.sym
  d_sym_22 ::
    T_IsPartialEquivalence_16 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_22 v0
    = case coe v0 of
        C_IsPartialEquivalence'46'constructor_273 v1 v2 -> coe v1
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsPartialEquivalence.trans
  d_trans_24 ::
    T_IsPartialEquivalence_16 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_24 v0
    = case coe v0 of
        C_IsPartialEquivalence'46'constructor_273 v1 v2 -> coe v2
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsEquivalence
  d_IsEquivalence_26 a0 a1 a2 a3 = ()
  data T_IsEquivalence_26
    = C_IsEquivalence'46'constructor_745 (AgdaAny -> AgdaAny)
                                         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                         (AgdaAny ->
                                          AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
  -- Relation.Binary.Structures.IsEquivalence.refl
  d_refl_34 :: T_IsEquivalence_26 -> AgdaAny -> AgdaAny
  d_refl_34 v0
    = case coe v0 of
        C_IsEquivalence'46'constructor_745 v1 v2 v3 -> coe v1
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsEquivalence.sym
  d_sym_36 ::
    T_IsEquivalence_26 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_36 v0
    = case coe v0 of
        C_IsEquivalence'46'constructor_745 v1 v2 v3 -> coe v2
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsEquivalence.trans
  d_trans_38 ::
    T_IsEquivalence_26 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_38 v0
    = case coe v0 of
        C_IsEquivalence'46'constructor_745 v1 v2 v3 -> coe v3
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsEquivalence.reflexive
  d_reflexive_40 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    T_IsEquivalence_26 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_40 ~v0 ~v1 ~v2 ~v3 v4 v5 ~v6 ~v7
    = du_reflexive_40 v4 v5
  du_reflexive_40 :: T_IsEquivalence_26 -> AgdaAny -> AgdaAny
  du_reflexive_40 v0 v1 = coe d_refl_34 v0 v1
  -- Relation.Binary.Structures.IsEquivalence.isPartialEquivalence
  d_isPartialEquivalence_42 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    T_IsEquivalence_26 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_42 ~v0 ~v1 ~v2 ~v3 v4
    = du_isPartialEquivalence_42 v4
  du_isPartialEquivalence_42 ::
    T_IsEquivalence_26 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_42 v0
    = coe
        C_IsPartialEquivalence'46'constructor_273 (coe d_sym_36 (coe v0))
        (coe d_trans_38 (coe v0))
  -- Relation.Binary.Structures.IsDecEquivalence
  d_IsDecEquivalence_44 a0 a1 a2 a3 = ()
  data T_IsDecEquivalence_44
    = C_IsDecEquivalence'46'constructor_3083 T_IsEquivalence_26
                                             (AgdaAny ->
                                              AgdaAny ->
                                              MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20)
  -- Relation.Binary.Structures.IsDecEquivalence.isEquivalence
  d_isEquivalence_50 :: T_IsDecEquivalence_44 -> T_IsEquivalence_26
  d_isEquivalence_50 v0
    = case coe v0 of
        C_IsDecEquivalence'46'constructor_3083 v1 v2 -> coe v1
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecEquivalence._≟_
  d__'8799'__52 ::
    T_IsDecEquivalence_44 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__52 v0
    = case coe v0 of
        C_IsDecEquivalence'46'constructor_3083 v1 v2 -> coe v2
        _                                            -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecEquivalence._.isPartialEquivalence
  d_isPartialEquivalence_56 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    T_IsDecEquivalence_44 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_56 ~v0 ~v1 ~v2 ~v3 v4
    = du_isPartialEquivalence_56 v4
  du_isPartialEquivalence_56 ::
    T_IsDecEquivalence_44 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_56 v0
    = coe du_isPartialEquivalence_42 (coe d_isEquivalence_50 (coe v0))
  -- Relation.Binary.Structures.IsDecEquivalence._.refl
  d_refl_58 :: T_IsDecEquivalence_44 -> AgdaAny -> AgdaAny
  d_refl_58 v0 = coe d_refl_34 (coe d_isEquivalence_50 (coe v0))
  -- Relation.Binary.Structures.IsDecEquivalence._.reflexive
  d_reflexive_60 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny -> ()) ->
    T_IsDecEquivalence_44 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_60 ~v0 ~v1 ~v2 ~v3 v4 = du_reflexive_60 v4
  du_reflexive_60 ::
    T_IsDecEquivalence_44 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_60 v0 v1 v2 v3
    = coe du_reflexive_40 (coe d_isEquivalence_50 (coe v0)) v1
  -- Relation.Binary.Structures.IsDecEquivalence._.sym
  d_sym_62 ::
    T_IsDecEquivalence_44 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_62 v0 = coe d_sym_36 (coe d_isEquivalence_50 (coe v0))
  -- Relation.Binary.Structures.IsDecEquivalence._.trans
  d_trans_64 ::
    T_IsDecEquivalence_44 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_64 v0 = coe d_trans_38 (coe d_isEquivalence_50 (coe v0))
  -- Relation.Binary.Structures.IsPreorder
  d_IsPreorder_70 a0 a1 a2 a3 a4 a5 = ()
  data T_IsPreorder_70
    = C_IsPreorder'46'constructor_4003 T_IsEquivalence_26
                                       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                       (AgdaAny ->
                                        AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
  -- Relation.Binary.Structures.IsPreorder.isEquivalence
  d_isEquivalence_80 :: T_IsPreorder_70 -> T_IsEquivalence_26
  d_isEquivalence_80 v0
    = case coe v0 of
        C_IsPreorder'46'constructor_4003 v1 v2 v3 -> coe v1
        _                                         -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsPreorder.reflexive
  d_reflexive_82 ::
    T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_reflexive_82 v0
    = case coe v0 of
        C_IsPreorder'46'constructor_4003 v1 v2 v3 -> coe v2
        _                                         -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsPreorder.trans
  d_trans_84 ::
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_84 v0
    = case coe v0 of
        C_IsPreorder'46'constructor_4003 v1 v2 v3 -> coe v3
        _                                         -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsPreorder.Eq.isPartialEquivalence
  d_isPartialEquivalence_88 ::
    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 -> ()) ->
    T_IsPreorder_70 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_88 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_88 v6
  du_isPartialEquivalence_88 ::
    T_IsPreorder_70 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_88 v0
    = coe du_isPartialEquivalence_42 (coe d_isEquivalence_80 (coe v0))
  -- Relation.Binary.Structures.IsPreorder.Eq.refl
  d_refl_90 :: T_IsPreorder_70 -> AgdaAny -> AgdaAny
  d_refl_90 v0 = coe d_refl_34 (coe d_isEquivalence_80 (coe v0))
  -- Relation.Binary.Structures.IsPreorder.Eq.reflexive
  d_reflexive_92 ::
    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 -> ()) ->
    T_IsPreorder_70 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_92 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_92 v6
  du_reflexive_92 ::
    T_IsPreorder_70 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_92 v0 v1 v2 v3
    = coe du_reflexive_40 (coe d_isEquivalence_80 (coe v0)) v1
  -- Relation.Binary.Structures.IsPreorder.Eq.sym
  d_sym_94 ::
    T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_94 v0 = coe d_sym_36 (coe d_isEquivalence_80 (coe v0))
  -- Relation.Binary.Structures.IsPreorder.Eq.trans
  d_trans_96 ::
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_96 v0 = coe d_trans_38 (coe d_isEquivalence_80 (coe v0))
  -- Relation.Binary.Structures.IsPreorder.refl
  d_refl_98 ::
    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 -> ()) -> T_IsPreorder_70 -> AgdaAny -> AgdaAny
  d_refl_98 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 = du_refl_98 v6 v7
  du_refl_98 :: T_IsPreorder_70 -> AgdaAny -> AgdaAny
  du_refl_98 v0 v1
    = coe
        d_reflexive_82 v0 v1 v1
        (coe d_refl_34 (d_isEquivalence_80 (coe v0)) v1)
  -- Relation.Binary.Structures.IsPreorder.≲-respˡ-≈
  d_'8818''45'resp'737''45''8776'_100 ::
    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 -> ()) ->
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'737''45''8776'_100 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7
                                      v8 v9 v10 v11
    = du_'8818''45'resp'737''45''8776'_100 v6 v7 v8 v9 v10 v11
  du_'8818''45'resp'737''45''8776'_100 ::
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'737''45''8776'_100 v0 v1 v2 v3 v4 v5
    = coe
        d_trans_84 v0 v3 v2 v1
        (coe
           d_reflexive_82 v0 v3 v2
           (coe d_sym_36 (d_isEquivalence_80 (coe v0)) v2 v3 v4))
        v5
  -- Relation.Binary.Structures.IsPreorder.≲-respʳ-≈
  d_'8818''45'resp'691''45''8776'_106 ::
    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 -> ()) ->
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'691''45''8776'_106 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7
                                      v8 v9 v10 v11
    = du_'8818''45'resp'691''45''8776'_106 v6 v7 v8 v9 v10 v11
  du_'8818''45'resp'691''45''8776'_106 ::
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'691''45''8776'_106 v0 v1 v2 v3 v4 v5
    = coe d_trans_84 v0 v1 v2 v3 v5 (coe d_reflexive_82 v0 v2 v3 v4)
  -- Relation.Binary.Structures.IsPreorder.≲-resp-≈
  d_'8818''45'resp'45''8776'_112 ::
    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 -> ()) ->
    T_IsPreorder_70 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8818''45'resp'45''8776'_112 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'45''8776'_112 v6
  du_'8818''45'resp'45''8776'_112 ::
    T_IsPreorder_70 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8818''45'resp'45''8776'_112 v0
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe du_'8818''45'resp'691''45''8776'_106 (coe v0))
        (coe du_'8818''45'resp'737''45''8776'_100 (coe v0))
  -- Relation.Binary.Structures.IsPreorder.∼-respˡ-≈
  d_'8764''45'resp'737''45''8776'_114 ::
    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 -> ()) ->
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'737''45''8776'_114 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'737''45''8776'_114 v6
  du_'8764''45'resp'737''45''8776'_114 ::
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'737''45''8776'_114 v0
    = coe du_'8818''45'resp'737''45''8776'_100 (coe v0)
  -- Relation.Binary.Structures.IsPreorder.∼-respʳ-≈
  d_'8764''45'resp'691''45''8776'_116 ::
    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 -> ()) ->
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'691''45''8776'_116 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'691''45''8776'_116 v6
  du_'8764''45'resp'691''45''8776'_116 ::
    T_IsPreorder_70 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'691''45''8776'_116 v0
    = coe du_'8818''45'resp'691''45''8776'_106 (coe v0)
  -- Relation.Binary.Structures.IsPreorder.∼-resp-≈
  d_'8764''45'resp'45''8776'_118 ::
    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 -> ()) ->
    T_IsPreorder_70 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8764''45'resp'45''8776'_118 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'45''8776'_118 v6
  du_'8764''45'resp'45''8776'_118 ::
    T_IsPreorder_70 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8764''45'resp'45''8776'_118 v0
    = coe du_'8818''45'resp'45''8776'_112 (coe v0)
  -- Relation.Binary.Structures.IsTotalPreorder
  d_IsTotalPreorder_124 a0 a1 a2 a3 a4 a5 = ()
  data T_IsTotalPreorder_124
    = C_IsTotalPreorder'46'constructor_8325 T_IsPreorder_70
                                            (AgdaAny ->
                                             AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30)
  -- Relation.Binary.Structures.IsTotalPreorder.isPreorder
  d_isPreorder_132 :: T_IsTotalPreorder_124 -> T_IsPreorder_70
  d_isPreorder_132 v0
    = case coe v0 of
        C_IsTotalPreorder'46'constructor_8325 v1 v2 -> coe v1
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsTotalPreorder.total
  d_total_134 ::
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_total_134 v0
    = case coe v0 of
        C_IsTotalPreorder'46'constructor_8325 v1 v2 -> coe v2
        _                                           -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsTotalPreorder._.isEquivalence
  d_isEquivalence_138 :: T_IsTotalPreorder_124 -> T_IsEquivalence_26
  d_isEquivalence_138 v0
    = coe d_isEquivalence_80 (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.refl
  d_refl_140 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny
  d_refl_140 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_140 v6
  du_refl_140 :: T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny
  du_refl_140 v0 = coe du_refl_98 (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.reflexive
  d_reflexive_142 ::
    T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_reflexive_142 v0
    = coe d_reflexive_82 (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.trans
  d_trans_144 ::
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_144 v0 = coe d_trans_84 (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.∼-resp-≈
  d_'8764''45'resp'45''8776'_146 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8764''45'resp'45''8776'_146 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'45''8776'_146 v6
  du_'8764''45'resp'45''8776'_146 ::
    T_IsTotalPreorder_124 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8764''45'resp'45''8776'_146 v0
    = coe
        du_'8764''45'resp'45''8776'_118 (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.∼-respʳ-≈
  d_'8764''45'resp'691''45''8776'_148 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'691''45''8776'_148 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'691''45''8776'_148 v6
  du_'8764''45'resp'691''45''8776'_148 ::
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'691''45''8776'_148 v0
    = coe
        du_'8764''45'resp'691''45''8776'_116
        (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.∼-respˡ-≈
  d_'8764''45'resp'737''45''8776'_150 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'737''45''8776'_150 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'737''45''8776'_150 v6
  du_'8764''45'resp'737''45''8776'_150 ::
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'737''45''8776'_150 v0
    = coe
        du_'8764''45'resp'737''45''8776'_114
        (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.≲-resp-≈
  d_'8818''45'resp'45''8776'_152 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8818''45'resp'45''8776'_152 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'45''8776'_152 v6
  du_'8818''45'resp'45''8776'_152 ::
    T_IsTotalPreorder_124 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8818''45'resp'45''8776'_152 v0
    = coe
        du_'8818''45'resp'45''8776'_112 (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.≲-respʳ-≈
  d_'8818''45'resp'691''45''8776'_154 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'691''45''8776'_154 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'691''45''8776'_154 v6
  du_'8818''45'resp'691''45''8776'_154 ::
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'691''45''8776'_154 v0
    = coe
        du_'8818''45'resp'691''45''8776'_106
        (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.≲-respˡ-≈
  d_'8818''45'resp'737''45''8776'_156 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'737''45''8776'_156 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'737''45''8776'_156 v6
  du_'8818''45'resp'737''45''8776'_156 ::
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'737''45''8776'_156 v0
    = coe
        du_'8818''45'resp'737''45''8776'_100
        (coe d_isPreorder_132 (coe v0))
  -- Relation.Binary.Structures.IsTotalPreorder._.Eq.isPartialEquivalence
  d_isPartialEquivalence_160 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_160 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_160 v6
  du_isPartialEquivalence_160 ::
    T_IsTotalPreorder_124 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_160 v0
    = let v1 = d_isPreorder_132 (coe v0) in
      coe
        (coe du_isPartialEquivalence_42 (coe d_isEquivalence_80 (coe v1)))
  -- Relation.Binary.Structures.IsTotalPreorder._.Eq.refl
  d_refl_162 :: T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny
  d_refl_162 v0
    = coe
        d_refl_34 (coe d_isEquivalence_80 (coe d_isPreorder_132 (coe v0)))
  -- Relation.Binary.Structures.IsTotalPreorder._.Eq.reflexive
  d_reflexive_164 ::
    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 -> ()) ->
    T_IsTotalPreorder_124 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_164 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_164 v6
  du_reflexive_164 ::
    T_IsTotalPreorder_124 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_164 v0
    = let v1 = d_isPreorder_132 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe du_reflexive_40 (coe d_isEquivalence_80 (coe v1)) v2)
  -- Relation.Binary.Structures.IsTotalPreorder._.Eq.sym
  d_sym_166 ::
    T_IsTotalPreorder_124 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_166 v0
    = coe
        d_sym_36 (coe d_isEquivalence_80 (coe d_isPreorder_132 (coe v0)))
  -- Relation.Binary.Structures.IsTotalPreorder._.Eq.trans
  d_trans_168 ::
    T_IsTotalPreorder_124 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_168 v0
    = coe
        d_trans_38 (coe d_isEquivalence_80 (coe d_isPreorder_132 (coe v0)))
  -- Relation.Binary.Structures.IsPartialOrder
  d_IsPartialOrder_174 a0 a1 a2 a3 a4 a5 = ()
  data T_IsPartialOrder_174
    = C_IsPartialOrder'46'constructor_9853 T_IsPreorder_70
                                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
  -- Relation.Binary.Structures.IsPartialOrder.isPreorder
  d_isPreorder_182 :: T_IsPartialOrder_174 -> T_IsPreorder_70
  d_isPreorder_182 v0
    = case coe v0 of
        C_IsPartialOrder'46'constructor_9853 v1 v2 -> coe v1
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsPartialOrder.antisym
  d_antisym_184 ::
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_antisym_184 v0
    = case coe v0 of
        C_IsPartialOrder'46'constructor_9853 v1 v2 -> coe v2
        _                                          -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsPartialOrder._.isEquivalence
  d_isEquivalence_188 :: T_IsPartialOrder_174 -> T_IsEquivalence_26
  d_isEquivalence_188 v0
    = coe d_isEquivalence_80 (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.refl
  d_refl_190 ::
    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 -> ()) ->
    T_IsPartialOrder_174 -> AgdaAny -> AgdaAny
  d_refl_190 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_190 v6
  du_refl_190 :: T_IsPartialOrder_174 -> AgdaAny -> AgdaAny
  du_refl_190 v0 = coe du_refl_98 (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.reflexive
  d_reflexive_192 ::
    T_IsPartialOrder_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_reflexive_192 v0
    = coe d_reflexive_82 (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.trans
  d_trans_194 ::
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_194 v0 = coe d_trans_84 (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.∼-resp-≈
  d_'8764''45'resp'45''8776'_196 ::
    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 -> ()) ->
    T_IsPartialOrder_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8764''45'resp'45''8776'_196 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'45''8776'_196 v6
  du_'8764''45'resp'45''8776'_196 ::
    T_IsPartialOrder_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8764''45'resp'45''8776'_196 v0
    = coe
        du_'8764''45'resp'45''8776'_118 (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.∼-respʳ-≈
  d_'8764''45'resp'691''45''8776'_198 ::
    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 -> ()) ->
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'691''45''8776'_198 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'691''45''8776'_198 v6
  du_'8764''45'resp'691''45''8776'_198 ::
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'691''45''8776'_198 v0
    = coe
        du_'8764''45'resp'691''45''8776'_116
        (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.∼-respˡ-≈
  d_'8764''45'resp'737''45''8776'_200 ::
    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 -> ()) ->
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'737''45''8776'_200 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'737''45''8776'_200 v6
  du_'8764''45'resp'737''45''8776'_200 ::
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'737''45''8776'_200 v0
    = coe
        du_'8764''45'resp'737''45''8776'_114
        (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.≲-resp-≈
  d_'8818''45'resp'45''8776'_202 ::
    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 -> ()) ->
    T_IsPartialOrder_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8818''45'resp'45''8776'_202 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'45''8776'_202 v6
  du_'8818''45'resp'45''8776'_202 ::
    T_IsPartialOrder_174 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8818''45'resp'45''8776'_202 v0
    = coe
        du_'8818''45'resp'45''8776'_112 (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.≲-respʳ-≈
  d_'8818''45'resp'691''45''8776'_204 ::
    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 -> ()) ->
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'691''45''8776'_204 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'691''45''8776'_204 v6
  du_'8818''45'resp'691''45''8776'_204 ::
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'691''45''8776'_204 v0
    = coe
        du_'8818''45'resp'691''45''8776'_106
        (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.≲-respˡ-≈
  d_'8818''45'resp'737''45''8776'_206 ::
    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 -> ()) ->
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'737''45''8776'_206 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'737''45''8776'_206 v6
  du_'8818''45'resp'737''45''8776'_206 ::
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'737''45''8776'_206 v0
    = coe
        du_'8818''45'resp'737''45''8776'_100
        (coe d_isPreorder_182 (coe v0))
  -- Relation.Binary.Structures.IsPartialOrder._.Eq.isPartialEquivalence
  d_isPartialEquivalence_210 ::
    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 -> ()) ->
    T_IsPartialOrder_174 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_210 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_210 v6
  du_isPartialEquivalence_210 ::
    T_IsPartialOrder_174 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_210 v0
    = let v1 = d_isPreorder_182 (coe v0) in
      coe
        (coe du_isPartialEquivalence_42 (coe d_isEquivalence_80 (coe v1)))
  -- Relation.Binary.Structures.IsPartialOrder._.Eq.refl
  d_refl_212 :: T_IsPartialOrder_174 -> AgdaAny -> AgdaAny
  d_refl_212 v0
    = coe
        d_refl_34 (coe d_isEquivalence_80 (coe d_isPreorder_182 (coe v0)))
  -- Relation.Binary.Structures.IsPartialOrder._.Eq.reflexive
  d_reflexive_214 ::
    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 -> ()) ->
    T_IsPartialOrder_174 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_214 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_214 v6
  du_reflexive_214 ::
    T_IsPartialOrder_174 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_214 v0
    = let v1 = d_isPreorder_182 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe du_reflexive_40 (coe d_isEquivalence_80 (coe v1)) v2)
  -- Relation.Binary.Structures.IsPartialOrder._.Eq.sym
  d_sym_216 ::
    T_IsPartialOrder_174 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_216 v0
    = coe
        d_sym_36 (coe d_isEquivalence_80 (coe d_isPreorder_182 (coe v0)))
  -- Relation.Binary.Structures.IsPartialOrder._.Eq.trans
  d_trans_218 ::
    T_IsPartialOrder_174 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_218 v0
    = coe
        d_trans_38 (coe d_isEquivalence_80 (coe d_isPreorder_182 (coe v0)))
  -- Relation.Binary.Structures.IsDecPartialOrder
  d_IsDecPartialOrder_224 a0 a1 a2 a3 a4 a5 = ()
  data T_IsDecPartialOrder_224
    = C_IsDecPartialOrder'46'constructor_11683 T_IsPartialOrder_174
                                               (AgdaAny ->
                                                AgdaAny ->
                                                MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20)
                                               (AgdaAny ->
                                                AgdaAny ->
                                                MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20)
  -- Relation.Binary.Structures.IsDecPartialOrder.isPartialOrder
  d_isPartialOrder_234 ::
    T_IsDecPartialOrder_224 -> T_IsPartialOrder_174
  d_isPartialOrder_234 v0
    = case coe v0 of
        C_IsDecPartialOrder'46'constructor_11683 v1 v2 v3 -> coe v1
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecPartialOrder._≟_
  d__'8799'__236 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__236 v0
    = case coe v0 of
        C_IsDecPartialOrder'46'constructor_11683 v1 v2 v3 -> coe v2
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecPartialOrder._≤?_
  d__'8804''63'__238 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8804''63'__238 v0
    = case coe v0 of
        C_IsDecPartialOrder'46'constructor_11683 v1 v2 v3 -> coe v3
        _                                                 -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecPartialOrder._.antisym
  d_antisym_242 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_antisym_242 v0
    = coe d_antisym_184 (coe d_isPartialOrder_234 (coe v0))
  -- Relation.Binary.Structures.IsDecPartialOrder._.isEquivalence
  d_isEquivalence_244 ::
    T_IsDecPartialOrder_224 -> T_IsEquivalence_26
  d_isEquivalence_244 v0
    = coe
        d_isEquivalence_80
        (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.isPreorder
  d_isPreorder_246 :: T_IsDecPartialOrder_224 -> T_IsPreorder_70
  d_isPreorder_246 v0
    = coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0))
  -- Relation.Binary.Structures.IsDecPartialOrder._.refl
  d_refl_248 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> AgdaAny -> AgdaAny
  d_refl_248 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_248 v6
  du_refl_248 :: T_IsDecPartialOrder_224 -> AgdaAny -> AgdaAny
  du_refl_248 v0
    = let v1 = d_isPartialOrder_234 (coe v0) in
      coe (coe du_refl_98 (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.reflexive
  d_reflexive_250 ::
    T_IsDecPartialOrder_224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_reflexive_250 v0
    = coe
        d_reflexive_82
        (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.trans
  d_trans_252 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_252 v0
    = coe
        d_trans_84
        (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.∼-resp-≈
  d_'8764''45'resp'45''8776'_254 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8764''45'resp'45''8776'_254 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'45''8776'_254 v6
  du_'8764''45'resp'45''8776'_254 ::
    T_IsDecPartialOrder_224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8764''45'resp'45''8776'_254 v0
    = let v1 = d_isPartialOrder_234 (coe v0) in
      coe
        (coe
           du_'8764''45'resp'45''8776'_118 (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.∼-respʳ-≈
  d_'8764''45'resp'691''45''8776'_256 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'691''45''8776'_256 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'691''45''8776'_256 v6
  du_'8764''45'resp'691''45''8776'_256 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'691''45''8776'_256 v0
    = let v1 = d_isPartialOrder_234 (coe v0) in
      coe
        (coe
           du_'8764''45'resp'691''45''8776'_116
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.∼-respˡ-≈
  d_'8764''45'resp'737''45''8776'_258 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'737''45''8776'_258 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'737''45''8776'_258 v6
  du_'8764''45'resp'737''45''8776'_258 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'737''45''8776'_258 v0
    = let v1 = d_isPartialOrder_234 (coe v0) in
      coe
        (coe
           du_'8764''45'resp'737''45''8776'_114
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.≲-resp-≈
  d_'8818''45'resp'45''8776'_260 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8818''45'resp'45''8776'_260 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'45''8776'_260 v6
  du_'8818''45'resp'45''8776'_260 ::
    T_IsDecPartialOrder_224 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8818''45'resp'45''8776'_260 v0
    = let v1 = d_isPartialOrder_234 (coe v0) in
      coe
        (coe
           du_'8818''45'resp'45''8776'_112 (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.≲-respʳ-≈
  d_'8818''45'resp'691''45''8776'_262 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'691''45''8776'_262 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'691''45''8776'_262 v6
  du_'8818''45'resp'691''45''8776'_262 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'691''45''8776'_262 v0
    = let v1 = d_isPartialOrder_234 (coe v0) in
      coe
        (coe
           du_'8818''45'resp'691''45''8776'_106
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder._.≲-respˡ-≈
  d_'8818''45'resp'737''45''8776'_264 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'737''45''8776'_264 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'737''45''8776'_264 v6
  du_'8818''45'resp'737''45''8776'_264 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'737''45''8776'_264 v0
    = let v1 = d_isPartialOrder_234 (coe v0) in
      coe
        (coe
           du_'8818''45'resp'737''45''8776'_100
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq.isDecEquivalence
  d_isDecEquivalence_268 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> T_IsDecEquivalence_44
  d_isDecEquivalence_268 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecEquivalence_268 v6
  du_isDecEquivalence_268 ::
    T_IsDecPartialOrder_224 -> T_IsDecEquivalence_44
  du_isDecEquivalence_268 v0
    = coe
        C_IsDecEquivalence'46'constructor_3083
        (coe
           d_isEquivalence_80
           (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0))))
        (coe d__'8799'__236 (coe v0))
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq._._≟_
  d__'8799'__272 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__272 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'8799'__272 v6
  du__'8799'__272 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__272 v0 = coe d__'8799'__236 (coe v0)
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq._.isEquivalence
  d_isEquivalence_274 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> T_IsEquivalence_26
  d_isEquivalence_274 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isEquivalence_274 v6
  du_isEquivalence_274 ::
    T_IsDecPartialOrder_224 -> T_IsEquivalence_26
  du_isEquivalence_274 v0
    = coe
        d_isEquivalence_80
        (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0)))
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq._.isPartialEquivalence
  d_isPartialEquivalence_276 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_276 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_276 v6
  du_isPartialEquivalence_276 ::
    T_IsDecPartialOrder_224 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_276 v0
    = let v1 = coe du_isDecEquivalence_268 (coe v0) in
      coe
        (coe du_isPartialEquivalence_42 (coe d_isEquivalence_50 (coe v1)))
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq._.refl
  d_refl_278 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> AgdaAny -> AgdaAny
  d_refl_278 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_278 v6
  du_refl_278 :: T_IsDecPartialOrder_224 -> AgdaAny -> AgdaAny
  du_refl_278 v0
    = coe
        d_refl_34
        (coe
           d_isEquivalence_80
           (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0))))
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq._.reflexive
  d_reflexive_280 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_280 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_280 v6
  du_reflexive_280 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_280 v0
    = let v1 = coe du_isDecEquivalence_268 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe du_reflexive_40 (coe d_isEquivalence_50 (coe v1)) v2)
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq._.sym
  d_sym_282 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_282 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_sym_282 v6
  du_sym_282 ::
    T_IsDecPartialOrder_224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_282 v0
    = coe
        d_sym_36
        (coe
           d_isEquivalence_80
           (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0))))
  -- Relation.Binary.Structures.IsDecPartialOrder.Eq._.trans
  d_trans_284 ::
    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 -> ()) ->
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_284 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_trans_284 v6
  du_trans_284 ::
    T_IsDecPartialOrder_224 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_284 v0
    = coe
        d_trans_38
        (coe
           d_isEquivalence_80
           (coe d_isPreorder_182 (coe d_isPartialOrder_234 (coe v0))))
  -- Relation.Binary.Structures.IsStrictPartialOrder
  d_IsStrictPartialOrder_290 a0 a1 a2 a3 a4 a5 = ()
  data T_IsStrictPartialOrder_290
    = C_IsStrictPartialOrder'46'constructor_14045 T_IsEquivalence_26
                                                  (AgdaAny ->
                                                   AgdaAny ->
                                                   AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
                                                  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  -- Relation.Binary.Structures.IsStrictPartialOrder.isEquivalence
  d_isEquivalence_302 ::
    T_IsStrictPartialOrder_290 -> T_IsEquivalence_26
  d_isEquivalence_302 v0
    = case coe v0 of
        C_IsStrictPartialOrder'46'constructor_14045 v1 v3 v4 -> coe v1
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsStrictPartialOrder.irrefl
  d_irrefl_304 ::
    T_IsStrictPartialOrder_290 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_irrefl_304 = erased
  -- Relation.Binary.Structures.IsStrictPartialOrder.trans
  d_trans_306 ::
    T_IsStrictPartialOrder_290 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_306 v0
    = case coe v0 of
        C_IsStrictPartialOrder'46'constructor_14045 v1 v3 v4 -> coe v3
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsStrictPartialOrder.<-resp-≈
  d_'60''45'resp'45''8776'_308 ::
    T_IsStrictPartialOrder_290 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'45''8776'_308 v0
    = case coe v0 of
        C_IsStrictPartialOrder'46'constructor_14045 v1 v3 v4 -> coe v4
        _                                                    -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsStrictPartialOrder.Eq.isPartialEquivalence
  d_isPartialEquivalence_312 ::
    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 -> ()) ->
    T_IsStrictPartialOrder_290 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_312 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_312 v6
  du_isPartialEquivalence_312 ::
    T_IsStrictPartialOrder_290 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_312 v0
    = coe du_isPartialEquivalence_42 (coe d_isEquivalence_302 (coe v0))
  -- Relation.Binary.Structures.IsStrictPartialOrder.Eq.refl
  d_refl_314 :: T_IsStrictPartialOrder_290 -> AgdaAny -> AgdaAny
  d_refl_314 v0 = coe d_refl_34 (coe d_isEquivalence_302 (coe v0))
  -- Relation.Binary.Structures.IsStrictPartialOrder.Eq.reflexive
  d_reflexive_316 ::
    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 -> ()) ->
    T_IsStrictPartialOrder_290 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_316 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_316 v6
  du_reflexive_316 ::
    T_IsStrictPartialOrder_290 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_316 v0 v1 v2 v3
    = coe du_reflexive_40 (coe d_isEquivalence_302 (coe v0)) v1
  -- Relation.Binary.Structures.IsStrictPartialOrder.Eq.sym
  d_sym_318 ::
    T_IsStrictPartialOrder_290 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_318 v0 = coe d_sym_36 (coe d_isEquivalence_302 (coe v0))
  -- Relation.Binary.Structures.IsStrictPartialOrder.Eq.trans
  d_trans_320 ::
    T_IsStrictPartialOrder_290 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_320 v0 = coe d_trans_38 (coe d_isEquivalence_302 (coe v0))
  -- Relation.Binary.Structures.IsStrictPartialOrder.asym
  d_asym_322 ::
    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 -> ()) ->
    T_IsStrictPartialOrder_290 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_asym_322 = erased
  -- Relation.Binary.Structures.IsStrictPartialOrder.<-respʳ-≈
  d_'60''45'resp'691''45''8776'_328 ::
    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 -> ()) ->
    T_IsStrictPartialOrder_290 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'691''45''8776'_328 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 v8
                                    v9
    = du_'60''45'resp'691''45''8776'_328 v6 v7 v8 v9
  du_'60''45'resp'691''45''8776'_328 ::
    T_IsStrictPartialOrder_290 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'691''45''8776'_328 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
        (d_'60''45'resp'45''8776'_308 (coe v0)) v1 v2 v3
  -- Relation.Binary.Structures.IsStrictPartialOrder.<-respˡ-≈
  d_'60''45'resp'737''45''8776'_330 ::
    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 -> ()) ->
    T_IsStrictPartialOrder_290 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'737''45''8776'_330 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 v7 v8
                                    v9
    = du_'60''45'resp'737''45''8776'_330 v6 v7 v8 v9
  du_'60''45'resp'737''45''8776'_330 ::
    T_IsStrictPartialOrder_290 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'737''45''8776'_330 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
        (d_'60''45'resp'45''8776'_308 (coe v0)) v1 v2 v3
  -- Relation.Binary.Structures.IsDecStrictPartialOrder
  d_IsDecStrictPartialOrder_336 a0 a1 a2 a3 a4 a5 = ()
  data T_IsDecStrictPartialOrder_336
    = C_IsDecStrictPartialOrder'46'constructor_18663 T_IsStrictPartialOrder_290
                                                     (AgdaAny ->
                                                      AgdaAny ->
                                                      MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20)
                                                     (AgdaAny ->
                                                      AgdaAny ->
                                                      MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20)
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.isStrictPartialOrder
  d_isStrictPartialOrder_346 ::
    T_IsDecStrictPartialOrder_336 -> T_IsStrictPartialOrder_290
  d_isStrictPartialOrder_346 v0
    = case coe v0 of
        C_IsDecStrictPartialOrder'46'constructor_18663 v1 v2 v3 -> coe v1
        _                                                       -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecStrictPartialOrder._≟_
  d__'8799'__348 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__348 v0
    = case coe v0 of
        C_IsDecStrictPartialOrder'46'constructor_18663 v1 v2 v3 -> coe v2
        _                                                       -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecStrictPartialOrder._<?_
  d__'60''63'__350 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'60''63'__350 v0
    = case coe v0 of
        C_IsDecStrictPartialOrder'46'constructor_18663 v1 v2 v3 -> coe v3
        _                                                       -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.<-resp-≈
  d_'60''45'resp'45''8776'_354 ::
    T_IsDecStrictPartialOrder_336 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'45''8776'_354 v0
    = coe
        d_'60''45'resp'45''8776'_308
        (coe d_isStrictPartialOrder_346 (coe v0))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.<-respʳ-≈
  d_'60''45'resp'691''45''8776'_356 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'691''45''8776'_356 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'691''45''8776'_356 v6
  du_'60''45'resp'691''45''8776'_356 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'691''45''8776'_356 v0
    = coe
        du_'60''45'resp'691''45''8776'_328
        (coe d_isStrictPartialOrder_346 (coe v0))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.<-respˡ-≈
  d_'60''45'resp'737''45''8776'_358 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'737''45''8776'_358 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'737''45''8776'_358 v6
  du_'60''45'resp'737''45''8776'_358 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'737''45''8776'_358 v0
    = coe
        du_'60''45'resp'737''45''8776'_330
        (coe d_isStrictPartialOrder_346 (coe v0))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.asym
  d_asym_360 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_asym_360 = erased
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.irrefl
  d_irrefl_362 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_irrefl_362 = erased
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.isEquivalence
  d_isEquivalence_364 ::
    T_IsDecStrictPartialOrder_336 -> T_IsEquivalence_26
  d_isEquivalence_364 v0
    = coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.trans
  d_trans_366 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_366 v0
    = coe d_trans_306 (coe d_isStrictPartialOrder_346 (coe v0))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.Eq.isPartialEquivalence
  d_isPartialEquivalence_370 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_370 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_370 v6
  du_isPartialEquivalence_370 ::
    T_IsDecStrictPartialOrder_336 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_370 v0
    = let v1 = d_isStrictPartialOrder_346 (coe v0) in
      coe
        (coe du_isPartialEquivalence_42 (coe d_isEquivalence_302 (coe v1)))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.Eq.refl
  d_refl_372 :: T_IsDecStrictPartialOrder_336 -> AgdaAny -> AgdaAny
  d_refl_372 v0
    = coe
        d_refl_34
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0)))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.Eq.reflexive
  d_reflexive_374 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_374 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_374 v6
  du_reflexive_374 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_374 v0
    = let v1 = d_isStrictPartialOrder_346 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe du_reflexive_40 (coe d_isEquivalence_302 (coe v1)) v2)
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.Eq.sym
  d_sym_376 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_376 v0
    = coe
        d_sym_36
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0)))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.SPO.Eq.trans
  d_trans_378 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_378 v0
    = coe
        d_trans_38
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0)))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq.isDecEquivalence
  d_isDecEquivalence_382 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 -> T_IsDecEquivalence_44
  d_isDecEquivalence_382 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecEquivalence_382 v6
  du_isDecEquivalence_382 ::
    T_IsDecStrictPartialOrder_336 -> T_IsDecEquivalence_44
  du_isDecEquivalence_382 v0
    = coe
        C_IsDecEquivalence'46'constructor_3083
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0)))
        (coe d__'8799'__348 (coe v0))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq._._≟_
  d__'8799'__386 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__386 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'8799'__386 v6
  du__'8799'__386 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__386 v0 = coe d__'8799'__348 (coe v0)
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq._.isEquivalence
  d_isEquivalence_388 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 -> T_IsEquivalence_26
  d_isEquivalence_388 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isEquivalence_388 v6
  du_isEquivalence_388 ::
    T_IsDecStrictPartialOrder_336 -> T_IsEquivalence_26
  du_isEquivalence_388 v0
    = coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq._.isPartialEquivalence
  d_isPartialEquivalence_390 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_390 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_390 v6
  du_isPartialEquivalence_390 ::
    T_IsDecStrictPartialOrder_336 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_390 v0
    = let v1 = coe du_isDecEquivalence_382 (coe v0) in
      coe
        (coe du_isPartialEquivalence_42 (coe d_isEquivalence_50 (coe v1)))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq._.refl
  d_refl_392 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 -> AgdaAny -> AgdaAny
  d_refl_392 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_392 v6
  du_refl_392 :: T_IsDecStrictPartialOrder_336 -> AgdaAny -> AgdaAny
  du_refl_392 v0
    = coe
        d_refl_34
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0)))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq._.reflexive
  d_reflexive_394 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_394 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_394 v6
  du_reflexive_394 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_394 v0
    = let v1 = coe du_isDecEquivalence_382 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe du_reflexive_40 (coe d_isEquivalence_50 (coe v1)) v2)
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq._.sym
  d_sym_396 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_396 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_sym_396 v6
  du_sym_396 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_396 v0
    = coe
        d_sym_36
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0)))
  -- Relation.Binary.Structures.IsDecStrictPartialOrder.Eq._.trans
  d_trans_398 ::
    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 -> ()) ->
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_398 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_trans_398 v6
  du_trans_398 ::
    T_IsDecStrictPartialOrder_336 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_398 v0
    = coe
        d_trans_38
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_346 (coe v0)))
  -- Relation.Binary.Structures.IsTotalOrder
  d_IsTotalOrder_404 a0 a1 a2 a3 a4 a5 = ()
  data T_IsTotalOrder_404
    = C_IsTotalOrder'46'constructor_20555 T_IsPartialOrder_174
                                          (AgdaAny ->
                                           AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30)
  -- Relation.Binary.Structures.IsTotalOrder.isPartialOrder
  d_isPartialOrder_412 :: T_IsTotalOrder_404 -> T_IsPartialOrder_174
  d_isPartialOrder_412 v0
    = case coe v0 of
        C_IsTotalOrder'46'constructor_20555 v1 v2 -> coe v1
        _                                         -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsTotalOrder.total
  d_total_414 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_total_414 v0
    = case coe v0 of
        C_IsTotalOrder'46'constructor_20555 v1 v2 -> coe v2
        _                                         -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsTotalOrder._.antisym
  d_antisym_418 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_antisym_418 v0
    = coe d_antisym_184 (coe d_isPartialOrder_412 (coe v0))
  -- Relation.Binary.Structures.IsTotalOrder._.isEquivalence
  d_isEquivalence_420 :: T_IsTotalOrder_404 -> T_IsEquivalence_26
  d_isEquivalence_420 v0
    = coe
        d_isEquivalence_80
        (coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0)))
  -- Relation.Binary.Structures.IsTotalOrder._.isPreorder
  d_isPreorder_422 :: T_IsTotalOrder_404 -> T_IsPreorder_70
  d_isPreorder_422 v0
    = coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0))
  -- Relation.Binary.Structures.IsTotalOrder._.refl
  d_refl_424 ::
    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 -> ()) ->
    T_IsTotalOrder_404 -> AgdaAny -> AgdaAny
  d_refl_424 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_424 v6
  du_refl_424 :: T_IsTotalOrder_404 -> AgdaAny -> AgdaAny
  du_refl_424 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe (coe du_refl_98 (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsTotalOrder._.reflexive
  d_reflexive_426 ::
    T_IsTotalOrder_404 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_reflexive_426 v0
    = coe
        d_reflexive_82
        (coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0)))
  -- Relation.Binary.Structures.IsTotalOrder._.trans
  d_trans_428 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_428 v0
    = coe
        d_trans_84
        (coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0)))
  -- Relation.Binary.Structures.IsTotalOrder._.∼-resp-≈
  d_'8764''45'resp'45''8776'_430 ::
    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 -> ()) ->
    T_IsTotalOrder_404 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8764''45'resp'45''8776'_430 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'45''8776'_430 v6
  du_'8764''45'resp'45''8776'_430 ::
    T_IsTotalOrder_404 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8764''45'resp'45''8776'_430 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (coe
           du_'8764''45'resp'45''8776'_118 (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsTotalOrder._.∼-respʳ-≈
  d_'8764''45'resp'691''45''8776'_432 ::
    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 -> ()) ->
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'691''45''8776'_432 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'691''45''8776'_432 v6
  du_'8764''45'resp'691''45''8776'_432 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'691''45''8776'_432 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (coe
           du_'8764''45'resp'691''45''8776'_116
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsTotalOrder._.∼-respˡ-≈
  d_'8764''45'resp'737''45''8776'_434 ::
    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 -> ()) ->
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'737''45''8776'_434 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'737''45''8776'_434 v6
  du_'8764''45'resp'737''45''8776'_434 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'737''45''8776'_434 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (coe
           du_'8764''45'resp'737''45''8776'_114
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsTotalOrder._.≲-resp-≈
  d_'8818''45'resp'45''8776'_436 ::
    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 -> ()) ->
    T_IsTotalOrder_404 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8818''45'resp'45''8776'_436 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'45''8776'_436 v6
  du_'8818''45'resp'45''8776'_436 ::
    T_IsTotalOrder_404 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8818''45'resp'45''8776'_436 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (coe
           du_'8818''45'resp'45''8776'_112 (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsTotalOrder._.≲-respʳ-≈
  d_'8818''45'resp'691''45''8776'_438 ::
    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 -> ()) ->
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'691''45''8776'_438 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'691''45''8776'_438 v6
  du_'8818''45'resp'691''45''8776'_438 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'691''45''8776'_438 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (coe
           du_'8818''45'resp'691''45''8776'_106
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsTotalOrder._.≲-respˡ-≈
  d_'8818''45'resp'737''45''8776'_440 ::
    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 -> ()) ->
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'737''45''8776'_440 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'737''45''8776'_440 v6
  du_'8818''45'resp'737''45''8776'_440 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'737''45''8776'_440 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (coe
           du_'8818''45'resp'737''45''8776'_100
           (coe d_isPreorder_182 (coe v1)))
  -- Relation.Binary.Structures.IsTotalOrder._.Eq.isPartialEquivalence
  d_isPartialEquivalence_444 ::
    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 -> ()) ->
    T_IsTotalOrder_404 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_444 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_444 v6
  du_isPartialEquivalence_444 ::
    T_IsTotalOrder_404 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_444 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (let v2 = d_isPreorder_182 (coe v1) in
         coe
           (coe du_isPartialEquivalence_42 (coe d_isEquivalence_80 (coe v2))))
  -- Relation.Binary.Structures.IsTotalOrder._.Eq.refl
  d_refl_446 :: T_IsTotalOrder_404 -> AgdaAny -> AgdaAny
  d_refl_446 v0
    = coe
        d_refl_34
        (coe
           d_isEquivalence_80
           (coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0))))
  -- Relation.Binary.Structures.IsTotalOrder._.Eq.reflexive
  d_reflexive_448 ::
    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 -> ()) ->
    T_IsTotalOrder_404 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_448 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_448 v6
  du_reflexive_448 ::
    T_IsTotalOrder_404 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_448 v0
    = let v1 = d_isPartialOrder_412 (coe v0) in
      coe
        (let v2 = d_isPreorder_182 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe du_reflexive_40 (coe d_isEquivalence_80 (coe v2)) v3))
  -- Relation.Binary.Structures.IsTotalOrder._.Eq.sym
  d_sym_450 ::
    T_IsTotalOrder_404 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_450 v0
    = coe
        d_sym_36
        (coe
           d_isEquivalence_80
           (coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0))))
  -- Relation.Binary.Structures.IsTotalOrder._.Eq.trans
  d_trans_452 ::
    T_IsTotalOrder_404 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_452 v0
    = coe
        d_trans_38
        (coe
           d_isEquivalence_80
           (coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0))))
  -- Relation.Binary.Structures.IsTotalOrder.isTotalPreorder
  d_isTotalPreorder_454 ::
    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 -> ()) ->
    T_IsTotalOrder_404 -> T_IsTotalPreorder_124
  d_isTotalPreorder_454 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isTotalPreorder_454 v6
  du_isTotalPreorder_454 ::
    T_IsTotalOrder_404 -> T_IsTotalPreorder_124
  du_isTotalPreorder_454 v0
    = coe
        C_IsTotalPreorder'46'constructor_8325
        (coe d_isPreorder_182 (coe d_isPartialOrder_412 (coe v0)))
        (coe d_total_414 (coe v0))
  -- Relation.Binary.Structures.IsDecTotalOrder
  d_IsDecTotalOrder_460 a0 a1 a2 a3 a4 a5 = ()
  data T_IsDecTotalOrder_460
    = C_IsDecTotalOrder'46'constructor_22695 T_IsTotalOrder_404
                                             (AgdaAny ->
                                              AgdaAny ->
                                              MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20)
                                             (AgdaAny ->
                                              AgdaAny ->
                                              MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20)
  -- Relation.Binary.Structures.IsDecTotalOrder.isTotalOrder
  d_isTotalOrder_470 :: T_IsDecTotalOrder_460 -> T_IsTotalOrder_404
  d_isTotalOrder_470 v0
    = case coe v0 of
        C_IsDecTotalOrder'46'constructor_22695 v1 v2 v3 -> coe v1
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecTotalOrder._≟_
  d__'8799'__472 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__472 v0
    = case coe v0 of
        C_IsDecTotalOrder'46'constructor_22695 v1 v2 v3 -> coe v2
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecTotalOrder._≤?_
  d__'8804''63'__474 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8804''63'__474 v0
    = case coe v0 of
        C_IsDecTotalOrder'46'constructor_22695 v1 v2 v3 -> coe v3
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDecTotalOrder._.antisym
  d_antisym_478 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_antisym_478 v0
    = coe
        d_antisym_184
        (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0)))
  -- Relation.Binary.Structures.IsDecTotalOrder._.isEquivalence
  d_isEquivalence_480 :: T_IsDecTotalOrder_460 -> T_IsEquivalence_26
  d_isEquivalence_480 v0
    = coe
        d_isEquivalence_80
        (coe
           d_isPreorder_182
           (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.isPartialOrder
  d_isPartialOrder_482 ::
    T_IsDecTotalOrder_460 -> T_IsPartialOrder_174
  d_isPartialOrder_482 v0
    = coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0))
  -- Relation.Binary.Structures.IsDecTotalOrder._.isPreorder
  d_isPreorder_484 :: T_IsDecTotalOrder_460 -> T_IsPreorder_70
  d_isPreorder_484 v0
    = coe
        d_isPreorder_182
        (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0)))
  -- Relation.Binary.Structures.IsDecTotalOrder._.isTotalPreorder
  d_isTotalPreorder_486 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> T_IsTotalPreorder_124
  d_isTotalPreorder_486 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isTotalPreorder_486 v6
  du_isTotalPreorder_486 ::
    T_IsDecTotalOrder_460 -> T_IsTotalPreorder_124
  du_isTotalPreorder_486 v0
    = coe du_isTotalPreorder_454 (coe d_isTotalOrder_470 (coe v0))
  -- Relation.Binary.Structures.IsDecTotalOrder._.refl
  d_refl_488 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> AgdaAny -> AgdaAny
  d_refl_488 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_488 v6
  du_refl_488 :: T_IsDecTotalOrder_460 -> AgdaAny -> AgdaAny
  du_refl_488 v0
    = let v1 = d_isTotalOrder_470 (coe v0) in
      coe
        (let v2 = d_isPartialOrder_412 (coe v1) in
         coe (coe du_refl_98 (coe d_isPreorder_182 (coe v2))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.reflexive
  d_reflexive_490 ::
    T_IsDecTotalOrder_460 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_reflexive_490 v0
    = coe
        d_reflexive_82
        (coe
           d_isPreorder_182
           (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.total
  d_total_492 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_total_492 v0 = coe d_total_414 (coe d_isTotalOrder_470 (coe v0))
  -- Relation.Binary.Structures.IsDecTotalOrder._.trans
  d_trans_494 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_494 v0
    = coe
        d_trans_84
        (coe
           d_isPreorder_182
           (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.∼-resp-≈
  d_'8764''45'resp'45''8776'_496 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8764''45'resp'45''8776'_496 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'45''8776'_496 v6
  du_'8764''45'resp'45''8776'_496 ::
    T_IsDecTotalOrder_460 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8764''45'resp'45''8776'_496 v0
    = let v1 = d_isTotalOrder_470 (coe v0) in
      coe
        (let v2 = d_isPartialOrder_412 (coe v1) in
         coe
           (coe
              du_'8764''45'resp'45''8776'_118 (coe d_isPreorder_182 (coe v2))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.∼-respʳ-≈
  d_'8764''45'resp'691''45''8776'_498 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'691''45''8776'_498 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'691''45''8776'_498 v6
  du_'8764''45'resp'691''45''8776'_498 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'691''45''8776'_498 v0
    = let v1 = d_isTotalOrder_470 (coe v0) in
      coe
        (let v2 = d_isPartialOrder_412 (coe v1) in
         coe
           (coe
              du_'8764''45'resp'691''45''8776'_116
              (coe d_isPreorder_182 (coe v2))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.∼-respˡ-≈
  d_'8764''45'resp'737''45''8776'_500 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8764''45'resp'737''45''8776'_500 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8764''45'resp'737''45''8776'_500 v6
  du_'8764''45'resp'737''45''8776'_500 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8764''45'resp'737''45''8776'_500 v0
    = let v1 = d_isTotalOrder_470 (coe v0) in
      coe
        (let v2 = d_isPartialOrder_412 (coe v1) in
         coe
           (coe
              du_'8764''45'resp'737''45''8776'_114
              (coe d_isPreorder_182 (coe v2))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.≲-resp-≈
  d_'8818''45'resp'45''8776'_502 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8818''45'resp'45''8776'_502 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'45''8776'_502 v6
  du_'8818''45'resp'45''8776'_502 ::
    T_IsDecTotalOrder_460 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8818''45'resp'45''8776'_502 v0
    = let v1 = d_isTotalOrder_470 (coe v0) in
      coe
        (let v2 = d_isPartialOrder_412 (coe v1) in
         coe
           (coe
              du_'8818''45'resp'45''8776'_112 (coe d_isPreorder_182 (coe v2))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.≲-respʳ-≈
  d_'8818''45'resp'691''45''8776'_504 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'691''45''8776'_504 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'691''45''8776'_504 v6
  du_'8818''45'resp'691''45''8776'_504 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'691''45''8776'_504 v0
    = let v1 = d_isTotalOrder_470 (coe v0) in
      coe
        (let v2 = d_isPartialOrder_412 (coe v1) in
         coe
           (coe
              du_'8818''45'resp'691''45''8776'_106
              (coe d_isPreorder_182 (coe v2))))
  -- Relation.Binary.Structures.IsDecTotalOrder._.≲-respˡ-≈
  d_'8818''45'resp'737''45''8776'_506 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8818''45'resp'737''45''8776'_506 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'8818''45'resp'737''45''8776'_506 v6
  du_'8818''45'resp'737''45''8776'_506 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8818''45'resp'737''45''8776'_506 v0
    = let v1 = d_isTotalOrder_470 (coe v0) in
      coe
        (let v2 = d_isPartialOrder_412 (coe v1) in
         coe
           (coe
              du_'8818''45'resp'737''45''8776'_100
              (coe d_isPreorder_182 (coe v2))))
  -- Relation.Binary.Structures.IsDecTotalOrder.isDecPartialOrder
  d_isDecPartialOrder_508 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> T_IsDecPartialOrder_224
  d_isDecPartialOrder_508 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecPartialOrder_508 v6
  du_isDecPartialOrder_508 ::
    T_IsDecTotalOrder_460 -> T_IsDecPartialOrder_224
  du_isDecPartialOrder_508 v0
    = coe
        C_IsDecPartialOrder'46'constructor_11683
        (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0)))
        (coe d__'8799'__472 (coe v0)) (coe d__'8804''63'__474 (coe v0))
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq.isDecEquivalence
  d_isDecEquivalence_512 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> T_IsDecEquivalence_44
  d_isDecEquivalence_512 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecEquivalence_512 v6
  du_isDecEquivalence_512 ::
    T_IsDecTotalOrder_460 -> T_IsDecEquivalence_44
  du_isDecEquivalence_512 v0
    = coe
        C_IsDecEquivalence'46'constructor_3083
        (coe
           d_isEquivalence_80
           (coe
              d_isPreorder_182
              (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0)))))
        (coe d__'8799'__472 (coe v0))
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq._._≟_
  d__'8799'__516 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__516 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'8799'__516 v6
  du__'8799'__516 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__516 v0 = coe d__'8799'__472 (coe v0)
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq._.isEquivalence
  d_isEquivalence_518 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> T_IsEquivalence_26
  d_isEquivalence_518 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isEquivalence_518 v6
  du_isEquivalence_518 :: T_IsDecTotalOrder_460 -> T_IsEquivalence_26
  du_isEquivalence_518 v0
    = coe
        d_isEquivalence_80
        (coe
           d_isPreorder_182
           (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0))))
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq._.isPartialEquivalence
  d_isPartialEquivalence_520 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_520 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_520 v6
  du_isPartialEquivalence_520 ::
    T_IsDecTotalOrder_460 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_520 v0
    = let v1 = coe du_isDecEquivalence_512 (coe v0) in
      coe
        (coe du_isPartialEquivalence_42 (coe d_isEquivalence_50 (coe v1)))
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq._.refl
  d_refl_522 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> AgdaAny -> AgdaAny
  d_refl_522 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_522 v6
  du_refl_522 :: T_IsDecTotalOrder_460 -> AgdaAny -> AgdaAny
  du_refl_522 v0
    = coe
        d_refl_34
        (coe
           d_isEquivalence_80
           (coe
              d_isPreorder_182
              (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0)))))
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq._.reflexive
  d_reflexive_524 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_524 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_524 v6
  du_reflexive_524 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_524 v0
    = let v1 = coe du_isDecEquivalence_512 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe du_reflexive_40 (coe d_isEquivalence_50 (coe v1)) v2)
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq._.sym
  d_sym_526 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_526 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_sym_526 v6
  du_sym_526 ::
    T_IsDecTotalOrder_460 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_526 v0
    = coe
        d_sym_36
        (coe
           d_isEquivalence_80
           (coe
              d_isPreorder_182
              (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0)))))
  -- Relation.Binary.Structures.IsDecTotalOrder.Eq._.trans
  d_trans_528 ::
    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 -> ()) ->
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_528 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_trans_528 v6
  du_trans_528 ::
    T_IsDecTotalOrder_460 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_528 v0
    = coe
        d_trans_38
        (coe
           d_isEquivalence_80
           (coe
              d_isPreorder_182
              (coe d_isPartialOrder_412 (coe d_isTotalOrder_470 (coe v0)))))
  -- Relation.Binary.Structures.IsStrictTotalOrder
  d_IsStrictTotalOrder_534 a0 a1 a2 a3 a4 a5 = ()
  data T_IsStrictTotalOrder_534
    = C_IsStrictTotalOrder'46'constructor_24953 T_IsStrictPartialOrder_290
                                                (AgdaAny ->
                                                 AgdaAny ->
                                                 MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158)
  -- Relation.Binary.Structures.IsStrictTotalOrder.isStrictPartialOrder
  d_isStrictPartialOrder_542 ::
    T_IsStrictTotalOrder_534 -> T_IsStrictPartialOrder_290
  d_isStrictPartialOrder_542 v0
    = case coe v0 of
        C_IsStrictTotalOrder'46'constructor_24953 v1 v2 -> coe v1
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsStrictTotalOrder.compare
  d_compare_544 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158
  d_compare_544 v0
    = case coe v0 of
        C_IsStrictTotalOrder'46'constructor_24953 v1 v2 -> coe v2
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsStrictTotalOrder._.<-resp-≈
  d_'60''45'resp'45''8776'_548 ::
    T_IsStrictTotalOrder_534 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'45''8776'_548 v0
    = coe
        d_'60''45'resp'45''8776'_308
        (coe d_isStrictPartialOrder_542 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder._.<-respʳ-≈
  d_'60''45'resp'691''45''8776'_550 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'691''45''8776'_550 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'691''45''8776'_550 v6
  du_'60''45'resp'691''45''8776'_550 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'691''45''8776'_550 v0
    = coe
        du_'60''45'resp'691''45''8776'_328
        (coe d_isStrictPartialOrder_542 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder._.<-respˡ-≈
  d_'60''45'resp'737''45''8776'_552 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'737''45''8776'_552 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'737''45''8776'_552 v6
  du_'60''45'resp'737''45''8776'_552 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'737''45''8776'_552 v0
    = coe
        du_'60''45'resp'737''45''8776'_330
        (coe d_isStrictPartialOrder_542 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder._.asym
  d_asym_554 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_asym_554 = erased
  -- Relation.Binary.Structures.IsStrictTotalOrder._.irrefl
  d_irrefl_556 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_irrefl_556 = erased
  -- Relation.Binary.Structures.IsStrictTotalOrder._.isEquivalence
  d_isEquivalence_558 ::
    T_IsStrictTotalOrder_534 -> T_IsEquivalence_26
  d_isEquivalence_558 v0
    = coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder._.trans
  d_trans_560 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_560 v0
    = coe d_trans_306 (coe d_isStrictPartialOrder_542 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder._≟_
  d__'8799'__562 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__562 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'8799'__562 v6
  du__'8799'__562 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__562 v0
    = coe
        MAlonzo.Code.Relation.Binary.Consequences.du_tri'8658'dec'8776'_492
        (coe d_compare_544 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder._<?_
  d__'60''63'__564 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'60''63'__564 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'60''63'__564 v6
  du__'60''63'__564 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'60''63'__564 v0
    = coe
        MAlonzo.Code.Relation.Binary.Consequences.du_tri'8658'dec'60'_528
        (coe d_compare_544 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder.isDecStrictPartialOrder
  d_isDecStrictPartialOrder_566 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 -> T_IsDecStrictPartialOrder_336
  d_isDecStrictPartialOrder_566 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecStrictPartialOrder_566 v6
  du_isDecStrictPartialOrder_566 ::
    T_IsStrictTotalOrder_534 -> T_IsDecStrictPartialOrder_336
  du_isDecStrictPartialOrder_566 v0
    = coe
        C_IsDecStrictPartialOrder'46'constructor_18663
        (coe d_isStrictPartialOrder_542 (coe v0))
        (coe du__'8799'__562 (coe v0)) (coe du__'60''63'__564 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq.isDecEquivalence
  d_isDecEquivalence_570 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 -> T_IsDecEquivalence_44
  d_isDecEquivalence_570 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecEquivalence_570 v6
  du_isDecEquivalence_570 ::
    T_IsStrictTotalOrder_534 -> T_IsDecEquivalence_44
  du_isDecEquivalence_570 v0
    = coe
        C_IsDecEquivalence'46'constructor_3083
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v0)))
        (coe du__'8799'__562 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq._._≟_
  d__'8799'__574 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__574 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'8799'__574 v6
  du__'8799'__574 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__574 v0 = coe du__'8799'__562 (coe v0)
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq._.isEquivalence
  d_isEquivalence_576 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 -> T_IsEquivalence_26
  d_isEquivalence_576 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isEquivalence_576 v6
  du_isEquivalence_576 ::
    T_IsStrictTotalOrder_534 -> T_IsEquivalence_26
  du_isEquivalence_576 v0
    = coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v0))
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq._.isPartialEquivalence
  d_isPartialEquivalence_578 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_578 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_578 v6
  du_isPartialEquivalence_578 ::
    T_IsStrictTotalOrder_534 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_578 v0
    = let v1 = coe du_isDecEquivalence_570 (coe v0) in
      coe
        (coe du_isPartialEquivalence_42 (coe d_isEquivalence_50 (coe v1)))
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq._.refl
  d_refl_580 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 -> AgdaAny -> AgdaAny
  d_refl_580 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_580 v6
  du_refl_580 :: T_IsStrictTotalOrder_534 -> AgdaAny -> AgdaAny
  du_refl_580 v0
    = coe
        d_refl_34
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v0)))
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq._.reflexive
  d_reflexive_582 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_582 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_582 v6
  du_reflexive_582 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_582 v0
    = let v1 = coe du_isDecEquivalence_570 (coe v0) in
      coe
        (\ v2 v3 v4 ->
           coe du_reflexive_40 (coe d_isEquivalence_50 (coe v1)) v2)
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq._.sym
  d_sym_584 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_584 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_sym_584 v6
  du_sym_584 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_584 v0
    = coe
        d_sym_36
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v0)))
  -- Relation.Binary.Structures.IsStrictTotalOrder.Eq._.trans
  d_trans_586 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_586 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_trans_586 v6
  du_trans_586 ::
    T_IsStrictTotalOrder_534 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_586 v0
    = coe
        d_trans_38
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v0)))
  -- Relation.Binary.Structures.IsStrictTotalOrder.isDecEquivalence
  d_isDecEquivalence_588 ::
    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 -> ()) ->
    T_IsStrictTotalOrder_534 -> T_IsDecEquivalence_44
  d_isDecEquivalence_588 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecEquivalence_588 v6
  du_isDecEquivalence_588 ::
    T_IsStrictTotalOrder_534 -> T_IsDecEquivalence_44
  du_isDecEquivalence_588 v0
    = coe
        C_IsDecEquivalence'46'constructor_3083
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v0)))
        (coe du__'8799'__562 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder
  d_IsDenseLinearOrder_594 a0 a1 a2 a3 a4 a5 = ()
  data T_IsDenseLinearOrder_594
    = C_IsDenseLinearOrder'46'constructor_28131 T_IsStrictTotalOrder_534
                                                (AgdaAny ->
                                                 AgdaAny ->
                                                 AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
  -- Relation.Binary.Structures.IsDenseLinearOrder.isStrictTotalOrder
  d_isStrictTotalOrder_602 ::
    T_IsDenseLinearOrder_594 -> T_IsStrictTotalOrder_534
  d_isStrictTotalOrder_602 v0
    = case coe v0 of
        C_IsDenseLinearOrder'46'constructor_28131 v1 v2 -> coe v1
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDenseLinearOrder.dense
  d_dense_604 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_dense_604 v0
    = case coe v0 of
        C_IsDenseLinearOrder'46'constructor_28131 v1 v2 -> coe v2
        _                                               -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsDenseLinearOrder._._<?_
  d__'60''63'__608 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'60''63'__608 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'60''63'__608 v6
  du__'60''63'__608 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'60''63'__608 v0
    = coe du__'60''63'__564 (coe d_isStrictTotalOrder_602 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder._._≟_
  d__'8799'__610 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__610 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'8799'__610 v6
  du__'8799'__610 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__610 v0
    = coe du__'8799'__562 (coe d_isStrictTotalOrder_602 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.<-resp-≈
  d_'60''45'resp'45''8776'_612 ::
    T_IsDenseLinearOrder_594 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'45''8776'_612 v0
    = coe
        d_'60''45'resp'45''8776'_308
        (coe
           d_isStrictPartialOrder_542 (coe d_isStrictTotalOrder_602 (coe v0)))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.<-respʳ-≈
  d_'60''45'resp'691''45''8776'_614 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'691''45''8776'_614 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'691''45''8776'_614 v6
  du_'60''45'resp'691''45''8776'_614 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'691''45''8776'_614 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (coe
           du_'60''45'resp'691''45''8776'_328
           (coe d_isStrictPartialOrder_542 (coe v1)))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.<-respˡ-≈
  d_'60''45'resp'737''45''8776'_616 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'60''45'resp'737''45''8776'_616 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_'60''45'resp'737''45''8776'_616 v6
  du_'60''45'resp'737''45''8776'_616 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'60''45'resp'737''45''8776'_616 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (coe
           du_'60''45'resp'737''45''8776'_330
           (coe d_isStrictPartialOrder_542 (coe v1)))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.asym
  d_asym_618 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_asym_618 = erased
  -- Relation.Binary.Structures.IsDenseLinearOrder._.compare
  d_compare_620 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Binary.Definitions.T_Tri_158
  d_compare_620 v0
    = coe d_compare_544 (coe d_isStrictTotalOrder_602 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.irrefl
  d_irrefl_622 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_irrefl_622 = erased
  -- Relation.Binary.Structures.IsDenseLinearOrder._.isDecEquivalence
  d_isDecEquivalence_624 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 -> T_IsDecEquivalence_44
  d_isDecEquivalence_624 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecEquivalence_624 v6
  du_isDecEquivalence_624 ::
    T_IsDenseLinearOrder_594 -> T_IsDecEquivalence_44
  du_isDecEquivalence_624 v0
    = coe
        du_isDecEquivalence_588 (coe d_isStrictTotalOrder_602 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.isDecStrictPartialOrder
  d_isDecStrictPartialOrder_626 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 -> T_IsDecStrictPartialOrder_336
  d_isDecStrictPartialOrder_626 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecStrictPartialOrder_626 v6
  du_isDecStrictPartialOrder_626 ::
    T_IsDenseLinearOrder_594 -> T_IsDecStrictPartialOrder_336
  du_isDecStrictPartialOrder_626 v0
    = coe
        du_isDecStrictPartialOrder_566
        (coe d_isStrictTotalOrder_602 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.isEquivalence
  d_isEquivalence_628 ::
    T_IsDenseLinearOrder_594 -> T_IsEquivalence_26
  d_isEquivalence_628 v0
    = coe
        d_isEquivalence_302
        (coe
           d_isStrictPartialOrder_542 (coe d_isStrictTotalOrder_602 (coe v0)))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.isStrictPartialOrder
  d_isStrictPartialOrder_630 ::
    T_IsDenseLinearOrder_594 -> T_IsStrictPartialOrder_290
  d_isStrictPartialOrder_630 v0
    = coe
        d_isStrictPartialOrder_542 (coe d_isStrictTotalOrder_602 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.trans
  d_trans_632 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_632 v0
    = coe
        d_trans_306
        (coe
           d_isStrictPartialOrder_542 (coe d_isStrictTotalOrder_602 (coe v0)))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq._≟_
  d__'8799'__636 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d__'8799'__636 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du__'8799'__636 v6
  du__'8799'__636 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du__'8799'__636 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe (coe du__'8799'__562 (coe v1))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq.isDecEquivalence
  d_isDecEquivalence_638 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 -> T_IsDecEquivalence_44
  d_isDecEquivalence_638 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isDecEquivalence_638 v6
  du_isDecEquivalence_638 ::
    T_IsDenseLinearOrder_594 -> T_IsDecEquivalence_44
  du_isDecEquivalence_638 v0
    = coe
        du_isDecEquivalence_570 (coe d_isStrictTotalOrder_602 (coe v0))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq.isEquivalence
  d_isEquivalence_640 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 -> T_IsEquivalence_26
  d_isEquivalence_640 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isEquivalence_640 v6
  du_isEquivalence_640 ::
    T_IsDenseLinearOrder_594 -> T_IsEquivalence_26
  du_isEquivalence_640 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (coe d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v1)))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq.isPartialEquivalence
  d_isPartialEquivalence_642 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 -> T_IsPartialEquivalence_16
  d_isPartialEquivalence_642 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6
    = du_isPartialEquivalence_642 v6
  du_isPartialEquivalence_642 ::
    T_IsDenseLinearOrder_594 -> T_IsPartialEquivalence_16
  du_isPartialEquivalence_642 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (let v2 = coe du_isDecEquivalence_570 (coe v1) in
         coe
           (coe du_isPartialEquivalence_42 (coe d_isEquivalence_50 (coe v2))))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq.refl
  d_refl_644 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 -> AgdaAny -> AgdaAny
  d_refl_644 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_refl_644 v6
  du_refl_644 :: T_IsDenseLinearOrder_594 -> AgdaAny -> AgdaAny
  du_refl_644 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (coe
           d_refl_34
           (coe
              d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v1))))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq.reflexive
  d_reflexive_646 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  d_reflexive_646 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_reflexive_646 v6
  du_reflexive_646 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
  du_reflexive_646 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (let v2 = coe du_isDecEquivalence_570 (coe v1) in
         coe
           (\ v3 v4 v5 ->
              coe du_reflexive_40 (coe d_isEquivalence_50 (coe v2)) v3))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq.sym
  d_sym_648 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_648 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_sym_648 v6
  du_sym_648 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sym_648 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (coe
           d_sym_36
           (coe
              d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v1))))
  -- Relation.Binary.Structures.IsDenseLinearOrder._.Eq.trans
  d_trans_650 ::
    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 -> ()) ->
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_650 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5 v6 = du_trans_650 v6
  du_trans_650 ::
    T_IsDenseLinearOrder_594 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_650 v0
    = let v1 = d_isStrictTotalOrder_602 (coe v0) in
      coe
        (coe
           d_trans_38
           (coe
              d_isEquivalence_302 (coe d_isStrictPartialOrder_542 (coe v1))))
  -- Relation.Binary.Structures.IsApartnessRelation
  d_IsApartnessRelation_656 a0 a1 a2 a3 a4 a5 = ()
  data T_IsApartnessRelation_656
    = C_IsApartnessRelation'46'constructor_30225 (AgdaAny ->
                                                  AgdaAny -> AgdaAny -> AgdaAny)
                                                 (AgdaAny ->
                                                  AgdaAny ->
                                                  AgdaAny ->
                                                  AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30)
  -- Relation.Binary.Structures.IsApartnessRelation.irrefl
  d_irrefl_666 ::
    T_IsApartnessRelation_656 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_irrefl_666 = erased
  -- Relation.Binary.Structures.IsApartnessRelation.sym
  d_sym_668 ::
    T_IsApartnessRelation_656 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sym_668 v0
    = case coe v0 of
        C_IsApartnessRelation'46'constructor_30225 v2 v3 -> coe v2
        _                                                -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsApartnessRelation.cotrans
  d_cotrans_670 ::
    T_IsApartnessRelation_656 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_cotrans_670 v0
    = case coe v0 of
        C_IsApartnessRelation'46'constructor_30225 v2 v3 -> coe v3
        _                                                -> MAlonzo.RTE.mazUnreachableError
  -- Relation.Binary.Structures.IsApartnessRelation._¬#_
  d__'172''35'__672 ::
    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 -> ()) ->
    T_IsApartnessRelation_656 -> AgdaAny -> AgdaAny -> ()
  d__'172''35'__672 = erased
  