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.Properties.Poset where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Data.Irrelevant qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Consequences qualified
  import MAlonzo.Code.Relation.Binary.Construct.NonStrictToStrict qualified
  import MAlonzo.Code.Relation.Binary.Properties.Preorder qualified
  import MAlonzo.Code.Relation.Binary.Structures qualified
  import MAlonzo.Code.Relation.Nullary.Decidable.Core qualified
  import MAlonzo.Code.Relation.Nullary.Reflects qualified
  import MAlonzo.RTE (AgdaAny, add64, addInt, coe, eq64, eqInt, erased, geqInt, lt64, ltInt, mul64,
                      mulInt, quot64, quotInt, rem64, remInt, sub64, subInt, word64FromNat,
                      word64ToNat)
  import MAlonzo.RTE qualified
  
  -- Relation.Binary.Properties.Poset._._≳_
  d__'8819'__24 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> ()
  d__'8819'__24 = erased
  -- Relation.Binary.Properties.Poset._._⋦_
  d__'8934'__26 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> ()
  d__'8934'__26 = erased
  -- Relation.Binary.Properties.Poset._.Eq._≉_
  d__'8777'__64 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> ()
  d__'8777'__64 = erased
  -- Relation.Binary.Properties.Poset.PreorderProperties.converse-isPreorder
  d_converse'45'isPreorder_134 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
  d_converse'45'isPreorder_134 ~v0 ~v1 ~v2 v3
    = du_converse'45'isPreorder_134 v3
  du_converse'45'isPreorder_134 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
  du_converse'45'isPreorder_134 v0
    = coe
        MAlonzo.Code.Relation.Binary.Properties.Preorder.du_converse'45'isPreorder_78
        (coe MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v0))
  -- Relation.Binary.Properties.Poset.PreorderProperties.converse-preorder
  d_converse'45'preorder_136 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
  d_converse'45'preorder_136 ~v0 ~v1 ~v2 v3
    = du_converse'45'preorder_136 v3
  du_converse'45'preorder_136 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
  du_converse'45'preorder_136 v0
    = coe
        MAlonzo.Code.Relation.Binary.Properties.Preorder.du_converse'45'preorder_80
        (coe MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v0))
  -- Relation.Binary.Properties.Poset.≥-isPartialOrder
  d_'8805''45'isPartialOrder_142 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
  d_'8805''45'isPartialOrder_142 ~v0 ~v1 ~v2 v3
    = du_'8805''45'isPartialOrder_142 v3
  du_'8805''45'isPartialOrder_142 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
  du_'8805''45'isPartialOrder_142 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsPartialOrder'46'constructor_9853
        (coe
           MAlonzo.Code.Relation.Binary.Properties.Preorder.du_converse'45'isPreorder_78
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v0)))
        (coe
           (\ v1 v2 v3 v4 ->
              coe
                MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
                (MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                   (coe v0))
                v1 v2 v4 v3))
  -- Relation.Binary.Properties.Poset.≥-poset
  d_'8805''45'poset_144 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  d_'8805''45'poset_144 ~v0 ~v1 ~v2 v3 = du_'8805''45'poset_144 v3
  du_'8805''45'poset_144 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  du_'8805''45'poset_144 v0
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_6389
        (coe du_'8805''45'isPartialOrder_142 (coe v0))
  -- Relation.Binary.Properties.Poset._.antisym
  d_antisym_148 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_antisym_148 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_antisym_148 v3 v4 v5 v6 v7
  du_antisym_148 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_antisym_148 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
        (MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
           (coe v0))
        v1 v2 v4 v3
  -- Relation.Binary.Properties.Poset._.refl
  d_refl_150 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny
  d_refl_150 ~v0 ~v1 ~v2 v3 = du_refl_150 v3
  du_refl_150 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny
  du_refl_150 v0
    = let v1 = coe du_'8805''45'poset_144 (coe v0) in
      coe
        (let v2
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v1) in
         coe
           (coe
              MAlonzo.Code.Relation.Binary.Structures.du_refl_98
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v2))))
  -- Relation.Binary.Properties.Poset._.reflexive
  d_reflexive_152 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_reflexive_152 ~v0 ~v1 ~v2 v3 = du_reflexive_152 v3
  du_reflexive_152 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_reflexive_152 v0
    = let v1 = coe du_'8805''45'poset_144 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                 (coe v1))))
  -- Relation.Binary.Properties.Poset._.trans
  d_trans_154 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_trans_154 ~v0 ~v1 ~v2 v3 = du_trans_154 v3
  du_trans_154 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_trans_154 v0
    = let v1 = coe du_'8805''45'poset_144 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_trans_84
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                 (coe v1))))
  -- Relation.Binary.Properties.Poset.≰-respˡ-≈
  d_'8816''45'resp'737''45''8776'_156 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8816''45'resp'737''45''8776'_156 = erased
  -- Relation.Binary.Properties.Poset.≰-respʳ-≈
  d_'8816''45'resp'691''45''8776'_162 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8816''45'resp'691''45''8776'_162 = erased
  -- Relation.Binary.Properties.Poset._<_
  d__'60'__168 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> ()
  d__'60'__168 = erased
  -- Relation.Binary.Properties.Poset.<-isStrictPartialOrder
  d_'60''45'isStrictPartialOrder_170 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_290
  d_'60''45'isStrictPartialOrder_170 ~v0 ~v1 ~v2 v3
    = du_'60''45'isStrictPartialOrder_170 v3
  du_'60''45'isStrictPartialOrder_170 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsStrictPartialOrder_290
  du_'60''45'isStrictPartialOrder_170 v0
    = coe
        MAlonzo.Code.Relation.Binary.Construct.NonStrictToStrict.du_'60''45'isStrictPartialOrder_444
        (coe
           MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336 (coe v0))
  -- Relation.Binary.Properties.Poset.<-strictPartialOrder
  d_'60''45'strictPartialOrder_172 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_556
  d_'60''45'strictPartialOrder_172 ~v0 ~v1 ~v2 v3
    = du_'60''45'strictPartialOrder_172 v3
  du_'60''45'strictPartialOrder_172 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_StrictPartialOrder_556
  du_'60''45'strictPartialOrder_172 v0
    = coe
        MAlonzo.Code.Relation.Binary.Bundles.C_StrictPartialOrder'46'constructor_11097
        (coe du_'60''45'isStrictPartialOrder_170 (coe v0))
  -- Relation.Binary.Properties.Poset._._≮_
  d__'8814'__176 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny -> AgdaAny -> ()
  d__'8814'__176 = erased
  -- Relation.Binary.Properties.Poset._.asym
  d_asym_178 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_asym_178 = erased
  -- Relation.Binary.Properties.Poset._.irrefl
  d_irrefl_180 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_irrefl_180 = erased
  -- Relation.Binary.Properties.Poset._.<-resp-≈
  d_'60''45'resp'45''8776'_182 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'45''8776'_182 ~v0 ~v1 ~v2 v3
    = du_'60''45'resp'45''8776'_182 v3
  du_'60''45'resp'45''8776'_182 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'60''45'resp'45''8776'_182 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_'60''45'resp'45''8776'_308
        (coe du_'60''45'isStrictPartialOrder_170 (coe v0))
  -- Relation.Binary.Properties.Poset._.<-respʳ-≈
  d_'60''45'resp'691''45''8776'_184 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'691''45''8776'_184 ~v0 ~v1 ~v2 v3
    = du_'60''45'resp'691''45''8776'_184 v3
  du_'60''45'resp'691''45''8776'_184 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'60''45'resp'691''45''8776'_184 v0
    = let v1 = coe du_'60''45'strictPartialOrder_172 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.du_'60''45'resp'691''45''8776'_328
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isStrictPartialOrder_578
              (coe v1)))
  -- Relation.Binary.Properties.Poset._.<-respˡ-≈
  d_'60''45'resp'737''45''8776'_186 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'resp'737''45''8776'_186 ~v0 ~v1 ~v2 v3
    = du_'60''45'resp'737''45''8776'_186 v3
  du_'60''45'resp'737''45''8776'_186 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'60''45'resp'737''45''8776'_186 v0
    = let v1 = coe du_'60''45'strictPartialOrder_172 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.du_'60''45'resp'737''45''8776'_330
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isStrictPartialOrder_578
              (coe v1)))
  -- Relation.Binary.Properties.Poset._.trans
  d_trans_188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_trans_188 ~v0 ~v1 ~v2 v3 = du_trans_188 v3
  du_trans_188 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_trans_188 v0
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_trans_306
        (coe du_'60''45'isStrictPartialOrder_170 (coe v0))
  -- Relation.Binary.Properties.Poset.<⇒≉
  d_'60''8658''8777'_194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'60''8658''8777'_194 = erased
  -- Relation.Binary.Properties.Poset.≤∧≉⇒<
  d_'8804''8743''8777''8658''60'_200 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8804''8743''8777''8658''60'_200 ~v0 ~v1 ~v2 ~v3 ~v4 ~v5
    = du_'8804''8743''8777''8658''60'_200
  du_'8804''8743''8777''8658''60'_200 ::
    AgdaAny ->
    (AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20) ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8804''8743''8777''8658''60'_200
    = coe
        MAlonzo.Code.Relation.Binary.Construct.NonStrictToStrict.du_'8804''8743''8777''8658''60'_44
  -- Relation.Binary.Properties.Poset.<⇒≱
  d_'60''8658''8817'_206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'60''8658''8817'_206 = erased
  -- Relation.Binary.Properties.Poset.≤⇒≯
  d_'8804''8658''8815'_212 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Data.Irrelevant.T_Irrelevant_20
  d_'8804''8658''8815'_212 = erased
  -- Relation.Binary.Properties.Poset.≤-dec⇒≈-dec
  d_'8804''45'dec'8658''8776''45'dec_214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  d_'8804''45'dec'8658''8776''45'dec_214 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_'8804''45'dec'8658''8776''45'dec_214 v3 v4 v5 v6
  du_'8804''45'dec'8658''8776''45'dec_214 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20
  du_'8804''45'dec'8658''8776''45'dec_214 v0 v1 v2 v3
    = let v4 = coe v1 v2 v3 in
      coe
        (let v5 = coe v1 v3 v2 in
         coe
           (case coe v4 of
              MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 v6 v7
                -> if coe v6
                     then case coe v7 of
                            MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 v8
                              -> case coe v5 of
                                   MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32 v9 v10
                                     -> if coe v9
                                          then case coe v10 of
                                                 MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22 v11
                                                   -> coe
                                                        MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                        (coe v9)
                                                        (coe
                                                           MAlonzo.Code.Relation.Nullary.Reflects.C_of'696'_22
                                                           (coe
                                                              MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
                                                              (MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                                                                 (coe v0))
                                                              v2 v3 v8 v11))
                                                 _ -> MAlonzo.RTE.mazUnreachableError
                                          else coe
                                                 seq (coe v10)
                                                 (coe
                                                    MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                                                    (coe v9)
                                                    (coe
                                                       MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26))
                                   _ -> MAlonzo.RTE.mazUnreachableError
                            _ -> MAlonzo.RTE.mazUnreachableError
                     else coe
                            seq (coe v7)
                            (coe
                               MAlonzo.Code.Relation.Nullary.Decidable.Core.C__because__32
                               (coe v6)
                               (coe MAlonzo.Code.Relation.Nullary.Reflects.C_of'8319'_26))
              _ -> MAlonzo.RTE.mazUnreachableError))
  -- Relation.Binary.Properties.Poset.≤-dec⇒isDecPartialOrder
  d_'8804''45'dec'8658'isDecPartialOrder_258 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecPartialOrder_224
  d_'8804''45'dec'8658'isDecPartialOrder_258 ~v0 ~v1 ~v2 v3 v4
    = du_'8804''45'dec'8658'isDecPartialOrder_258 v3 v4
  du_'8804''45'dec'8658'isDecPartialOrder_258 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny ->
     AgdaAny ->
     MAlonzo.Code.Relation.Nullary.Decidable.Core.T_Dec_20) ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsDecPartialOrder_224
  du_'8804''45'dec'8658'isDecPartialOrder_258 v0 v1
    = coe
        MAlonzo.Code.Relation.Binary.Structures.C_IsDecPartialOrder'46'constructor_11683
        (coe
           MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336 (coe v0))
        (coe du_'8804''45'dec'8658''8776''45'dec_214 (coe v0) (coe v1))
        (coe v1)
  -- Relation.Binary.Properties.Poset.mono⇒cong
  d_mono'8658'cong_264 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_mono'8658'cong_264 ~v0 ~v1 ~v2 v3 v4
    = du_mono'8658'cong_264 v3 v4
  du_mono'8658'cong_264 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_mono'8658'cong_264 v0 v1
    = coe
        MAlonzo.Code.Relation.Binary.Consequences.du_mono'8658'cong_276
        (let v2
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v0) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (coe v3)))))
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                 (coe v0))))
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
              (coe v0)))
        (coe v1)
  -- Relation.Binary.Properties.Poset.antimono⇒cong
  d_antimono'8658'cong_268 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_antimono'8658'cong_268 ~v0 ~v1 ~v2 v3 v4
    = du_antimono'8658'cong_268 v3 v4
  du_antimono'8658'cong_268 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_antimono'8658'cong_268 v0 v1
    = coe
        MAlonzo.Code.Relation.Binary.Consequences.du_antimono'8658'cong_290
        (let v2
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v0) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v2) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                    (coe v3)))))
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                 (coe v0))))
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
              (coe v0)))
        (coe v1)
  