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.Data.List.Extrema.Core where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Construct.LiftedChoice qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.Base qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.Max qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.Min qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp qualified
  import MAlonzo.Code.Data.Sum.Base qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd qualified
  import MAlonzo.Code.Relation.Binary.Construct.NonStrictToStrict qualified
  import MAlonzo.Code.Relation.Binary.Structures 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
  
  -- Data.List.Extrema.Core._._<_
  d__'60'__96 ::
    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_TotalOrder_764 ->
    AgdaAny -> AgdaAny -> ()
  d__'60'__96 = erased
  -- Data.List.Extrema.Core._._⊓_
  d__'8851'__192 ::
    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_TotalOrder_764 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'8851'__192 ~v0 ~v1 ~v2 v3 = du__'8851'__192 v3
  du__'8851'__192 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du__'8851'__192 v0
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du__'8851'__94
        (coe v0)
  -- Data.List.Extrema.Core.<-transʳ
  d_'60''45'trans'691'_284 ::
    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_TotalOrder_764 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'trans'691'_284 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_'60''45'trans'691'_284 v3 v4 v5 v6
  du_'60''45'trans'691'_284 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'60''45'trans'691'_284 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Relation.Binary.Construct.NonStrictToStrict.du_'8804''45''60''45'trans_274
        (let v4
               = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (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 v4)))))
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_isPartialOrder_412
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isTotalOrder_786 (coe v0))))
        (let v4
               = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
         coe
           (let v5
                  = coe
                      MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v4) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_100
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v5)))))
        (coe v1) (coe v2) (coe v3)
  -- Data.List.Extrema.Core.<-transˡ
  d_'60''45'trans'737'_286 ::
    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_TotalOrder_764 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'60''45'trans'737'_286 ~v0 ~v1 ~v2 v3 v4 v5 v6
    = du_'60''45'trans'737'_286 v3 v4 v5 v6
  du_'60''45'trans'737'_286 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'60''45'trans'737'_286 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Relation.Binary.Construct.NonStrictToStrict.du_'60''45''8804''45'trans_256
        (let v4
               = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
         coe
           (let v5
                  = coe
                      MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v4) in
            coe
              (let v6
                     = coe
                         MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180 (coe v5) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                    (coe
                       MAlonzo.Code.Relation.Binary.Bundles.d_isEquivalence_60
                       (coe v6))))))
        (let v4
               = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (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 v4)))))
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
           (coe
              MAlonzo.Code.Relation.Binary.Structures.d_isPartialOrder_412
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isTotalOrder_786 (coe v0))))
        (let v4
               = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
         coe
           (let v5
                  = coe
                      MAlonzo.Code.Relation.Binary.Bundles.du_preorder_344 (coe v4) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_106
                 (coe
                    MAlonzo.Code.Relation.Binary.Bundles.d_isPreorder_154 (coe v5)))))
        (coe v1) (coe v2) (coe v3)
  -- Data.List.Extrema.Core._.lemma₁
  d_lemma'8321'_302 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_lemma'8321'_302 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6 v7 v8 v9 v10 v11
    = du_lemma'8321'_302 v3 v6 v7 v8 v9 v10 v11
  du_lemma'8321'_302 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_lemma'8321'_302 v0 v1 v2 v3 v4 v5 v6
    = let v7
            = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_trans_84
           (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                 (coe v7)))
           (coe v1 v3) (coe v1 v2) v4
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
                 (coe v0))
              (coe v1 v2) (coe v1 v3) (coe v6))
           v5)
  -- Data.List.Extrema.Core._.lemma₂
  d_lemma'8322'_314 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_lemma'8322'_314 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6 v7 v8 v9 v10 v11
    = du_lemma'8322'_314 v3 v6 v7 v8 v9 v10 v11
  du_lemma'8322'_314 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_lemma'8322'_314 v0 v1 v2 v3 v4 v5 v6
    = let v7
            = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Structures.d_trans_84
           (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                 (coe v7)))
           (coe v1 v2) (coe v1 v3) v4
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
              (coe
                 MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
                 (coe v0))
              (coe v1 v2) (coe v1 v3) (coe v6))
           v5)
  -- Data.List.Extrema.Core._.lemma₃
  d_lemma'8323'_326 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_lemma'8323'_326 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6 v7 v8 v9 v10 v11
    = du_lemma'8323'_326 v3 v6 v7 v8 v9 v10 v11
  du_lemma'8323'_326 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_lemma'8323'_326 v0 v1 v2 v3 v4 v5 v6
    = coe
        du_'60''45'trans'691'_284 v0 (coe v1 v3) (coe v1 v2) v4
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0))
           (coe v1 v2) (coe v1 v3) (coe v6))
        v5
  -- Data.List.Extrema.Core._.lemma₄
  d_lemma'8324'_338 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_lemma'8324'_338 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6 v7 v8 v9 v10 v11
    = du_lemma'8324'_338 v3 v6 v7 v8 v9 v10 v11
  du_lemma'8324'_338 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14 ->
    AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_lemma'8324'_338 v0 v1 v2 v3 v4 v5 v6
    = coe
        du_'60''45'trans'691'_284 v0 (coe v1 v2) (coe v1 v3) v4
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0))
           (coe v1 v2) (coe v1 v3) (coe v6))
        v5
  -- Data.List.Extrema.Core.⊓ᴸ
  d_'8851''7480'_344 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''7480'_344 ~v0 ~v1 ~v2 v3 ~v4 ~v5 = du_'8851''7480'_344 v3
  du_'8851''7480'_344 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''7480'_344 v0
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_Lift_30
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0)))
  -- Data.List.Extrema.Core.⊔ᴸ
  d_'8852''7480'_346 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8852''7480'_346 ~v0 ~v1 ~v2 v3 ~v4 ~v5 = du_'8852''7480'_346 v3
  du_'8852''7480'_346 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8852''7480'_346 v0
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_Lift_30
        (let v1
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                   (coe v0) in
         coe
           (let v2
                  = coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                      (coe v0) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
                 (coe
                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                    (coe v1))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                    (coe v2)))))
  -- Data.List.Extrema.Core.⊓ᴸ-sel
  d_'8851''7480''45'sel_350 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8851''7480''45'sel_350 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6
    = du_'8851''7480''45'sel_350 v3 v6
  du_'8851''7480''45'sel_350 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_'8851''7480''45'sel_350 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_sel'45''8801'_130
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0)))
        (coe v1)
  -- Data.List.Extrema.Core.⊓ᴸ-presᵒ-≤v
  d_'8851''7480''45'pres'7506''45''8804'v_362 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30 -> AgdaAny
  d_'8851''7480''45'pres'7506''45''8804'v_362 ~v0 ~v1 ~v2 v3 ~v4 ~v5
                                              v6 v7
    = du_'8851''7480''45'pres'7506''45''8804'v_362 v3 v6 v7
  du_'8851''7480''45'pres'7506''45''8804'v_362 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30 -> AgdaAny
  du_'8851''7480''45'pres'7506''45''8804'v_362 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7506'_400
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0)))
        (coe v1)
        (coe
           (\ v3 v4 ->
              coe
                du_lemma'8321'_302 (coe v0) (coe v1) (coe v3) (coe v4) (coe v2)))
        (coe
           (\ v3 v4 ->
              coe
                du_lemma'8322'_314 (coe v0) (coe v1) (coe v3) (coe v4) (coe v2)))
  -- Data.List.Extrema.Core.⊓ᴸ-presᵒ-<v
  d_'8851''7480''45'pres'7506''45''60'v_374 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''7480''45'pres'7506''45''60'v_374 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6
                                            v7
    = du_'8851''7480''45'pres'7506''45''60'v_374 v3 v6 v7
  du_'8851''7480''45'pres'7506''45''60'v_374 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''7480''45'pres'7506''45''60'v_374 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7506'_400
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0)))
        (coe v1)
        (coe
           (\ v3 v4 ->
              coe
                du_lemma'8323'_326 (coe v0) (coe v1) (coe v3) (coe v4) (coe v2)))
        (coe
           (\ v3 v4 ->
              coe
                du_lemma'8324'_338 (coe v0) (coe v1) (coe v3) (coe v4) (coe v2)))
  -- Data.List.Extrema.Core.⊓ᴸ-presᵇ-v≤
  d_'8851''7480''45'pres'7495''45'v'8804'_386 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''7480''45'pres'7495''45'v'8804'_386 ~v0 ~v1 ~v2 v3 ~v4 ~v5
                                              v6 ~v7 v8 v9
    = du_'8851''7480''45'pres'7495''45'v'8804'_386 v3 v6 v8 v9
  du_'8851''7480''45'pres'7495''45'v'8804'_386 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''7480''45'pres'7495''45'v'8804'_386 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7495'_520
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0)))
        (coe v1) (coe v2) (coe v3)
  -- Data.List.Extrema.Core.⊓ᴸ-presᵇ-v<
  d_'8851''7480''45'pres'7495''45'v'60'_402 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    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_'8851''7480''45'pres'7495''45'v'60'_402 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6
                                            ~v7 v8 v9
    = du_'8851''7480''45'pres'7495''45'v'60'_402 v3 v6 v8 v9
  du_'8851''7480''45'pres'7495''45'v'60'_402 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> 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_'8851''7480''45'pres'7495''45'v'60'_402 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7495'_520
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0)))
        (coe v1) (coe v2) (coe v3)
  -- Data.List.Extrema.Core.⊓ᴸ-forcesᵇ-v≤
  d_'8851''7480''45'forces'7495''45'v'8804'_418 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''7480''45'forces'7495''45'v'8804'_418 ~v0 ~v1 ~v2 v3 ~v4
                                                ~v5 v6 v7
    = du_'8851''7480''45'forces'7495''45'v'8804'_418 v3 v6 v7
  du_'8851''7480''45'forces'7495''45'v'8804'_418 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''7480''45'forces'7495''45'v'8804'_418 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_forces'7495'_562
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
              (coe v0)))
        (coe v1)
        (coe
           (\ v3 v4 v5 v6 ->
              let v7
                    = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
              coe
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                   (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                         (coe v7)))
                   v2 (coe v1 v3) (coe v1 v4) v5
                   (coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
                      (coe
                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
                         (coe v0))
                      (coe v1 v3) (coe v1 v4) (coe v6)))))
        (coe
           (\ v3 v4 v5 v6 ->
              let v7
                    = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
              coe
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                   (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                         (coe v7)))
                   v2 (coe v1 v4) (coe v1 v3) v5
                   (coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858 (coe v0))
                      (coe
                         MAlonzo.Code.Algebra.Construct.NaturalChoice.Min.du_minOperator_176
                         (coe v0))
                      (coe v1 v3) (coe v1 v4) (coe v6)))))
  -- Data.List.Extrema.Core.⊔ᴸ-sel
  d_'8852''7480''45'sel_434 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8852''7480''45'sel_434 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6
    = du_'8852''7480''45'sel_434 v3 v6
  du_'8852''7480''45'sel_434 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_'8852''7480''45'sel_434 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_sel'45''8801'_130
        (let v2
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                   (coe v0) in
         coe
           (let v3
                  = coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                      (coe v0) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
                 (coe
                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                    (coe v2))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                    (coe v3)))))
        (coe v1)
  -- Data.List.Extrema.Core.⊔ᴸ-presᵒ-v≤
  d_'8852''7480''45'pres'7506''45'v'8804'_446 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30 -> AgdaAny
  d_'8852''7480''45'pres'7506''45'v'8804'_446 ~v0 ~v1 ~v2 v3 ~v4 ~v5
                                              v6 v7
    = du_'8852''7480''45'pres'7506''45'v'8804'_446 v3 v6 v7
  du_'8852''7480''45'pres'7506''45'v'8804'_446 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30 -> AgdaAny
  du_'8852''7480''45'pres'7506''45'v'8804'_446 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7506'_400
        (let v3
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                   (coe v0) in
         coe
           (let v4
                  = coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                      (coe v0) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
                 (coe
                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                    (coe v3))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                    (coe v4)))))
        (coe v1)
        (coe
           (\ v3 v4 v5 v6 ->
              let v7
                    = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
              coe
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                   (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                         (coe v7)))
                   v2 (coe v1 v3) (coe v1 v4) v5
                   (let v8
                          = coe
                              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                              (coe v0) in
                    coe
                      (let v9
                             = coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                                 (coe v0) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
                            (coe
                               MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                               (coe v8))
                            (coe
                               MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                               (coe v9))
                            (coe v1 v3) (coe v1 v4) (coe v6)))))))
        (coe
           (\ v3 v4 v5 v6 ->
              let v7
                    = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
              coe
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                   (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                         (coe v7)))
                   v2 (coe v1 v4) (coe v1 v3) v5
                   (let v8
                          = coe
                              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                              (coe v0) in
                    coe
                      (let v9
                             = coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                                 (coe v0) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
                            (coe
                               MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                               (coe v8))
                            (coe
                               MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                               (coe v9))
                            (coe v1 v3) (coe v1 v4) (coe v6)))))))
  -- Data.List.Extrema.Core.⊔ᴸ-presᵒ-v<
  d_'8852''7480''45'pres'7506''45'v'60'_468 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8852''7480''45'pres'7506''45'v'60'_468 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6
                                            v7
    = du_'8852''7480''45'pres'7506''45'v'60'_468 v3 v6 v7
  du_'8852''7480''45'pres'7506''45'v'60'_468 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny ->
    MAlonzo.Code.Data.Sum.Base.T__'8846'__30 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8852''7480''45'pres'7506''45'v'60'_468 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7506'_400
        (let v3
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                   (coe v0) in
         coe
           (let v4
                  = coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                      (coe v0) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
                 (coe
                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                    (coe v3))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                    (coe v4)))))
        (coe v1)
        (coe
           (\ v3 v4 v5 v6 ->
              coe
                du_'60''45'trans'737'_286 v0 v2 (coe v1 v3) (coe v1 v4) v5
                (let v7
                       = coe
                           MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                           (coe v0) in
                 coe
                   (let v8
                          = coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                              (coe v0) in
                    coe
                      (coe
                         MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
                         (coe
                            MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                            (coe v7))
                         (coe
                            MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                            (coe v8))
                         (coe v1 v3) (coe v1 v4) (coe v6))))))
        (coe
           (\ v3 v4 v5 v6 ->
              coe
                du_'60''45'trans'737'_286 v0 v2 (coe v1 v4) (coe v1 v3) v5
                (let v7
                       = coe
                           MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                           (coe v0) in
                 coe
                   (let v8
                          = coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                              (coe v0) in
                    coe
                      (coe
                         MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
                         (coe
                            MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                            (coe v7))
                         (coe
                            MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                            (coe v8))
                         (coe v1 v3) (coe v1 v4) (coe v6))))))
  -- Data.List.Extrema.Core.⊔ᴸ-presᵇ-≤v
  d_'8852''7480''45'pres'7495''45''8804'v_490 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8852''7480''45'pres'7495''45''8804'v_490 ~v0 ~v1 ~v2 v3 ~v4 ~v5
                                              v6 ~v7 v8 v9
    = du_'8852''7480''45'pres'7495''45''8804'v_490 v3 v6 v8 v9
  du_'8852''7480''45'pres'7495''45''8804'v_490 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8852''7480''45'pres'7495''45''8804'v_490 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7495'_520
        (let v4
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                   (coe v0) in
         coe
           (let v5
                  = coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                      (coe v0) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
                 (coe
                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                    (coe v4))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                    (coe v5)))))
        (coe v1) (coe v2) (coe v3)
  -- Data.List.Extrema.Core.⊔ᴸ-presᵇ-<v
  d_'8852''7480''45'pres'7495''45''60'v_506 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    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_'8852''7480''45'pres'7495''45''60'v_506 ~v0 ~v1 ~v2 v3 ~v4 ~v5 v6
                                            ~v7 v8 v9
    = du_'8852''7480''45'pres'7495''45''60'v_506 v3 v6 v8 v9
  du_'8852''7480''45'pres'7495''45''60'v_506 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> 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_'8852''7480''45'pres'7495''45''60'v_506 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_preserves'7495'_520
        (let v4
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                   (coe v0) in
         coe
           (let v5
                  = coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                      (coe v0) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
                 (coe
                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                    (coe v4))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                    (coe v5)))))
        (coe v1) (coe v2) (coe v3)
  -- Data.List.Extrema.Core.⊔ᴸ-forcesᵇ-≤v
  d_'8852''7480''45'forces'7495''45''8804'v_522 ::
    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_TotalOrder_764 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    () ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8852''7480''45'forces'7495''45''8804'v_522 ~v0 ~v1 ~v2 v3 ~v4
                                                ~v5 v6 v7
    = du_'8852''7480''45'forces'7495''45''8804'v_522 v3 v6 v7
  du_'8852''7480''45'forces'7495''45''8804'v_522 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalOrder_764 ->
    (AgdaAny -> AgdaAny) ->
    AgdaAny ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8852''7480''45'forces'7495''45''8804'v_522 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Construct.LiftedChoice.du_forces'7495'_562
        (let v3
               = coe
                   MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                   (coe v0) in
         coe
           (let v4
                  = coe
                      MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                      (coe v0) in
            coe
              (coe
                 MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
                 (coe
                    MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                    (coe v3))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                    (coe v4)))))
        (coe v1)
        (coe
           (\ v3 v4 v5 v6 ->
              let v7
                    = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
              coe
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                   (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                         (coe v7)))
                   (coe v1 v4) (coe v1 v3) v2
                   (let v8
                          = coe
                              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                              (coe v0) in
                    coe
                      (let v9
                             = coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                                 (coe v0) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
                            (coe
                               MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                               (coe v8))
                            (coe
                               MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                               (coe v9))
                            (coe v1 v3) (coe v1 v4) (coe v6))))
                   v5)))
        (coe
           (\ v3 v4 v5 v6 ->
              let v7
                    = coe MAlonzo.Code.Relation.Binary.Bundles.du_poset_796 (coe v0) in
              coe
                (coe
                   MAlonzo.Code.Relation.Binary.Structures.d_trans_84
                   (MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
                         (coe v7)))
                   (coe v1 v3) (coe v1 v4) v2
                   (let v8
                          = coe
                              MAlonzo.Code.Relation.Binary.Bundles.du_totalPreorder_858
                              (coe v0) in
                    coe
                      (let v9
                             = coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Max.du_maxOperator_186
                                 (coe v0) in
                       coe
                         (coe
                            MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
                            (coe
                               MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
                               (coe v8))
                            (coe
                               MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
                               (coe v9))
                            (coe v1 v3) (coe v1 v4) (coe v6))))
                   v5)))
  