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.Algebra.Construct.NaturalChoice.MaxOp where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Bundles qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.Base qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp qualified
  import MAlonzo.Code.Algebra.Structures 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.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
  
  -- Algebra.Construct.NaturalChoice.MaxOp._._≈_
  d__'8776'__22 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> ()
  d__'8776'__22 = erased
  -- Algebra.Construct.NaturalChoice.MaxOp._._≲_
  d__'8818'__24 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> ()
  d__'8818'__24 = erased
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x≤y⇒x⊓z≤y
  d_x'8804'y'8658'x'8851'z'8804'y_98 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'x'8851'z'8804'y_98 ~v0 ~v1 ~v2 v3 v4
    = du_x'8804'y'8658'x'8851'z'8804'y_98 v3 v4
  du_x'8804'y'8658'x'8851'z'8804'y_98 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8658'x'8851'z'8804'y_98 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x≤y⇒z⊓x≤y
  d_x'8804'y'8658'z'8851'x'8804'y_100 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'z'8851'x'8804'y_100 ~v0 ~v1 ~v2 v3 v4
    = du_x'8804'y'8658'z'8851'x'8804'y_100 v3 v4
  du_x'8804'y'8658'z'8851'x'8804'y_100 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8658'z'8851'x'8804'y_100 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x≤y⊓z⇒x≤y
  d_x'8804'y'8851'z'8658'x'8804'y_102 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'y_102 ~v0 ~v1 ~v2 v3 v4
    = du_x'8804'y'8851'z'8658'x'8804'y_102 v3 v4
  du_x'8804'y'8851'z'8658'x'8804'y_102 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8851'z'8658'x'8804'y_102 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x≤y⊓z⇒x≤z
  d_x'8804'y'8851'z'8658'x'8804'z_104 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'z_104 ~v0 ~v1 ~v2 v3 v4
    = du_x'8804'y'8851'z'8658'x'8804'z_104 v3 v4
  du_x'8804'y'8851'z'8658'x'8804'z_104 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8851'z'8658'x'8804'z_104 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x⊓y≈x⇒x≤y
  d_x'8851'y'8776'x'8658'x'8804'y_106 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'x'8658'x'8804'y_106 ~v0 ~v1 ~v2 v3 v4
    = du_x'8851'y'8776'x'8658'x'8804'y_106 v3 v4
  du_x'8851'y'8776'x'8658'x'8804'y_106 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8776'x'8658'x'8804'y_106 v0 v1
    = 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 v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x⊓y≈y⇒y≤x
  d_x'8851'y'8776'y'8658'y'8804'x_108 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'y'8658'y'8804'x_108 ~v0 ~v1 ~v2 v3 v4
    = du_x'8851'y'8776'y'8658'y'8804'x_108 v3 v4
  du_x'8851'y'8776'y'8658'y'8804'x_108 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8776'y'8658'y'8804'x_108 v0 v1
    = 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 v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x⊓y≤x
  d_x'8851'y'8804'x_110 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'x_110 ~v0 ~v1 ~v2 v3 v4
    = du_x'8851'y'8804'x_110 v3 v4
  du_x'8851'y'8804'x_110 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8804'x_110 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.x⊓y≤y
  d_x'8851'y'8804'y_112 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'y_112 ~v0 ~v1 ~v2 v3 v4
    = du_x'8851'y'8804'y_112 v3 v4
  du_x'8851'y'8804'y_112 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8804'y_112 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-assoc
  d_'8851''45'assoc_114 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'assoc_114 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'assoc_114 v3 v4
  du_'8851''45'assoc_114 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'assoc_114 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'assoc_2944
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-band
  d_'8851''45'band_116 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Band_596
  d_'8851''45'band_116 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'band_116 v3 v4
  du_'8851''45'band_116 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Band_596
  du_'8851''45'band_116 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-comm
  d_'8851''45'comm_118 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'comm_118 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'comm_118 v3 v4
  du_'8851''45'comm_118 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'comm_118 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'comm_2856
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-commutativeSemigroup
  d_'8851''45'commutativeSemigroup_120 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  d_'8851''45'commutativeSemigroup_120 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'commutativeSemigroup_120 v3 v4
  du_'8851''45'commutativeSemigroup_120 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  du_'8851''45'commutativeSemigroup_120 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-cong
  d_'8851''45'cong_122 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong_122 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'cong_122 v3 v4
  du_'8851''45'cong_122 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong_122 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong_2930
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-congʳ
  d_'8851''45'cong'691'_124 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'691'_124 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'cong'691'_124 v3 v4
  du_'8851''45'cong'691'_124 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong'691'_124 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'691'_2920
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-congˡ
  d_'8851''45'cong'737'_126 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'737'_126 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'cong'737'_126 v3 v4
  du_'8851''45'cong'737'_126 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong'737'_126 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'737'_2882
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-glb
  d_'8851''45'glb_128 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'glb_128 ~v0 ~v1 ~v2 v3 v4 = du_'8851''45'glb_128 v3 v4
  du_'8851''45'glb_128 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'glb_128 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-idem
  d_'8851''45'idem_130 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny
  d_'8851''45'idem_130 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'idem_130 v3 v4
  du_'8851''45'idem_130 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny
  du_'8851''45'idem_130 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'idem_2984
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-identity
  d_'8851''45'identity_132 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'identity_132 ~v0 ~v1 ~v2 ~v3 v4 v5 v6
    = du_'8851''45'identity_132 v4 v5 v6
  du_'8851''45'identity_132 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45'identity_132 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
                v0 v1 v3 (coe v2 v3)))
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                v0 v3 v1 (coe v2 v3)))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-identityʳ
  d_'8851''45'identity'691'_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'691'_134 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7
    = du_'8851''45'identity'691'_134 v4 v5 v6 v7
  du_'8851''45'identity'691'_134 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'identity'691'_134 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
        v0 v3 v1 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-identityˡ
  d_'8851''45'identity'737'_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'737'_136 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7
    = du_'8851''45'identity'737'_136 v4 v5 v6 v7
  du_'8851''45'identity'737'_136 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'identity'737'_136 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
        v0 v1 v3 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-isBand
  d_'8851''45'isBand_138 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8851''45'isBand_138 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isBand_138 v3 v4
  du_'8851''45'isBand_138 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_'8851''45'isBand_138 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-isCommutativeSemigroup
  d_'8851''45'isCommutativeSemigroup_140 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'8851''45'isCommutativeSemigroup_140 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isCommutativeSemigroup_140 v3 v4
  du_'8851''45'isCommutativeSemigroup_140 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_'8851''45'isCommutativeSemigroup_140 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-isMagma
  d_'8851''45'isMagma_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8851''45'isMagma_142 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isMagma_142 v3 v4
  du_'8851''45'isMagma_142 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'8851''45'isMagma_142 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-isMonoid
  d_'8851''45'isMonoid_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'8851''45'isMonoid_144 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isMonoid_144 v3 v4
  du_'8851''45'isMonoid_144 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'8851''45'isMonoid_144 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMonoid_3042
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-isSelectiveMagma
  d_'8851''45'isSelectiveMagma_146 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_'8851''45'isSelectiveMagma_146 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isSelectiveMagma_146 v3 v4
  du_'8851''45'isSelectiveMagma_146 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  du_'8851''45'isSelectiveMagma_146 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-isSemigroup
  d_'8851''45'isSemigroup_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8851''45'isSemigroup_148 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'isSemigroup_148 v3 v4
  du_'8851''45'isSemigroup_148 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'8851''45'isSemigroup_148 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-magma
  d_'8851''45'magma_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'8851''45'magma_150 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'magma_150 v3 v4
  du_'8851''45'magma_150 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Magma_68
  du_'8851''45'magma_150 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-mono-≤
  d_'8851''45'mono'45''8804'_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'45''8804'_152 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'mono'45''8804'_152 v3 v4
  du_'8851''45'mono'45''8804'_152 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'45''8804'_152 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-monoid
  d_'8851''45'monoid_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
  d_'8851''45'monoid_154 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'monoid_154 v3 v4
  du_'8851''45'monoid_154 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
  du_'8851''45'monoid_154 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'monoid_3060
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-monoʳ-≤
  d_'8851''45'mono'691''45''8804'_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'691''45''8804'_156 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'mono'691''45''8804'_156 v3 v4
  du_'8851''45'mono'691''45''8804'_156 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'691''45''8804'_156 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-monoˡ-≤
  d_'8851''45'mono'737''45''8804'_158 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'737''45''8804'_158 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'mono'737''45''8804'_158 v3 v4
  du_'8851''45'mono'737''45''8804'_158 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'737''45''8804'_158 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-sel
  d_'8851''45'sel_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8851''45'sel_162 ~v0 ~v1 ~v2 v3 v4 = du_'8851''45'sel_162 v3 v4
  du_'8851''45'sel_162 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_'8851''45'sel_162 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-selectiveMagma
  d_'8851''45'selectiveMagma_164 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  d_'8851''45'selectiveMagma_164 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'selectiveMagma_164 v3 v4
  du_'8851''45'selectiveMagma_164 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  du_'8851''45'selectiveMagma_164 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-semigroup
  d_'8851''45'semigroup_166 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  d_'8851''45'semigroup_166 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'semigroup_166 v3 v4
  du_'8851''45'semigroup_166 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  du_'8851''45'semigroup_166 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-triangulate
  d_'8851''45'triangulate_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'triangulate_168 ~v0 ~v1 ~v2 v3 v4
    = du_'8851''45'triangulate_168 v3 v4
  du_'8851''45'triangulate_168 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'triangulate_168 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'triangulate_3292
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-zero
  d_'8851''45'zero_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'zero_170 ~v0 ~v1 ~v2 ~v3 v4 v5 v6
    = du_'8851''45'zero_170 v4 v5 v6
  du_'8851''45'zero_170 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45'zero_170 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                v0 v1 v3 (coe v2 v3)))
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
                v0 v3 v1 (coe v2 v3)))
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-zeroʳ
  d_'8851''45'zero'691'_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'691'_172 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7
    = du_'8851''45'zero'691'_172 v4 v5 v6 v7
  du_'8851''45'zero'691'_172 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'zero'691'_172 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
        v0 v3 v1 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MaxOp.Min.⊓-zeroˡ
  d_'8851''45'zero'737'_174 ::
    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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'737'_174 ~v0 ~v1 ~v2 ~v3 v4 v5 v6 v7
    = du_'8851''45'zero'737'_174 v4 v5 v6 v7
  du_'8851''45'zero'737'_174 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'zero'737'_174 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
        v0 v1 v3 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MaxOp.mono-≤-distrib-⊔
  d_mono'45''8804''45'distrib'45''8852'_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_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_mono'45''8804''45'distrib'45''8852'_182 ~v0 ~v1 ~v2 v3 v4 v5 v6
                                            v7
    = du_mono'45''8804''45'distrib'45''8852'_182 v3 v4 v5 v6 v7
  du_mono'45''8804''45'distrib'45''8852'_182 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_mono'45''8804''45'distrib'45''8852'_182 v0 v1 v2 v3 v4
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_mono'45''8804''45'distrib'45''8851'_3114
        (coe
           MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd.du_totalPreorder_746
           (coe v0))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.du_MaxOp'8658'MinOp_174
           (coe v1))
        (coe v2) (coe v3) (coe (\ v5 v6 -> coe v4 v6 v5))
  