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.MinMaxOp 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.Bundles.Raw qualified
  import MAlonzo.Code.Algebra.Consequences.Setoid qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.Base qualified
  import MAlonzo.Code.Algebra.Construct.NaturalChoice.MaxOp 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.Function.Base qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Construct.Flip.EqAndOrd qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Double qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Syntax 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
  
  -- Algebra.Construct.NaturalChoice.MinMaxOp._._≈_
  d__'8776'__24 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> ()
  d__'8776'__24 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp._._≲_
  d__'8818'__26 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> ()
  d__'8818'__26 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp._._⊓_
  d__'8851'__90 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d__'8851'__90 ~v0 v1 ~v2 = du__'8851'__90 v1
  du__'8851'__90 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du__'8851'__90 v0
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
        (coe v0)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._._Absorbs_
  d__Absorbs__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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__Absorbs__106 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp._._DistributesOver_
  d__DistributesOver__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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__DistributesOver__108 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp._._DistributesOverʳ_
  d__DistributesOver'691'__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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__DistributesOver'691'__110 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp._._DistributesOverˡ_
  d__DistributesOver'737'__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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d__DistributesOver'737'__112 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.Absorptive
  d_Absorptive_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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Absorptive_118 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.mono-≤-distrib-⊓
  d_mono'45''8804''45'distrib'45''8851'_2948 ::
    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_MinOperator_98 ->
    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''8851'_2948 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_mono'45''8804''45'distrib'45''8851'_2948 v3 v4
  du_mono'45''8804''45'distrib'45''8851'_2948 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_mono'45''8804''45'distrib'45''8851'_2948 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_mono'45''8804''45'distrib'45''8851'_3114
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x≤y⇒x⊓z≤y
  d_x'8804'y'8658'x'8851'z'8804'y_2950 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'x'8851'z'8804'y_2950 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8804'y'8658'x'8851'z'8804'y_2950 v3 v4
  du_x'8804'y'8658'x'8851'z'8804'y_2950 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8658'x'8851'z'8804'y_2950 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'x'8851'z'8804'y_3160
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x≤y⇒z⊓x≤y
  d_x'8804'y'8658'z'8851'x'8804'y_2952 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'z'8851'x'8804'y_2952 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8804'y'8658'z'8851'x'8804'y_2952 v3 v4
  du_x'8804'y'8658'z'8851'x'8804'y_2952 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8658'z'8851'x'8804'y_2952 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8658'z'8851'x'8804'y_3172
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x≤y⊓z⇒x≤y
  d_x'8804'y'8851'z'8658'x'8804'y_2954 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'y_2954 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8804'y'8851'z'8658'x'8804'y_2954 v3 v4
  du_x'8804'y'8851'z'8658'x'8804'y_2954 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8851'z'8658'x'8804'y_2954 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'y_3184
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x≤y⊓z⇒x≤z
  d_x'8804'y'8851'z'8658'x'8804'z_2956 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'z_2956 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8804'y'8851'z'8658'x'8804'z_2956 v3 v4
  du_x'8804'y'8851'z'8658'x'8804'z_2956 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8804'y'8851'z'8658'x'8804'z_2956 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8804'y'8851'z'8658'x'8804'z_3198
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x⊓y≈x⇒x≤y
  d_x'8851'y'8776'x'8658'x'8804'y_2958 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'x'8658'x'8804'y_2958 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8851'y'8776'x'8658'x'8804'y_2958 v3 v4
  du_x'8851'y'8776'x'8658'x'8804'y_2958 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8776'x'8658'x'8804'y_2958 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'x'8658'x'8804'y_3068
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x⊓y≈y⇒y≤x
  d_x'8851'y'8776'y'8658'y'8804'x_2960 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'y'8658'y'8804'x_2960 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8851'y'8776'y'8658'y'8804'x_2960 v3 v4
  du_x'8851'y'8776'y'8658'y'8804'x_2960 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8776'y'8658'y'8804'x_2960 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8776'y'8658'y'8804'x_3100
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x⊓y≤x
  d_x'8851'y'8804'x_2962 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'x_2962 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8851'y'8804'x_2962 v3 v4
  du_x'8851'y'8804'x_2962 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8804'x_2962 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x⊓y≤y
  d_x'8851'y'8804'y_2964 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'y_2964 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_x'8851'y'8804'y_2964 v3 v4
  du_x'8851'y'8804'y_2964 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8804'y_2964 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'y_2834
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-assoc
  d_'8851''45'assoc_2966 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'assoc_2966 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'assoc_2966 v3 v4
  du_'8851''45'assoc_2966 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'assoc_2966 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'assoc_2944
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-band
  d_'8851''45'band_2968 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Band_596
  d_'8851''45'band_2968 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'band_2968 v3 v4
  du_'8851''45'band_2968 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Band_596
  du_'8851''45'band_2968 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'band_3052
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-comm
  d_'8851''45'comm_2970 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'comm_2970 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'comm_2970 v3 v4
  du_'8851''45'comm_2970 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'comm_2970 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'comm_2856
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-commutativeSemigroup
  d_'8851''45'commutativeSemigroup_2972 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  d_'8851''45'commutativeSemigroup_2972 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'commutativeSemigroup_2972 v3 v4
  du_'8851''45'commutativeSemigroup_2972 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  du_'8851''45'commutativeSemigroup_2972 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'commutativeSemigroup_3054
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-cong
  d_'8851''45'cong_2974 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong_2974 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'cong_2974 v3 v4
  du_'8851''45'cong_2974 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong_2974 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong_2930
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-congʳ
  d_'8851''45'cong'691'_2976 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'691'_2976 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'cong'691'_2976 v3 v4
  du_'8851''45'cong'691'_2976 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong'691'_2976 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'691'_2920
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-congˡ
  d_'8851''45'cong'737'_2978 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'737'_2978 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'cong'737'_2978 v3 v4
  du_'8851''45'cong'737'_2978 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'cong'737'_2978 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'737'_2882
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-glb
  d_'8851''45'glb_2980 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'glb_2980 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'glb_2980 v3 v4
  du_'8851''45'glb_2980 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'glb_2980 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'glb_3278
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-idem
  d_'8851''45'idem_2982 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny
  d_'8851''45'idem_2982 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'idem_2982 v3 v4
  du_'8851''45'idem_2982 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny
  du_'8851''45'idem_2982 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'idem_2984
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-identity
  d_'8851''45'identity_2984 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'identity_2984 ~v0 v1 ~v2 v3 v4
    = du_'8851''45'identity_2984 v1 v3 v4
  du_'8851''45'identity_2984 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45'identity_2984 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'8851'y'8776'y_126
                v0 v1 v3 (coe v2 v3)))
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                v0 v3 v1 (coe v2 v3)))
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-identityʳ
  d_'8851''45'identity'691'_2986 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'691'_2986 ~v0 v1 ~v2 v3 v4 v5
    = du_'8851''45'identity'691'_2986 v1 v3 v4 v5
  du_'8851''45'identity'691'_2986 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'identity'691'_2986 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
        v0 v3 v1 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-identityˡ
  d_'8851''45'identity'737'_2988 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'737'_2988 ~v0 v1 ~v2 v3 v4 v5
    = du_'8851''45'identity'737'_2988 v1 v3 v4 v5
  du_'8851''45'identity'737'_2988 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'identity'737'_2988 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
        v0 v1 v3 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-isBand
  d_'8851''45'isBand_2990 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8851''45'isBand_2990 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'isBand_2990 v3 v4
  du_'8851''45'isBand_2990 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_'8851''45'isBand_2990 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isBand_3034
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-isCommutativeSemigroup
  d_'8851''45'isCommutativeSemigroup_2992 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'8851''45'isCommutativeSemigroup_2992 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'isCommutativeSemigroup_2992 v3 v4
  du_'8851''45'isCommutativeSemigroup_2992 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  du_'8851''45'isCommutativeSemigroup_2992 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isCommutativeSemigroup_3036
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-isMagma
  d_'8851''45'isMagma_2994 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8851''45'isMagma_2994 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'isMagma_2994 v3 v4
  du_'8851''45'isMagma_2994 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'8851''45'isMagma_2994 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMagma_3030
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-isMonoid
  d_'8851''45'isMonoid_2996 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'8851''45'isMonoid_2996 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'isMonoid_2996 v3 v4
  du_'8851''45'isMonoid_2996 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  du_'8851''45'isMonoid_2996 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isMonoid_3042
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-isSelectiveMagma
  d_'8851''45'isSelectiveMagma_2998 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_'8851''45'isSelectiveMagma_2998 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'isSelectiveMagma_2998 v3 v4
  du_'8851''45'isSelectiveMagma_2998 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  du_'8851''45'isSelectiveMagma_2998 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSelectiveMagma_3038
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-isSemigroup
  d_'8851''45'isSemigroup_3000 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8851''45'isSemigroup_3000 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'isSemigroup_3000 v3 v4
  du_'8851''45'isSemigroup_3000 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'8851''45'isSemigroup_3000 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'isSemigroup_3032
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-magma
  d_'8851''45'magma_3002 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'8851''45'magma_3002 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'magma_3002 v3 v4
  du_'8851''45'magma_3002 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Magma_68
  du_'8851''45'magma_3002 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'magma_3048
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-mono-≤
  d_'8851''45'mono'45''8804'_3004 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'45''8804'_3004 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'mono'45''8804'_3004 v3 v4
  du_'8851''45'mono'45''8804'_3004 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'45''8804'_3004 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'45''8804'_3206
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-monoid
  d_'8851''45'monoid_3006 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
  d_'8851''45'monoid_3006 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'monoid_3006 v3 v4
  du_'8851''45'monoid_3006 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
  du_'8851''45'monoid_3006 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'monoid_3060
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-monoʳ-≤
  d_'8851''45'mono'691''45''8804'_3008 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'691''45''8804'_3008 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'mono'691''45''8804'_3008 v3 v4
  du_'8851''45'mono'691''45''8804'_3008 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'691''45''8804'_3008 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-monoˡ-≤
  d_'8851''45'mono'737''45''8804'_3010 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'737''45''8804'_3010 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'mono'737''45''8804'_3010 v3 v4
  du_'8851''45'mono'737''45''8804'_3010 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'mono'737''45''8804'_3010 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'737''45''8804'_3256
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-rawMagma
  d_'8851''45'rawMagma_3012 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  d_'8851''45'rawMagma_3012 ~v0 ~v1 ~v2 ~v3 v4 ~v5
    = du_'8851''45'rawMagma_3012 v4
  du_'8851''45'rawMagma_3012 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.Raw.T_RawMagma_36
  du_'8851''45'rawMagma_3012 v0
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'rawMagma_3046
        (coe v0)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-sel
  d_'8851''45'sel_3014 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8851''45'sel_3014 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'sel_3014 v3 v4
  du_'8851''45'sel_3014 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  du_'8851''45'sel_3014 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'sel_2988
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-selectiveMagma
  d_'8851''45'selectiveMagma_3016 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  d_'8851''45'selectiveMagma_3016 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'selectiveMagma_3016 v3 v4
  du_'8851''45'selectiveMagma_3016 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  du_'8851''45'selectiveMagma_3016 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'selectiveMagma_3056
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-semigroup
  d_'8851''45'semigroup_3018 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  d_'8851''45'semigroup_3018 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'semigroup_3018 v3 v4
  du_'8851''45'semigroup_3018 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  du_'8851''45'semigroup_3018 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'semigroup_3050
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-triangulate
  d_'8851''45'triangulate_3020 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'triangulate_3020 ~v0 ~v1 ~v2 v3 v4 ~v5
    = du_'8851''45'triangulate_3020 v3 v4
  du_'8851''45'triangulate_3020 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'triangulate_3020 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'triangulate_3292
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-zero
  d_'8851''45'zero_3022 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'zero_3022 ~v0 v1 ~v2 v3 v4
    = du_'8851''45'zero_3022 v1 v3 v4
  du_'8851''45'zero_3022 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45'zero_3022 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'8851'y'8776'x_120
                v0 v1 v3 (coe v2 v3)))
        (coe
           (\ v3 ->
              coe
                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                v0 v3 v1 (coe v2 v3)))
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-zeroʳ
  d_'8851''45'zero'691'_3024 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'691'_3024 ~v0 v1 ~v2 v3 v4 v5
    = du_'8851''45'zero'691'_3024 v1 v3 v4 v5
  du_'8851''45'zero'691'_3024 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'zero'691'_3024 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
        v0 v3 v1 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.⊓-zeroˡ
  d_'8851''45'zero'737'_3026 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'737'_3026 ~v0 v1 ~v2 v3 v4 v5
    = du_'8851''45'zero'737'_3026 v1 v3 v4 v5
  du_'8851''45'zero'737'_3026 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'zero'737'_3026 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
        v0 v1 v3 (coe v2 v3)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.mono-≤-distrib-⊔
  d_mono'45''8804''45'distrib'45''8852'_3030 ::
    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_MinOperator_98 ->
    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'_3030 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_mono'45''8804''45'distrib'45''8852'_3030 v3 v5
  du_mono'45''8804''45'distrib'45''8852'_3030 ::
    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'_3030 v0 v1
    = coe
        MAlonzo.Code.Algebra.Construct.NaturalChoice.MaxOp.du_mono'45''8804''45'distrib'45''8852'_182
        (coe v0) (coe v1)
  -- Algebra.Construct.NaturalChoice.MinMaxOp._.x⊓y≤x
  d_x'8851'y'8804'x_3032 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'x_3032 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8851'y'8804'x_3032 v3 v5
  du_x'8851'y'8804'x_3032 ::
    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_3032 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.MinMaxOp._.x≤y⇒x⊓z≤y
  d_x'8804'y'8658'x'8851'z'8804'y_3034 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'x'8851'z'8804'y_3034 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8804'y'8658'x'8851'z'8804'y_3034 v3 v5
  du_x'8804'y'8658'x'8851'z'8804'y_3034 ::
    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_3034 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.MinMaxOp._.x≤y⇒z⊓x≤y
  d_x'8804'y'8658'z'8851'x'8804'y_3036 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8658'z'8851'x'8804'y_3036 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8804'y'8658'z'8851'x'8804'y_3036 v3 v5
  du_x'8804'y'8658'z'8851'x'8804'y_3036 ::
    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_3036 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.MinMaxOp._.x⊓y≤y
  d_x'8851'y'8804'y_3038 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'y_3038 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8851'y'8804'y_3038 v3 v5
  du_x'8851'y'8804'y_3038 ::
    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_3038 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.MinMaxOp._.x⊓y≈x⇒x≤y
  d_x'8851'y'8776'x'8658'x'8804'y_3040 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'x'8658'x'8804'y_3040 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8851'y'8776'x'8658'x'8804'y_3040 v3 v5
  du_x'8851'y'8776'x'8658'x'8804'y_3040 ::
    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_3040 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.MinMaxOp._.x⊓y≈y⇒y≤x
  d_x'8851'y'8776'y'8658'y'8804'x_3042 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8776'y'8658'y'8804'x_3042 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8851'y'8776'y'8658'y'8804'x_3042 v3 v5
  du_x'8851'y'8776'y'8658'y'8804'x_3042 ::
    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_3042 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.MinMaxOp._.x≤y⊓z⇒x≤y
  d_x'8804'y'8851'z'8658'x'8804'y_3044 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'y_3044 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8804'y'8851'z'8658'x'8804'y_3044 v3 v5
  du_x'8804'y'8851'z'8658'x'8804'y_3044 ::
    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_3044 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.MinMaxOp._.x≤y⊓z⇒x≤z
  d_x'8804'y'8851'z'8658'x'8804'z_3046 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_x'8804'y'8851'z'8658'x'8804'z_3046 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_x'8804'y'8851'z'8658'x'8804'z_3046 v3 v5
  du_x'8804'y'8851'z'8658'x'8804'z_3046 ::
    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_3046 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.MinMaxOp._.⊓-assoc
  d_'8851''45'assoc_3048 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'assoc_3048 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'assoc_3048 v3 v5
  du_'8851''45'assoc_3048 ::
    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_3048 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.MinMaxOp._.⊓-band
  d_'8851''45'band_3050 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Band_596
  d_'8851''45'band_3050 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'band_3050 v3 v5
  du_'8851''45'band_3050 ::
    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_3050 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.MinMaxOp._.⊓-comm
  d_'8851''45'comm_3052 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'comm_3052 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'comm_3052 v3 v5
  du_'8851''45'comm_3052 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'comm_3052 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.MinMaxOp._.⊓-commutativeSemigroup
  d_'8851''45'commutativeSemigroup_3054 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_CommutativeSemigroup_662
  d_'8851''45'commutativeSemigroup_3054 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'commutativeSemigroup_3054 v3 v5
  du_'8851''45'commutativeSemigroup_3054 ::
    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_3054 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.MinMaxOp._.⊓-cong
  d_'8851''45'cong_3056 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong_3056 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'cong_3056 v3 v5
  du_'8851''45'cong_3056 ::
    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_3056 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.MinMaxOp._.⊓-congʳ
  d_'8851''45'cong'691'_3058 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'691'_3058 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'cong'691'_3058 v3 v5
  du_'8851''45'cong'691'_3058 ::
    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'_3058 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.MinMaxOp._.⊓-congˡ
  d_'8851''45'cong'737'_3060 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'cong'737'_3060 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'cong'737'_3060 v3 v5
  du_'8851''45'cong'737'_3060 ::
    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'_3060 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.MinMaxOp._.⊓-idem
  d_'8851''45'idem_3062 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny
  d_'8851''45'idem_3062 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'idem_3062 v3 v5
  du_'8851''45'idem_3062 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny
  du_'8851''45'idem_3062 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.MinMaxOp._.⊓-identity
  d_'8851''45'identity_3064 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'identity_3064 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6 v7
    = du_'8851''45'identity_3064 v5 v6 v7
  du_'8851''45'identity_3064 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45'identity_3064 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.MinMaxOp._.⊓-identityʳ
  d_'8851''45'identity'691'_3066 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'691'_3066 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6 v7 v8
    = du_'8851''45'identity'691'_3066 v5 v6 v7 v8
  du_'8851''45'identity'691'_3066 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'identity'691'_3066 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.MinMaxOp._.⊓-identityˡ
  d_'8851''45'identity'737'_3068 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'identity'737'_3068 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6 v7 v8
    = du_'8851''45'identity'737'_3068 v5 v6 v7 v8
  du_'8851''45'identity'737'_3068 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'identity'737'_3068 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.MinMaxOp._.⊓-isBand
  d_'8851''45'isBand_3070 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8851''45'isBand_3070 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'isBand_3070 v3 v5
  du_'8851''45'isBand_3070 ::
    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_3070 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.MinMaxOp._.⊓-isCommutativeSemigroup
  d_'8851''45'isCommutativeSemigroup_3072 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemigroup_548
  d_'8851''45'isCommutativeSemigroup_3072 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'isCommutativeSemigroup_3072 v3 v5
  du_'8851''45'isCommutativeSemigroup_3072 ::
    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_3072 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.MinMaxOp._.⊓-isMagma
  d_'8851''45'isMagma_3074 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8851''45'isMagma_3074 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'isMagma_3074 v3 v5
  du_'8851''45'isMagma_3074 ::
    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_3074 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.MinMaxOp._.⊓-isMonoid
  d_'8851''45'isMonoid_3076 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) ->
    MAlonzo.Code.Algebra.Structures.T_IsMonoid_686
  d_'8851''45'isMonoid_3076 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'isMonoid_3076 v3 v5
  du_'8851''45'isMonoid_3076 ::
    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_3076 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.MinMaxOp._.⊓-isSelectiveMagma
  d_'8851''45'isSelectiveMagma_3078 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSelectiveMagma_436
  d_'8851''45'isSelectiveMagma_3078 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'isSelectiveMagma_3078 v3 v5
  du_'8851''45'isSelectiveMagma_3078 ::
    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_3078 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.MinMaxOp._.⊓-isSemigroup
  d_'8851''45'isSemigroup_3080 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8851''45'isSemigroup_3080 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'isSemigroup_3080 v3 v5
  du_'8851''45'isSemigroup_3080 ::
    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_3080 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.MinMaxOp._.⊓-glb
  d_'8851''45'glb_3082 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'glb_3082 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'glb_3082 v3 v5
  du_'8851''45'glb_3082 ::
    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_3082 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.MinMaxOp._.⊓-magma
  d_'8851''45'magma_3084 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Magma_68
  d_'8851''45'magma_3084 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'magma_3084 v3 v5
  du_'8851''45'magma_3084 ::
    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_3084 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.MinMaxOp._.⊓-mono-≤
  d_'8851''45'mono'45''8804'_3086 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'45''8804'_3086 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'mono'45''8804'_3086 v3 v5
  du_'8851''45'mono'45''8804'_3086 ::
    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'_3086 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.MinMaxOp._.⊓-monoid
  d_'8851''45'monoid_3088 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Algebra.Bundles.T_Monoid_882
  d_'8851''45'monoid_3088 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'monoid_3088 v3 v5
  du_'8851''45'monoid_3088 ::
    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_3088 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.MinMaxOp._.⊓-monoʳ-≤
  d_'8851''45'mono'691''45''8804'_3090 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'691''45''8804'_3090 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'mono'691''45''8804'_3090 v3 v5
  du_'8851''45'mono'691''45''8804'_3090 ::
    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'_3090 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.MinMaxOp._.⊓-monoˡ-≤
  d_'8851''45'mono'737''45''8804'_3092 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'mono'737''45''8804'_3092 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'mono'737''45''8804'_3092 v3 v5
  du_'8851''45'mono'737''45''8804'_3092 ::
    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'_3092 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.MinMaxOp._.⊓-sel
  d_'8851''45'sel_3094 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Data.Sum.Base.T__'8846'__30
  d_'8851''45'sel_3094 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'sel_3094 v3 v5
  du_'8851''45'sel_3094 ::
    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_3094 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.MinMaxOp._.⊓-selectiveMagma
  d_'8851''45'selectiveMagma_3096 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_SelectiveMagma_122
  d_'8851''45'selectiveMagma_3096 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'selectiveMagma_3096 v3 v5
  du_'8851''45'selectiveMagma_3096 ::
    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_3096 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.MinMaxOp._.⊓-semigroup
  d_'8851''45'semigroup_3098 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Algebra.Bundles.T_Semigroup_536
  d_'8851''45'semigroup_3098 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'semigroup_3098 v3 v5
  du_'8851''45'semigroup_3098 ::
    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_3098 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.MinMaxOp._.⊓-triangulate
  d_'8851''45'triangulate_3100 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'triangulate_3100 ~v0 ~v1 ~v2 v3 ~v4 v5
    = du_'8851''45'triangulate_3100 v3 v5
  du_'8851''45'triangulate_3100 ::
    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_3100 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.MinMaxOp._.⊓-zero
  d_'8851''45'zero_3102 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'zero_3102 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6 v7
    = du_'8851''45'zero_3102 v5 v6 v7
  du_'8851''45'zero_3102 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny ->
    (AgdaAny -> AgdaAny) -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45'zero_3102 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.MinMaxOp._.⊓-zeroʳ
  d_'8851''45'zero'691'_3104 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'691'_3104 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6 v7 v8
    = du_'8851''45'zero'691'_3104 v5 v6 v7 v8
  du_'8851''45'zero'691'_3104 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'zero'691'_3104 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.MinMaxOp._.⊓-zeroˡ
  d_'8851''45'zero'737'_3106 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  d_'8851''45'zero'737'_3106 ~v0 ~v1 ~v2 ~v3 ~v4 v5 v6 v7 v8
    = du_'8851''45'zero'737'_3106 v5 v6 v7 v8
  du_'8851''45'zero'737'_3106 ::
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
  du_'8851''45'zero'737'_3106 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.MinMaxOp.⊓-distribˡ-⊔
  d_'8851''45'distrib'737''45''8852'_3108 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'distrib'737''45''8852'_3108 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
                                          v8
    = du_'8851''45'distrib'737''45''8852'_3108 v3 v4 v5 v6 v7 v8
  du_'8851''45'distrib'737''45''8852'_3108 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'distrib'737''45''8852'_3108 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v4 v5 in
      coe
        (case coe v6 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v7
             -> let v8
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v8)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v4 v5))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v4)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v5))
                     (let v9
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v9))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v4 v5))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3 v5)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v5))
                           (let v10
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v10))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v10)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v3 v5)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v5))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v5))
                                 (let v11
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v11))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             v1 v3 v4)
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             v1 v3 v5))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
                                    v2
                                    (coe
                                       MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v3)
                                       (\ v11 v12 -> v11) v4 v5)
                                    (coe
                                       MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                       (\ v11 v12 -> v12)
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v3)
                                       v4 v5)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
                                       (coe v0) (coe v1) (coe v3) (coe v4) (coe v5) (coe v7)))))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'737'_2882
                              (coe v0) (coe v1) (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v4 v5)
                              (coe v5)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
                                 v2 v4 v5 v7)))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v7
             -> let v8
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v8)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v4 v5))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v4)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v5))
                     (let v9
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v9))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v4 v5))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3 v4)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v5))
                           (let v10
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v10))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v10)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v3 v4)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v5))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                       v1 v3 v5))
                                 (let v11
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v11))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             v1 v3 v4)
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                             v1 v3 v5))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                                    v2
                                    (coe
                                       MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                       (\ v11 v12 -> v12)
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v3)
                                       v5 v4)
                                    (coe
                                       MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 v3)
                                       (\ v11 v12 -> v11) v5 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'mono'691''45''8804'_3266
                                       (coe v0) (coe v1) (coe v3) (coe v5) (coe v4) (coe v7)))))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'737'_2882
                              (coe v0) (coe v1) (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v4 v5)
                              (coe v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                                 v2 v4 v5 v7)))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊓-distribʳ-⊔
  d_'8851''45'distrib'691''45''8852'_3136 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'distrib'691''45''8852'_3136 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8851''45'distrib'691''45''8852'_3136 v3 v4 v5
  du_'8851''45'distrib'691''45''8852'_3136 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'distrib'691''45''8852'_3136 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'43'distr'737''8658'distr'691'_684
        (coe
           MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0)))
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
           (coe v2))
        (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 v2)))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'comm_2856
           (coe v0) (coe v1))
        (coe
           du_'8851''45'distrib'737''45''8852'_3108 (coe v0) (coe v1)
           (coe v2))
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊓-distrib-⊔
  d_'8851''45'distrib'45''8852'_3138 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45'distrib'45''8852'_3138 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8851''45'distrib'45''8852'_3138 v3 v4 v5
  du_'8851''45'distrib'45''8852'_3138 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45'distrib'45''8852'_3138 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_'8851''45'distrib'737''45''8852'_3108 (coe v0) (coe v1)
           (coe v2))
        (coe
           du_'8851''45'distrib'691''45''8852'_3136 (coe v0) (coe v1)
           (coe v2))
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊔-distribˡ-⊓
  d_'8852''45'distrib'737''45''8851'_3140 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8852''45'distrib'737''45''8851'_3140 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
                                          v8
    = du_'8852''45'distrib'737''45''8851'_3140 v3 v4 v5 v6 v7 v8
  du_'8852''45'distrib'737''45''8851'_3140 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8852''45'distrib'737''45''8851'_3140 v0 v1 v2 v3 v4 v5
    = let v6
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v4 v5 in
      coe
        (case coe v6 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v7
             -> let v8
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v8)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v4 v5))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v3 v4)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v3 v5))
                     (let v9
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v9))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v4 v5))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3 v4)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v5))
                           (let v10
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v10))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v10)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 v3 v4)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v5))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v5))
                                 (let v11
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v11))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                             v2 v3 v4)
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                             v2 v3 v5))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                    v1
                                    (coe
                                       MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                       (\ v11 v12 -> v12)
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2 v3)
                                       v5 v4)
                                    (coe
                                       MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2 v3)
                                       (\ v11 v12 -> v11) v5 v4)
                                    (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 v2))
                                       (coe v3) (coe v5) (coe v4) (coe v7)))))
                           (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 v2))
                              (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v4 v5)
                              (coe v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                 v1 v4 v5 v7)))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v7
             -> let v8
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v8)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v4 v5))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v3 v4)
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v3 v5))
                     (let v9
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v9))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v4 v5))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3 v5)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v5))
                           (let v10
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v10))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v10)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 v3 v5)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v5))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v4)
                                    (coe
                                       MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                       v2 v3 v5))
                                 (let v11
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v11))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                             v2 v3 v4)
                                          (coe
                                             MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                             v2 v3 v5))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                    v1
                                    (coe
                                       MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2 v3)
                                       (\ v11 v12 -> v11) v4 v5)
                                    (coe
                                       MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                                       (\ v11 v12 -> v12)
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2 v3)
                                       v4 v5)
                                    (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 v2))
                                       (coe v3) (coe v4) (coe v5) (coe v7)))))
                           (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 v2))
                              (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v4 v5)
                              (coe v5)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                 v1 v4 v5 v7)))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊔-distribʳ-⊓
  d_'8852''45'distrib'691''45''8851'_3168 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8852''45'distrib'691''45''8851'_3168 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8852''45'distrib'691''45''8851'_3168 v3 v4 v5
  du_'8852''45'distrib'691''45''8851'_3168 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_'8852''45'distrib'691''45''8851'_3168 v0 v1 v2
    = coe
        MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'43'distr'737''8658'distr'691'_684
        (coe
           MAlonzo.Code.Relation.Binary.Bundles.du_setoid_180
           (coe
              MAlonzo.Code.Relation.Binary.Bundles.du_preorder_252 (coe v0)))
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
           (coe v2))
        (MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
           (coe v1))
        (coe
           MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong_2930
           (coe v0) (coe 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 v2)))
        (coe
           du_'8852''45'distrib'737''45''8851'_3140 (coe v0) (coe v1)
           (coe v2))
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊔-distrib-⊓
  d_'8852''45'distrib'45''8851'_3170 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8852''45'distrib'45''8851'_3170 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8852''45'distrib'45''8851'_3170 v3 v4 v5
  du_'8852''45'distrib'45''8851'_3170 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8852''45'distrib'45''8851'_3170 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_'8852''45'distrib'737''45''8851'_3140 (coe v0) (coe v1)
           (coe v2))
        (coe
           du_'8852''45'distrib'691''45''8851'_3168 (coe v0) (coe v1)
           (coe v2))
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊓-absorbs-⊔
  d_'8851''45'absorbs'45''8852'_3172 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8851''45'absorbs'45''8852'_3172 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_'8851''45'absorbs'45''8852'_3172 v3 v4 v5 v6 v7
  du_'8851''45'absorbs'45''8852'_3172 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8851''45'absorbs'45''8852'_3172 v0 v1 v2 v3 v4
    = let v5
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v3 v4 in
      coe
        (case coe v5 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v6
             -> let v7
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v7)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v3 v4))
                     (coe v3)
                     (let v8
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v8))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v4))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3 v4)
                           v3
                           (let v9
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v9))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v3 v4)
                                 v3 v3
                                 (let v10
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v10))
                                       (coe v3)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                    v1 v3 v4 v6)))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'737'_2882
                              (coe v0) (coe v1) (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v4)
                              (coe v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
                                 v2 v3 v4 v6)))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v6
             -> let v7
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v7)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v3 v4))
                     (coe v3)
                     (let v8
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v8))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v4))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              v3 v3)
                           v3
                           (let v9
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v9))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 v3 v3)
                                 v3 v3
                                 (let v10
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v10))
                                       (coe v3)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'idem_2984
                                    (coe v0) (coe v1) (coe v3))))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_'8851''45'cong'737'_2882
                              (coe v0) (coe v1) (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v3 v4)
                              (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                                 v2 v3 v4 v6)))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊔-absorbs-⊓
  d_'8852''45'absorbs'45''8851'_3194 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8852''45'absorbs'45''8851'_3194 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_'8852''45'absorbs'45''8851'_3194 v3 v4 v5 v6 v7
  du_'8852''45'absorbs'45''8851'_3194 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_'8852''45'absorbs'45''8851'_3194 v0 v1 v2 v3 v4
    = let v5
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v3 v4 in
      coe
        (case coe v5 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v6
             -> let v7
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v7)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v4))
                     (coe v3)
                     (let v8
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v8))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v4))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3 v3)
                           v3
                           (let v9
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v9))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 v3 v3)
                                 v3 v3
                                 (let v10
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v10))
                                       (coe v3)))
                                 (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 v2))
                                    (coe v3))))
                           (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 v2))
                              (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v4)
                              (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                 v1 v3 v4 v6)))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v6
             -> let v7
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v7)
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v3 v4))
                     (coe v3)
                     (let v8
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v8))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v4))
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              v3 v4)
                           v3
                           (let v9
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v9))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 v3 v4)
                                 v3 v3
                                 (let v10
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v10))
                                       (coe v3)))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                                    v2 v3 v4 v6)))
                           (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 v2))
                              (coe v3)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v3 v4)
                              (coe v4)
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                 v1 v3 v4 v6)))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊔-⊓-absorptive
  d_'8852''45''8851''45'absorptive_3216 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8852''45''8851''45'absorptive_3216 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8852''45''8851''45'absorptive_3216 v3 v4 v5
  du_'8852''45''8851''45'absorptive_3216 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8852''45''8851''45'absorptive_3216 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_'8852''45'absorbs'45''8851'_3194 (coe v0) (coe v1) (coe v2))
        (coe
           du_'8851''45'absorbs'45''8852'_3172 (coe v0) (coe v1) (coe v2))
  -- Algebra.Construct.NaturalChoice.MinMaxOp.⊓-⊔-absorptive
  d_'8851''45''8852''45'absorptive_3218 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8851''45''8852''45'absorptive_3218 ~v0 ~v1 ~v2 v3 v4 v5
    = du_'8851''45''8852''45'absorptive_3218 v3 v4 v5
  du_'8851''45''8852''45'absorptive_3218 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_'8851''45''8852''45'absorptive_3218 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_'8851''45'absorbs'45''8852'_3172 (coe v0) (coe v1) (coe v2))
        (coe
           du_'8852''45'absorbs'45''8851'_3194 (coe v0) (coe v1) (coe v2))
  -- Algebra.Construct.NaturalChoice.MinMaxOp._≥_
  d__'8805'__3220 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> ()
  d__'8805'__3220 = erased
  -- Algebra.Construct.NaturalChoice.MinMaxOp.antimono-≤-distrib-⊓
  d_antimono'45''8804''45'distrib'45''8851'_3228 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_antimono'45''8804''45'distrib'45''8851'_3228 ~v0 ~v1 ~v2 v3 v4 v5
                                                 v6 v7 v8 v9 v10
    = du_antimono'45''8804''45'distrib'45''8851'_3228
        v3 v4 v5 v6 v7 v8 v9 v10
  du_antimono'45''8804''45'distrib'45''8851'_3228 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_antimono'45''8804''45'distrib'45''8851'_3228 v0 v1 v2 v3 v4 v5
                                                  v6 v7
    = let v8
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v6 v7 in
      coe
        (case coe v8 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v9
             -> let v10
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v10)
                     (coe
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v6 v7))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        (coe v3 v6) (coe v3 v7))
                     (let v11
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v11))
                           (coe
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v6 v7))
                           (coe v3 v6)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              (coe v3 v6) (coe v3 v7))
                           (let v12
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v12))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v12)))
                                 (coe v3 v6)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 (coe v3 v6) (coe v3 v7))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 (coe v3 v6) (coe v3 v7))
                                 (let v13
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v13))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2 (coe v3 v6) (coe v3 v7))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                                    v2 (coe v3 v6) (coe v3 v7) (coe v5 v6 v7 v9))))
                           (coe
                              v4
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v6 v7)
                              v6
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                 v1 v6 v7 v9)))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v9
             -> let v10
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v10)
                     (coe
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                           v6 v7))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                        (coe v3 v6) (coe v3 v7))
                     (let v11
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v11))
                           (coe
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v6 v7))
                           (coe v3 v7)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                              (coe v3 v6) (coe v3 v7))
                           (let v12
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v12))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v12)))
                                 (coe v3 v7)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 (coe v3 v6) (coe v3 v7))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                    v2 (coe v3 v6) (coe v3 v7))
                                 (let v13
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v13))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144
                                          v2 (coe v3 v6) (coe v3 v7))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
                                    v2 (coe v3 v6) (coe v3 v7) (coe v5 v7 v6 v9))))
                           (coe
                              v4
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                                 v6 v7)
                              v7
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                 v1 v6 v7 v9)))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinMaxOp.antimono-≤-distrib-⊔
  d_antimono'45''8804''45'distrib'45''8852'_3274 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_antimono'45''8804''45'distrib'45''8852'_3274 ~v0 ~v1 ~v2 v3 v4 v5
                                                 v6 v7 v8 v9 v10
    = du_antimono'45''8804''45'distrib'45''8852'_3274
        v3 v4 v5 v6 v7 v8 v9 v10
  du_antimono'45''8804''45'distrib'45''8852'_3274 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    (AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_antimono'45''8804''45'distrib'45''8852'_3274 v0 v1 v2 v3 v4 v5
                                                  v6 v7
    = let v8
            = coe
                MAlonzo.Code.Relation.Binary.Structures.d_total_134
                (MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0))
                v6 v7 in
      coe
        (case coe v8 of
           MAlonzo.Code.Data.Sum.Base.C_inj'8321'_38 v9
             -> let v10
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v10)
                     (coe
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v6 v7))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        (coe v3 v6) (coe v3 v7))
                     (let v11
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v11))
                           (coe
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v6 v7))
                           (coe v3 v7)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              (coe v3 v6) (coe v3 v7))
                           (let v12
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v12))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v12)))
                                 (coe v3 v7)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v3 v6) (coe v3 v7))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v3 v6) (coe v3 v7))
                                 (let v13
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v13))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 (coe v3 v6) (coe v3 v7))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8851'y'8776'y_126
                                    v1 (coe v3 v6) (coe v3 v7) (coe v5 v6 v7 v9))))
                           (coe
                              v4
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v6 v7)
                              v7
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8852'y'8776'y_150
                                 v2 v6 v7 v9)))))
           MAlonzo.Code.Data.Sum.Base.C_inj'8322'_42 v9
             -> let v10
                      = coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_equalitySubRelation_152 in
                coe
                  (coe
                     MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__126
                     (coe v10)
                     (coe
                        v3
                        (coe
                           MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                           v6 v7))
                     (coe
                        MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                        (coe v3 v6) (coe v3 v7))
                     (let v11
                            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                (coe
                                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                   (coe v0)) in
                      coe
                        (coe
                           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                           (coe
                              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                              (coe v11))
                           (coe
                              v3
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v6 v7))
                           (coe v3 v6)
                           (coe
                              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                              (coe v3 v6) (coe v3 v7))
                           (let v12
                                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                      (coe
                                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                         (coe v0)) in
                            coe
                              (coe
                                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
                                 (coe
                                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8776''45'go_106
                                    (coe v12))
                                 (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                                       (coe v12)))
                                 (coe v3 v6)
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v3 v6) (coe v3 v7))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                    v1 (coe v3 v6) (coe v3 v7))
                                 (let v13
                                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                            (coe
                                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                               (coe v0)) in
                                  coe
                                    (coe
                                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                                       (coe
                                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                          (coe v13))
                                       (coe
                                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114
                                          v1 (coe v3 v6) (coe v3 v7))))
                                 (coe
                                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8804'y'8658'x'8851'y'8776'x_120
                                    v1 (coe v3 v6) (coe v3 v7) (coe v5 v7 v6 v9))))
                           (coe
                              v4
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                 v6 v7)
                              v6
                              (coe
                                 MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d_x'8805'y'8658'x'8852'y'8776'x_156
                                 v2 v6 v7 v9)))))
           _ -> MAlonzo.RTE.mazUnreachableError)
  -- Algebra.Construct.NaturalChoice.MinMaxOp.x⊓y≤x⊔y
  d_x'8851'y'8804'x'8852'y_3318 ::
    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_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_x'8851'y'8804'x'8852'y_3318 ~v0 ~v1 ~v2 v3 v4 v5 v6 v7
    = du_x'8851'y'8804'x'8852'y_3318 v3 v4 v5 v6 v7
  du_x'8851'y'8804'x'8852'y_3318 ::
    MAlonzo.Code.Relation.Binary.Bundles.T_TotalPreorder_222 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MinOperator_98 ->
    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.T_MaxOperator_128 ->
    AgdaAny -> AgdaAny -> AgdaAny
  du_x'8851'y'8804'x'8852'y_3318 v0 v1 v2 v3 v4
    = let v5
            = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                (coe
                   MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                   (coe v0)) in
      coe
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_start_76
              (coe v5))
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
              v3 v4)
           (coe
              MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
              v3 v4)
           (let v6
                  = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                      (coe
                         MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                         (coe v0)) in
            coe
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8764'_300
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8818''45'go_96
                    (coe v6))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8851'__114 v1
                    v3 v4)
                 v3
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                    v3 v4)
                 (let v7
                        = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                            (coe
                               MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                               (coe v0)) in
                  coe
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8764'_300
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_'8818''45'go_96
                          (coe v7))
                       v3
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                          v3 v4)
                       (coe
                          MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                          v3 v4)
                       (let v8
                              = MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_132
                                  (coe
                                     MAlonzo.Code.Relation.Binary.Bundles.d_isTotalPreorder_244
                                     (coe v0)) in
                        coe
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                             (coe
                                MAlonzo.Code.Relation.Binary.Reasoning.Base.Double.du_stop_116
                                (coe v8))
                             (coe
                                MAlonzo.Code.Algebra.Construct.NaturalChoice.Base.d__'8852'__144 v2
                                v3 v4)))
                       (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 v2))
                          (coe v3) (coe v4))))
                 (coe
                    MAlonzo.Code.Algebra.Construct.NaturalChoice.MinOp.du_x'8851'y'8804'x_2808
                    (coe v0) (coe v1) (coe v3) (coe v4)))))
  