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.Lattice.Properties.DistributiveLattice where
  
  import Data.Text qualified
  import MAlonzo.Code.Agda.Builtin.Sigma qualified
  import MAlonzo.Code.Agda.Primitive qualified
  import MAlonzo.Code.Algebra.Lattice.Bundles qualified
  import MAlonzo.Code.Algebra.Lattice.Properties.Lattice qualified
  import MAlonzo.Code.Algebra.Lattice.Properties.Semilattice qualified
  import MAlonzo.Code.Algebra.Lattice.Structures qualified
  import MAlonzo.Code.Algebra.Structures qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Lattice.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Lattice.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.Lattice.Properties.DistributiveLattice._.IsDistributiveLattice
  d_IsDistributiveLattice_230 a0 a1 a2 a3 a4 = ()
  -- Algebra.Lattice.Properties.DistributiveLattice._.IsDistributiveLattice.isLattice
  d_isLattice_454 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036 ->
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
  d_isLattice_454 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3048 (coe v0)
  -- Algebra.Lattice.Properties.DistributiveLattice._.IsDistributiveLattice.∧-distrib-∨
  d_'8743''45'distrib'45''8744'_478 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8743''45'distrib'45''8744'_478 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3052
        (coe v0)
  -- Algebra.Lattice.Properties.DistributiveLattice._.IsDistributiveLattice.∨-distrib-∧
  d_'8744''45'distrib'45''8743'_496 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_'8744''45'distrib'45''8743'_496 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3050
        (coe v0)
  -- Algebra.Lattice.Properties.DistributiveLattice._.poset
  d_poset_686 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  d_poset_686 ~v0 ~v1 v2 = du_poset_686 v2
  du_poset_686 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  du_poset_686 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_poset_162
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_3194
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-idem
  d_'8743''45'idem_688 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    AgdaAny -> AgdaAny
  d_'8743''45'idem_688 ~v0 ~v1 v2 = du_'8743''45'idem_688 v2
  du_'8743''45'idem_688 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    AgdaAny -> AgdaAny
  du_'8743''45'idem_688 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'idem_3182
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isBand
  d_'8743''45'isBand_690 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8743''45'isBand_690 ~v0 ~v1 v2 = du_'8743''45'isBand_690 v2
  du_'8743''45'isBand_690 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_'8743''45'isBand_690 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isBand_3190
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isMagma
  d_'8743''45'isMagma_692 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8743''45'isMagma_692 ~v0 ~v1 v2 = du_'8743''45'isMagma_692 v2
  du_'8743''45'isMagma_692 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'8743''45'isMagma_692 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isMagma_3186
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isOrderTheoreticJoinSemilattice
  d_'8743''45'isOrderTheoreticJoinSemilattice_694 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  d_'8743''45'isOrderTheoreticJoinSemilattice_694 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticJoinSemilattice_694 v2
  du_'8743''45'isOrderTheoreticJoinSemilattice_694 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  du_'8743''45'isOrderTheoreticJoinSemilattice_694 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_3194
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isOrderTheoreticMeetSemilattice
  d_'8743''45'isOrderTheoreticMeetSemilattice_696 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  d_'8743''45'isOrderTheoreticMeetSemilattice_696 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticMeetSemilattice_696 v2
  du_'8743''45'isOrderTheoreticMeetSemilattice_696 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  du_'8743''45'isOrderTheoreticMeetSemilattice_696 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticMeetSemilattice_176
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_3194
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isSemigroup
  d_'8743''45'isSemigroup_698 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8743''45'isSemigroup_698 ~v0 ~v1 v2
    = du_'8743''45'isSemigroup_698 v2
  du_'8743''45'isSemigroup_698 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'8743''45'isSemigroup_698 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isSemigroup_3188
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isSemilattice
  d_'8743''45'isSemilattice_700 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_'8743''45'isSemilattice_700 ~v0 ~v1 v2
    = du_'8743''45'isSemilattice_700 v2
  du_'8743''45'isSemilattice_700 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_'8743''45'isSemilattice_700 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isSemilattice_3192
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-orderTheoreticJoinSemilattice
  d_'8743''45'orderTheoreticJoinSemilattice_702 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  d_'8743''45'orderTheoreticJoinSemilattice_702 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticJoinSemilattice_702 v2
  du_'8743''45'orderTheoreticJoinSemilattice_702 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  du_'8743''45'orderTheoreticJoinSemilattice_702 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticJoinSemilattice_182
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_3194
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-orderTheoreticMeetSemilattice
  d_'8743''45'orderTheoreticMeetSemilattice_704 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  d_'8743''45'orderTheoreticMeetSemilattice_704 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticMeetSemilattice_704 v2
  du_'8743''45'orderTheoreticMeetSemilattice_704 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  du_'8743''45'orderTheoreticMeetSemilattice_704 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticMeetSemilattice_180
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_3194
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-semilattice
  d_'8743''45'semilattice_706 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  d_'8743''45'semilattice_706 ~v0 ~v1 v2
    = du_'8743''45'semilattice_706 v2
  du_'8743''45'semilattice_706 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  du_'8743''45'semilattice_706 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_3194
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-∨-isLattice
  d_'8743''45''8744''45'isLattice_708 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
  d_'8743''45''8744''45'isLattice_708 ~v0 ~v1 v2
    = du_'8743''45''8744''45'isLattice_708 v2
  du_'8743''45''8744''45'isLattice_708 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
  du_'8743''45''8744''45'isLattice_708 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45''8744''45'isLattice_3230
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-∨-lattice
  d_'8743''45''8744''45'lattice_710 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
  d_'8743''45''8744''45'lattice_710 ~v0 ~v1 v2
    = du_'8743''45''8744''45'lattice_710 v2
  du_'8743''45''8744''45'lattice_710 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
  du_'8743''45''8744''45'lattice_710 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45''8744''45'lattice_3232
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-idem
  d_'8744''45'idem_712 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    AgdaAny -> AgdaAny
  d_'8744''45'idem_712 ~v0 ~v1 v2 = du_'8744''45'idem_712 v2
  du_'8744''45'idem_712 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    AgdaAny -> AgdaAny
  du_'8744''45'idem_712 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'idem_3206
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-isBand
  d_'8744''45'isBand_714 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8744''45'isBand_714 ~v0 ~v1 v2 = du_'8744''45'isBand_714 v2
  du_'8744''45'isBand_714 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_'8744''45'isBand_714 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isBand_3214
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-isMagma
  d_'8744''45'isMagma_716 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8744''45'isMagma_716 ~v0 ~v1 v2 = du_'8744''45'isMagma_716 v2
  du_'8744''45'isMagma_716 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'8744''45'isMagma_716 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isMagma_3210
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isOrderTheoreticJoinSemilattice
  d_'8743''45'isOrderTheoreticJoinSemilattice_718 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  d_'8743''45'isOrderTheoreticJoinSemilattice_718 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticJoinSemilattice_718 v2
  du_'8743''45'isOrderTheoreticJoinSemilattice_718 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  du_'8743''45'isOrderTheoreticJoinSemilattice_718 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_3218
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-isOrderTheoreticMeetSemilattice
  d_'8743''45'isOrderTheoreticMeetSemilattice_720 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  d_'8743''45'isOrderTheoreticMeetSemilattice_720 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticMeetSemilattice_720 v2
  du_'8743''45'isOrderTheoreticMeetSemilattice_720 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  du_'8743''45'isOrderTheoreticMeetSemilattice_720 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticMeetSemilattice_176
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_3218
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-isSemigroup
  d_'8744''45'isSemigroup_722 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8744''45'isSemigroup_722 ~v0 ~v1 v2
    = du_'8744''45'isSemigroup_722 v2
  du_'8744''45'isSemigroup_722 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'8744''45'isSemigroup_722 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isSemigroup_3212
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-isSemilattice
  d_'8744''45'isSemilattice_724 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_'8744''45'isSemilattice_724 ~v0 ~v1 v2
    = du_'8744''45'isSemilattice_724 v2
  du_'8744''45'isSemilattice_724 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_'8744''45'isSemilattice_724 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isSemilattice_3216
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-orderTheoreticJoinSemilattice
  d_'8743''45'orderTheoreticJoinSemilattice_726 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  d_'8743''45'orderTheoreticJoinSemilattice_726 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticJoinSemilattice_726 v2
  du_'8743''45'orderTheoreticJoinSemilattice_726 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  du_'8743''45'orderTheoreticJoinSemilattice_726 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticJoinSemilattice_182
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_3218
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∧-orderTheoreticMeetSemilattice
  d_'8743''45'orderTheoreticMeetSemilattice_728 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  d_'8743''45'orderTheoreticMeetSemilattice_728 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticMeetSemilattice_728 v2
  du_'8743''45'orderTheoreticMeetSemilattice_728 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  du_'8743''45'orderTheoreticMeetSemilattice_728 v0
    = let v1
            = coe
                MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0) in
      coe
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticMeetSemilattice_180
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_3218
              (coe v1)))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-semilattice
  d_'8744''45'semilattice_730 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  d_'8744''45'semilattice_730 ~v0 ~v1 v2
    = du_'8744''45'semilattice_730 v2
  du_'8744''45'semilattice_730 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  du_'8744''45'semilattice_730 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_3218
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-∧-isOrderTheoreticLattice
  d_'8744''45''8743''45'isOrderTheoreticLattice_732 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsLattice_340
  d_'8744''45''8743''45'isOrderTheoreticLattice_732 ~v0 ~v1 v2
    = du_'8744''45''8743''45'isOrderTheoreticLattice_732 v2
  du_'8744''45''8743''45'isOrderTheoreticLattice_732 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsLattice_340
  du_'8744''45''8743''45'isOrderTheoreticLattice_732 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45''8743''45'isOrderTheoreticLattice_3244
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice._.∨-∧-orderTheoreticLattice
  d_'8744''45''8743''45'orderTheoreticLattice_734 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_Lattice_386
  d_'8744''45''8743''45'orderTheoreticLattice_734 ~v0 ~v1 v2
    = du_'8744''45''8743''45'orderTheoreticLattice_734 v2
  du_'8744''45''8743''45'orderTheoreticLattice_734 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_Lattice_386
  du_'8744''45''8743''45'orderTheoreticLattice_734 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45''8743''45'orderTheoreticLattice_3300
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0))
  -- Algebra.Lattice.Properties.DistributiveLattice.∧-∨-isDistributiveLattice
  d_'8743''45''8744''45'isDistributiveLattice_736 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
  d_'8743''45''8744''45'isDistributiveLattice_736 ~v0 ~v1 v2
    = du_'8743''45''8744''45'isDistributiveLattice_736 v2
  du_'8743''45''8744''45'isDistributiveLattice_736 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3036
  du_'8743''45''8744''45'isDistributiveLattice_736 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.C_IsDistributiveLattice'46'constructor_40943
        (coe
           MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45''8744''45'isLattice_3230
           (coe MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_664 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3052
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isDistributiveLattice_608
              (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3050
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isDistributiveLattice_608
              (coe v0)))
  -- Algebra.Lattice.Properties.DistributiveLattice.∧-∨-distributiveLattice
  d_'8743''45''8744''45'distributiveLattice_738 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584
  d_'8743''45''8744''45'distributiveLattice_738 ~v0 ~v1 v2
    = du_'8743''45''8744''45'distributiveLattice_738 v2
  du_'8743''45''8744''45'distributiveLattice_738 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_584
  du_'8743''45''8744''45'distributiveLattice_738 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Bundles.C_DistributiveLattice'46'constructor_9515
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__606 (coe v0))
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__604 (coe v0))
        (coe du_'8743''45''8744''45'isDistributiveLattice_736 (coe v0))
  