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.Lattice 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.Semilattice qualified
  import MAlonzo.Code.Algebra.Lattice.Structures qualified
  import MAlonzo.Code.Algebra.Structures qualified
  import MAlonzo.Code.Data.Product.Base qualified
  import MAlonzo.Code.Relation.Binary.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Construct.NaturalOrder.Left qualified
  import MAlonzo.Code.Relation.Binary.Lattice.Bundles qualified
  import MAlonzo.Code.Relation.Binary.Lattice.Structures qualified
  import MAlonzo.Code.Relation.Binary.Reasoning.Base.Single 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.Lattice.Properties.Lattice._.Idempotent
  d_Idempotent_112 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_Idempotent_112 = erased
  -- Algebra.Lattice.Properties.Lattice._.IsBand
  d_IsBand_210 a0 a1 a2 a3 = ()
  -- Algebra.Lattice.Properties.Lattice._.IsMagma
  d_IsMagma_250 a0 a1 a2 a3 = ()
  -- Algebra.Lattice.Properties.Lattice._.IsSemigroup
  d_IsSemigroup_278 a0 a1 a2 a3 = ()
  -- Algebra.Lattice.Properties.Lattice._.IsBand.idem
  d_idem_392 ::
    MAlonzo.Code.Algebra.Structures.T_IsBand_508 -> AgdaAny -> AgdaAny
  d_idem_392 v0
    = coe MAlonzo.Code.Algebra.Structures.d_idem_518 (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsBand.isSemigroup
  d_isSemigroup_400 ::
    MAlonzo.Code.Algebra.Structures.T_IsBand_508 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_isSemigroup_400 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isSemigroup_516 (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsMagma.isEquivalence
  d_isEquivalence_1550 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_1550 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isEquivalence_184 (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsMagma.∙-cong
  d_'8729''45'cong_1564 ::
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8729''45'cong_1564 v0
    = coe MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_186 (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsSemigroup.assoc
  d_assoc_2404 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_assoc_2404 v0
    = coe MAlonzo.Code.Algebra.Structures.d_assoc_482 (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsSemigroup.isMagma
  d_isMagma_2408 ::
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_isMagma_2408 v0
    = coe MAlonzo.Code.Algebra.Structures.d_isMagma_480 (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice
  d_IsLattice_2732 a0 a1 a2 a3 a4 = ()
  -- Algebra.Lattice.Properties.Lattice._.IsSemilattice
  d_IsSemilattice_2736 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    (AgdaAny -> AgdaAny -> AgdaAny) -> ()
  d_IsSemilattice_2736 = erased
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.absorptive
  d_absorptive_3036 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_absorptive_3036 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_2998 (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.isEquivalence
  d_isEquivalence_3038 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
  d_isEquivalence_3038 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
        (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.∧-assoc
  d_'8743''45'assoc_3052 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8743''45'assoc_3052 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_2994
        (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.∧-comm
  d_'8743''45'comm_3054 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8743''45'comm_3054 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_2992
        (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.∧-cong
  d_'8743''45'cong_3056 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8743''45'cong_3056 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_2996
        (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.∨-assoc
  d_'8744''45'assoc_3064 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8744''45'assoc_3064 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_2988
        (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.∨-comm
  d_'8744''45'comm_3066 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    AgdaAny -> AgdaAny -> AgdaAny
  d_'8744''45'comm_3066 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_2986
        (coe v0)
  -- Algebra.Lattice.Properties.Lattice._.IsLattice.∨-cong
  d_'8744''45'cong_3068 ::
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962 ->
    AgdaAny ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_'8744''45'cong_3068 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_2990
        (coe v0)
  -- Algebra.Lattice.Properties.Lattice.∧-idem
  d_'8743''45'idem_3182 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny
  d_'8743''45'idem_3182 ~v0 ~v1 v2 v3 = du_'8743''45'idem_3182 v2 v3
  du_'8743''45'idem_3182 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny
  du_'8743''45'idem_3182 v0 v1
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v2 v3 v4 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v4)
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1)
        v1
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))))
           (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1)
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1
              (coe
                 MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1)))
           v1
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                       (coe
                          MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
              (coe
                 MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1)))
              v1 v1
              (let v2
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                            (coe
                               MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v2))
                    (coe v1)))
              (coe
                 MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3014
                 (MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)) v1
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1)))
           (coe
              MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3016
              (coe MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))
              (coe v1)
              (coe
                 MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1))
              (coe v1)
              (coe
                 MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3012
                 (MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)) v1
                 v1)))
  -- Algebra.Lattice.Properties.Lattice.∧-isMagma
  d_'8743''45'isMagma_3186 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8743''45'isMagma_3186 ~v0 ~v1 v2 = du_'8743''45'isMagma_3186 v2
  du_'8743''45'isMagma_3186 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'8743''45'isMagma_3186 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_2996
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
  -- Algebra.Lattice.Properties.Lattice.∧-isSemigroup
  d_'8743''45'isSemigroup_3188 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8743''45'isSemigroup_3188 ~v0 ~v1 v2
    = du_'8743''45'isSemigroup_3188 v2
  du_'8743''45'isSemigroup_3188 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'8743''45'isSemigroup_3188 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
        (coe du_'8743''45'isMagma_3186 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_2994
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
  -- Algebra.Lattice.Properties.Lattice.∧-isBand
  d_'8743''45'isBand_3190 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8743''45'isBand_3190 ~v0 ~v1 v2 = du_'8743''45'isBand_3190 v2
  du_'8743''45'isBand_3190 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_'8743''45'isBand_3190 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_11205
        (coe du_'8743''45'isSemigroup_3188 (coe v0))
        (coe du_'8743''45'idem_3182 (coe v0))
  -- Algebra.Lattice.Properties.Lattice.∧-isSemilattice
  d_'8743''45'isSemilattice_3192 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_'8743''45'isSemilattice_3192 ~v0 ~v1 v2
    = du_'8743''45'isSemilattice_3192 v2
  du_'8743''45'isSemilattice_3192 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_'8743''45'isSemilattice_3192 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeBand'46'constructor_13109
        (coe du_'8743''45'isBand_3190 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_2992
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
  -- Algebra.Lattice.Properties.Lattice.∧-semilattice
  d_'8743''45'semilattice_3194 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  d_'8743''45'semilattice_3194 ~v0 ~v1 v2
    = du_'8743''45'semilattice_3194 v2
  du_'8743''45'semilattice_3194 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  du_'8743''45'semilattice_3194 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Bundles.C_Semilattice'46'constructor_193
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 (coe v0))
        (coe du_'8743''45'isSemilattice_3192 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-isOrderTheoreticJoinSemilattice
  d_'8743''45'isOrderTheoreticJoinSemilattice_3198 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  d_'8743''45'isOrderTheoreticJoinSemilattice_3198 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticJoinSemilattice_3198 v2
  du_'8743''45'isOrderTheoreticJoinSemilattice_3198 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  du_'8743''45'isOrderTheoreticJoinSemilattice_3198 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
        (coe du_'8743''45'semilattice_3194 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-isOrderTheoreticMeetSemilattice
  d_'8743''45'isOrderTheoreticMeetSemilattice_3200 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  d_'8743''45'isOrderTheoreticMeetSemilattice_3200 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticMeetSemilattice_3200 v2
  du_'8743''45'isOrderTheoreticMeetSemilattice_3200 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  du_'8743''45'isOrderTheoreticMeetSemilattice_3200 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticMeetSemilattice_176
        (coe du_'8743''45'semilattice_3194 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-orderTheoreticJoinSemilattice
  d_'8743''45'orderTheoreticJoinSemilattice_3202 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  d_'8743''45'orderTheoreticJoinSemilattice_3202 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticJoinSemilattice_3202 v2
  du_'8743''45'orderTheoreticJoinSemilattice_3202 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  du_'8743''45'orderTheoreticJoinSemilattice_3202 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticJoinSemilattice_182
        (coe du_'8743''45'semilattice_3194 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-orderTheoreticMeetSemilattice
  d_'8743''45'orderTheoreticMeetSemilattice_3204 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  d_'8743''45'orderTheoreticMeetSemilattice_3204 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticMeetSemilattice_3204 v2
  du_'8743''45'orderTheoreticMeetSemilattice_3204 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  du_'8743''45'orderTheoreticMeetSemilattice_3204 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticMeetSemilattice_180
        (coe du_'8743''45'semilattice_3194 (coe v0))
  -- Algebra.Lattice.Properties.Lattice.∨-idem
  d_'8744''45'idem_3206 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny
  d_'8744''45'idem_3206 ~v0 ~v1 v2 v3 = du_'8744''45'idem_3206 v2 v3
  du_'8744''45'idem_3206 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny
  du_'8744''45'idem_3206 v0 v1
    = coe
        MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
        (\ v2 v3 v4 ->
           coe
             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v4)
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v1)
        v1
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_370
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
              (coe
                 MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
           (MAlonzo.Code.Relation.Binary.Structures.d_sym_36
              (coe
                 MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))))
           (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v1)
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1
              (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1))
           v1
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                       (coe
                          MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
              (coe
                 MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1))
              v1 v1
              (let v2
                     = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                         (coe
                            MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                            (coe
                               MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))) in
               coe
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                       (coe v2))
                    (coe v1)))
              (coe
                 MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3012
                 (MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)) v1
                 v1))
           (coe
              MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3024
              (coe MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))
              (coe v1)
              (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v1)
              (coe v1) (coe du_'8743''45'idem_3182 (coe v0) (coe v1))))
  -- Algebra.Lattice.Properties.Lattice.∨-isMagma
  d_'8744''45'isMagma_3210 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  d_'8744''45'isMagma_3210 ~v0 ~v1 v2 = du_'8744''45'isMagma_3210 v2
  du_'8744''45'isMagma_3210 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsMagma_176
  du_'8744''45'isMagma_3210 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsMagma'46'constructor_1867
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_2990
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
  -- Algebra.Lattice.Properties.Lattice.∨-isSemigroup
  d_'8744''45'isSemigroup_3212 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  d_'8744''45'isSemigroup_3212 ~v0 ~v1 v2
    = du_'8744''45'isSemigroup_3212 v2
  du_'8744''45'isSemigroup_3212 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsSemigroup_472
  du_'8744''45'isSemigroup_3212 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsSemigroup'46'constructor_10417
        (coe du_'8744''45'isMagma_3210 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_2988
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
  -- Algebra.Lattice.Properties.Lattice.∨-isBand
  d_'8744''45'isBand_3214 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  d_'8744''45'isBand_3214 ~v0 ~v1 v2 = du_'8744''45'isBand_3214 v2
  du_'8744''45'isBand_3214 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsBand_508
  du_'8744''45'isBand_3214 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsBand'46'constructor_11205
        (coe du_'8744''45'isSemigroup_3212 (coe v0))
        (coe du_'8744''45'idem_3206 (coe v0))
  -- Algebra.Lattice.Properties.Lattice.∨-isSemilattice
  d_'8744''45'isSemilattice_3216 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  d_'8744''45'isSemilattice_3216 ~v0 ~v1 v2
    = du_'8744''45'isSemilattice_3216 v2
  du_'8744''45'isSemilattice_3216 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_590
  du_'8744''45'isSemilattice_3216 v0
    = coe
        MAlonzo.Code.Algebra.Structures.C_IsCommutativeBand'46'constructor_13109
        (coe du_'8744''45'isBand_3214 (coe v0))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_2986
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
  -- Algebra.Lattice.Properties.Lattice.∨-semilattice
  d_'8744''45'semilattice_3218 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  d_'8744''45'semilattice_3218 ~v0 ~v1 v2
    = du_'8744''45'semilattice_3218 v2
  du_'8744''45'semilattice_3218 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
  du_'8744''45'semilattice_3218 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Bundles.C_Semilattice'46'constructor_193
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 (coe v0))
        (coe du_'8744''45'isSemilattice_3216 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-isOrderTheoreticJoinSemilattice
  d_'8743''45'isOrderTheoreticJoinSemilattice_3222 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  d_'8743''45'isOrderTheoreticJoinSemilattice_3222 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticJoinSemilattice_3222 v2
  du_'8743''45'isOrderTheoreticJoinSemilattice_3222 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
  du_'8743''45'isOrderTheoreticJoinSemilattice_3222 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
        (coe du_'8744''45'semilattice_3218 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-isOrderTheoreticMeetSemilattice
  d_'8743''45'isOrderTheoreticMeetSemilattice_3224 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  d_'8743''45'isOrderTheoreticMeetSemilattice_3224 ~v0 ~v1 v2
    = du_'8743''45'isOrderTheoreticMeetSemilattice_3224 v2
  du_'8743''45'isOrderTheoreticMeetSemilattice_3224 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_180
  du_'8743''45'isOrderTheoreticMeetSemilattice_3224 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticMeetSemilattice_176
        (coe du_'8744''45'semilattice_3218 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-orderTheoreticJoinSemilattice
  d_'8743''45'orderTheoreticJoinSemilattice_3226 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  d_'8743''45'orderTheoreticJoinSemilattice_3226 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticJoinSemilattice_3226 v2
  du_'8743''45'orderTheoreticJoinSemilattice_3226 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
  du_'8743''45'orderTheoreticJoinSemilattice_3226 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticJoinSemilattice_182
        (coe du_'8744''45'semilattice_3218 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.∧-orderTheoreticMeetSemilattice
  d_'8743''45'orderTheoreticMeetSemilattice_3228 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  d_'8743''45'orderTheoreticMeetSemilattice_3228 ~v0 ~v1 v2
    = du_'8743''45'orderTheoreticMeetSemilattice_3228 v2
  du_'8743''45'orderTheoreticMeetSemilattice_3228 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_200
  du_'8743''45'orderTheoreticMeetSemilattice_3228 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticMeetSemilattice_180
        (coe du_'8744''45'semilattice_3218 (coe v0))
  -- Algebra.Lattice.Properties.Lattice.∧-∨-isLattice
  d_'8743''45''8744''45'isLattice_3230 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
  d_'8743''45''8744''45'isLattice_3230 ~v0 ~v1 v2
    = du_'8743''45''8744''45'isLattice_3230 v2
  du_'8743''45''8744''45'isLattice_3230 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_2962
  du_'8743''45''8744''45'isLattice_3230 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Structures.C_IsLattice'46'constructor_36793
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_2992
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_2994
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_2996
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_2986
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_2988
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_2990
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe
           MAlonzo.Code.Data.Product.Base.du_swap_370
           (coe
              MAlonzo.Code.Algebra.Lattice.Structures.d_absorptive_2998
              (coe
                 MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))))
  -- Algebra.Lattice.Properties.Lattice.∧-∨-lattice
  d_'8743''45''8744''45'lattice_3232 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
  d_'8743''45''8744''45'lattice_3232 ~v0 ~v1 v2
    = du_'8743''45''8744''45'lattice_3232 v2
  du_'8743''45''8744''45'lattice_3232 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500
  du_'8743''45''8744''45'lattice_3232 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Bundles.C_Lattice'46'constructor_7925
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 (coe v0))
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 (coe v0))
        (coe du_'8743''45''8744''45'isLattice_3230 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._.poset
  d_poset_3236 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  d_poset_3236 ~v0 ~v1 v2 = du_poset_3236 v2
  du_poset_3236 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Bundles.T_Poset_314
  du_poset_3236 v0
    = coe
        MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_poset_162
        (coe du_'8743''45'semilattice_3194 (coe v0))
  -- Algebra.Lattice.Properties.Lattice._._≤_
  d__'8804'__3240 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> ()
  d__'8804'__3240 = erased
  -- Algebra.Lattice.Properties.Lattice.∨-∧-isOrderTheoreticLattice
  d_'8744''45''8743''45'isOrderTheoreticLattice_3244 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsLattice_340
  d_'8744''45''8743''45'isOrderTheoreticLattice_3244 ~v0 ~v1 v2
    = du_'8744''45''8743''45'isOrderTheoreticLattice_3244 v2
  du_'8744''45''8743''45'isOrderTheoreticLattice_3244 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsLattice_340
  du_'8744''45''8743''45'isOrderTheoreticLattice_3244 v0
    = coe
        MAlonzo.Code.Relation.Binary.Lattice.Structures.C_IsLattice'46'constructor_14941
        (coe
           MAlonzo.Code.Relation.Binary.Bundles.d_isPartialOrder_336
           (coe
              MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_poset_162
              (coe du_'8743''45'semilattice_3194 (coe v0))))
        (coe du_supremum_3288 (coe v0))
        (coe
           MAlonzo.Code.Relation.Binary.Construct.NaturalOrder.Left.du_infimum_3640
           (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 (coe v0))
           (coe du_'8743''45'isSemilattice_3192 (coe v0)))
  -- Algebra.Lattice.Properties.Lattice._._._≤_
  d__'8804'__3256 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> ()
  d__'8804'__3256 = erased
  -- Algebra.Lattice.Properties.Lattice._.sound
  d_sound_3268 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_sound_3268 ~v0 ~v1 v2 v3 v4 v5 = du_sound_3268 v2 v3 v4 v5
  du_sound_3268 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_sound_3268 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v2)
        v1
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v4 v5 v6 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v6)
           (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v2)
           v1
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                       (coe
                          MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
              (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v2)
              (coe
                 MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2 v1))
              v1
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                          (coe
                             MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2 v1))
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v2))
                 v1
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                             (coe
                                MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1
                       (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v2))
                    v1 v1
                    (let v4
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                                  (coe
                                     MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524
                                     (coe v0))) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v4))
                          (coe v1)))
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3014
                       (MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)) v1
                       v2))
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3016
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))
                    (coe v1)
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2 v1)
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v2)
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_2986
                       (MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)) v2
                       v1)))
              (coe
                 MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3016
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))
                 (coe v1) (coe v2)
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2 v1)
                 (coe v3))))
  -- Algebra.Lattice.Properties.Lattice._.complete
  d_complete_3280 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  d_complete_3280 ~v0 ~v1 v2 v3 v4 v5 = du_complete_3280 v2 v3 v4 v5
  du_complete_3280 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
  du_complete_3280 v0 v1 v2 v3
    = coe
        MAlonzo.Code.Relation.Binary.Structures.d_sym_36
        (MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
           (coe
              MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))
        (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2 v1)
        v2
        (coe
           MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
           (\ v4 v5 v6 ->
              coe
                MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 v6)
           (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2 v1)
           v2
           (coe
              MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                 (coe
                    MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                       (coe
                          MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
              (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2 v1)
              (coe
                 MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v2))
              v2
              (coe
                 MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                    (coe
                       MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                       (coe
                          MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                          (coe
                             MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v2))
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v2 v1))
                 v2
                 (coe
                    MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_368
                    (coe
                       MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                       (coe
                          MAlonzo.Code.Relation.Binary.Structures.d_trans_38
                          (coe
                             MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                             (coe
                                MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)))))
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v2
                       (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v2 v1))
                    v2 v2
                    (let v4
                           = MAlonzo.Code.Relation.Binary.Structures.d_refl_34
                               (coe
                                  MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_2984
                                  (coe
                                     MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524
                                     (coe v0))) in
                     coe
                       (coe
                          MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_492
                          (coe
                             MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                             (coe v4))
                          (coe v2)))
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3012
                       (MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)) v2
                       v1))
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3024
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))
                    (coe v2)
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v2)
                    (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v2 v1)
                    (coe
                       MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_2992
                       (MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0)) v1
                       v2)))
              (coe
                 MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3024
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d_isLattice_524 (coe v0))
                 (coe v2) (coe v1)
                 (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 v0 v1 v2)
                 (coe v3))))
  -- Algebra.Lattice.Properties.Lattice._.supremum
  d_supremum_3288 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  d_supremum_3288 ~v0 ~v1 v2 v3 v4 = du_supremum_3288 v2 v3 v4
  du_supremum_3288 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
  du_supremum_3288 v0 v1 v2
    = coe
        MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
        (coe
           du_sound_3268 (coe v0) (coe v1)
           (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v2)
           (coe
              MAlonzo.Code.Relation.Binary.Lattice.Structures.du_x'8804'x'8744'y_38
              (coe
                 MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
                 (coe du_'8744''45'semilattice_3218 (coe v0)))
              (coe v1) (coe v2)))
        (coe
           MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
           (coe
              du_sound_3268 (coe v0) (coe v2)
              (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v2)
              (coe
                 MAlonzo.Code.Relation.Binary.Lattice.Structures.du_y'8804'x'8744'y_50
                 (coe
                    MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
                    (coe du_'8744''45'semilattice_3218 (coe v0)))
                 (coe v1) (coe v2)))
           (coe
              (\ v3 v4 v5 ->
                 coe
                   du_sound_3268 (coe v0)
                   (coe MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 v0 v1 v2)
                   (coe v3)
                   (coe
                      MAlonzo.Code.Relation.Binary.Lattice.Structures.du_'8744''45'least_64
                      (coe
                         MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
                         (coe du_'8744''45'semilattice_3218 (coe v0)))
                      v1 v2 v3 (coe du_complete_3280 (coe v0) (coe v1) (coe v3) (coe v4))
                      (coe du_complete_3280 (coe v0) (coe v2) (coe v3) (coe v5))))))
  -- Algebra.Lattice.Properties.Lattice.∨-∧-orderTheoreticLattice
  d_'8744''45''8743''45'orderTheoreticLattice_3300 ::
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Agda.Primitive.T_Level_18 ->
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_Lattice_386
  d_'8744''45''8743''45'orderTheoreticLattice_3300 ~v0 ~v1 v2
    = du_'8744''45''8743''45'orderTheoreticLattice_3300 v2
  du_'8744''45''8743''45'orderTheoreticLattice_3300 ::
    MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_500 ->
    MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_Lattice_386
  du_'8744''45''8743''45'orderTheoreticLattice_3300 v0
    = coe
        MAlonzo.Code.Relation.Binary.Lattice.Bundles.C_Lattice'46'constructor_8977
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__520 (coe v0))
        (MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__522 (coe v0))
        (coe du_'8744''45''8743''45'isOrderTheoreticLattice_3244 (coe v0))
  