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LeanPool.NFWeakPartition.NAR4H5C095M3Part021

NF weak partition development: NAR4H5C095M3Part021.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0034 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) (dv_E_f : f ∉ E.fv) (dv_E_u : u ∉ E.fv) (dv_E_x : x ∉ E.fv) (dv_S_f : f ∉ S_cls.fv) (dv_S_u : u ∉ S_cls.fv) (dv_S_x : x ∉ S_cls.fv) (dv_f_u : f ≠ u) (dv_f_x : f ≠ x) :
Nominal.TAlphaWff [(nb095AlphaDummy291 D R S_cls E, nb095AlphaDummy292 u S_cls f E), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy291 D R S_cls E)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCrn (SemanticCore.Class.cv (nb095AlphaDummy000 D R S_cls E))) (Compiler.CompactSourceSyntax.synCin E (Compiler.CompactSourceSyntax.synCima (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif S_cls Compiler.CompactSourceSyntax.synCid)) (Compiler.CompactSourceSyntax.synCsn (SemanticCore.Class.cv (nb095AlphaDummy001 D R S_cls E))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy291 D R S_cls E)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCrn (SemanticCore.Class.cv (nb095AlphaDummy000 D R S_cls E))) (Compiler.CompactSourceSyntax.synCin E (Compiler.CompactSourceSyntax.synCima (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif S_cls Compiler.CompactSourceSyntax.synCid)) (Compiler.CompactSourceSyntax.synCsn (SemanticCore.Class.cv (nb095AlphaDummy001 D R S_cls E))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy292 u S_cls f E)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCrn (SemanticCore.Class.cv f)) (Compiler.CompactSourceSyntax.synCin E (Compiler.CompactSourceSyntax.synCima (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif S_cls Compiler.CompactSourceSyntax.synCid)) (Compiler.CompactSourceSyntax.synCsn (SemanticCore.Class.cv u)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy292 u S_cls f E)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCrn (SemanticCore.Class.cv f)) (Compiler.CompactSourceSyntax.synCin E (Compiler.CompactSourceSyntax.synCima (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif S_cls Compiler.CompactSourceSyntax.synCid)) (Compiler.CompactSourceSyntax.synCsn (SemanticCore.Class.cv u)))))).neg)

Checked nominal proof certificate identified upstream as nb095_split_alpha_0034.

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    noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0035 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) :
    Nominal.TAlphaWff [(nb095AlphaDummy300 D R S_cls E, nb095AlphaDummy302 f), (nb095AlphaDummy299 D R S_cls E, nb095AlphaDummy301 f), (nb095AlphaDummy329 D R S_cls E, nb095AlphaDummy330 f), (nb095AlphaDummy303 D R S_cls E, nb095AlphaDummy304 f), (nb095AlphaDummy296 D R S_cls E, nb095AlphaDummy298 f), (nb095AlphaDummy295 D R S_cls E, nb095AlphaDummy297 f), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy300 D R S_cls E)) (SemanticCore.Class.cv (nb095AlphaDummy295 D R S_cls E))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy299 D R S_cls E)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy300 D R S_cls E))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy302 f)) (SemanticCore.Class.cv (nb095AlphaDummy297 f))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy301 f)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy302 f))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg)

    Checked nominal proof certificate identified upstream as nb095_split_alpha_0035.

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      noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0036 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) :
      Nominal.TAlphaWff [(nb095AlphaDummy303 D R S_cls E, nb095AlphaDummy304 f), (nb095AlphaDummy296 D R S_cls E, nb095AlphaDummy298 f), (nb095AlphaDummy295 D R S_cls E, nb095AlphaDummy297 f), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy303 D R S_cls E)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb095AlphaDummy299 D R S_cls E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy300 D R S_cls E) (SemanticCore.Class.cv (nb095AlphaDummy296 D R S_cls E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy299 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy300 D R S_cls E)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy303 D R S_cls E)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb095AlphaDummy299 D R S_cls E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy300 D R S_cls E) (SemanticCore.Class.cv (nb095AlphaDummy295 D R S_cls E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy299 D R S_cls E)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy300 D R S_cls E))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy304 f)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb095AlphaDummy301 f) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy302 f) (SemanticCore.Class.cv (nb095AlphaDummy298 f)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy301 f)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy302 f)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy304 f)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb095AlphaDummy301 f) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy302 f) (SemanticCore.Class.cv (nb095AlphaDummy297 f)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy301 f)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy302 f))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg)

      Checked nominal proof certificate identified upstream as nb095_split_alpha_0036.

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        theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_compact_fv_empty_0312 (D R S_cls E : SemanticCore.Class) :
        nb095AlphaDummy383 D R S_cls E ∉ ∅
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        theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_compact_fv_empty_0313 (f : SemanticCore.Var) :
        nb095AlphaDummy384 f ∉ ∅
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        theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_compact_fv_empty_0314 (D R S_cls E : SemanticCore.Class) :
        nb095AlphaDummy381 D R S_cls E ∉ ∅
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        theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_compact_fv_empty_0315 (f : SemanticCore.Var) :
        nb095AlphaDummy382 f ∉ ∅