Nominal proof certificates grouped in dependency order.

Certificates from NAR4C054C001Part003.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0000 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy030, nb054AlphaDummy033 x y), (nb054AlphaDummy029, nb054AlphaDummy032 x y), (nb054AlphaDummy028, nb054AlphaDummy031 x y), (nb054AlphaDummy026, nb054AlphaDummy027 x y), (nb054AlphaDummy022, nb054AlphaDummy024 x y), (nb054AlphaDummy023, nb054AlphaDummy025 x y), (nb054AlphaDummy015, nb054AlphaDummy017 x y), (nb054AlphaDummy014, nb054AlphaDummy016 x y), (nb054AlphaDummy020, nb054AlphaDummy021 x y), (nb054AlphaDummy018, nb054AlphaDummy019 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb054AlphaDummy029) (SemanticCore.Class.cv nb054AlphaDummy030)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy028) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb054AlphaDummy029) (SemanticCore.Class.cv nb054AlphaDummy030))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb054AlphaDummy032 x y)) (SemanticCore.Class.cv (nb054AlphaDummy033 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy031 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb054AlphaDummy032 x y)) (SemanticCore.Class.cv (nb054AlphaDummy033 x y)))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0000.

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Certificates from NAR4C054C001Part004.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0001 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy015, nb054AlphaDummy017 x y), (nb054AlphaDummy014, nb054AlphaDummy016 x y), (nb054AlphaDummy020, nb054AlphaDummy021 x y), (nb054AlphaDummy018, nb054AlphaDummy019 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy014) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb054AlphaDummy015))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy016 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb054AlphaDummy017 x y))))

Checked nominal proof certificate identified upstream as nb054_split_alpha_0001.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0002 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy030, nb054AlphaDummy033 x y), (nb054AlphaDummy029, nb054AlphaDummy032 x y), (nb054AlphaDummy028, nb054AlphaDummy031 x y), (nb054AlphaDummy026, nb054AlphaDummy027 x y), (nb054AlphaDummy022, nb054AlphaDummy024 x y), (nb054AlphaDummy023, nb054AlphaDummy025 x y), (nb054AlphaDummy048, nb054AlphaDummy049 x y), (nb054AlphaDummy046, nb054AlphaDummy047 x y), (nb054AlphaDummy015, nb054AlphaDummy017 x y), (nb054AlphaDummy014, nb054AlphaDummy016 x y), (nb054AlphaDummy044, nb054AlphaDummy045 x y), (nb054AlphaDummy018, nb054AlphaDummy019 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb054AlphaDummy029) (SemanticCore.Class.cv nb054AlphaDummy030)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy028) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb054AlphaDummy029) (SemanticCore.Class.cv nb054AlphaDummy030))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb054AlphaDummy032 x y)) (SemanticCore.Class.cv (nb054AlphaDummy033 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy031 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb054AlphaDummy032 x y)) (SemanticCore.Class.cv (nb054AlphaDummy033 x y)))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0002.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0003 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy022, nb054AlphaDummy024 x y), (nb054AlphaDummy023, nb054AlphaDummy025 x y), (nb054AlphaDummy048, nb054AlphaDummy049 x y), (nb054AlphaDummy046, nb054AlphaDummy047 x y), (nb054AlphaDummy015, nb054AlphaDummy017 x y), (nb054AlphaDummy014, nb054AlphaDummy016 x y), (nb054AlphaDummy044, nb054AlphaDummy045 x y), (nb054AlphaDummy018, nb054AlphaDummy019 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy022) (SemanticCore.Class.cv nb054AlphaDummy015)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy023) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy022) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb054AlphaDummy022) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb054AlphaDummy022))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy024 x y)) (SemanticCore.Class.cv (nb054AlphaDummy017 x y))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy025 x y)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy024 x y)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb054AlphaDummy024 x y)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb054AlphaDummy024 x y)))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0003.

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Certificates from NAR4C054C001Part005.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054VariableOccurrence0 (x y : SemanticCore.Var) : Nominal.TAlphaClass [(nb054AlphaDummy015, nb054AlphaDummy017 x y), (nb054AlphaDummy014, nb054AlphaDummy016 x y), (nb054AlphaDummy044, nb054AlphaDummy045 x y), (nb054AlphaDummy018, nb054AlphaDummy019 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] (SemanticCore.Class.cv nb054AlphaDummy001) (SemanticCore.Class.cv y)

Checked nominal proof certificate identified upstream as nb054_variable_occurrence_0.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054_variable_occurrence_1 (x y : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaClass [(nb054AlphaDummy015, nb054AlphaDummy017 x y), (nb054AlphaDummy014, nb054AlphaDummy016 x y), (nb054AlphaDummy020, nb054AlphaDummy021 x y), (nb054AlphaDummy018, nb054AlphaDummy019 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] (SemanticCore.Class.cv nb054AlphaDummy000) (SemanticCore.Class.cv x)

Checked nominal proof certificate identified upstream as nb054_variable_occurrence_1.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0004 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy044, nb054AlphaDummy045 x y), (nb054AlphaDummy018, nb054AlphaDummy019 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy044) (SemanticCore.Class.cab nb054AlphaDummy014 (Compiler.CompactSourceSyntax.synWrex nb054AlphaDummy015 (SemanticCore.Class.cv nb054AlphaDummy001) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy014) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb054AlphaDummy015)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy044) (SemanticCore.Class.cab nb054AlphaDummy014 (Compiler.CompactSourceSyntax.synWrex nb054AlphaDummy015 (SemanticCore.Class.cv nb054AlphaDummy001) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy014) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb054AlphaDummy015)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy045 x y)) (SemanticCore.Class.cab (nb054AlphaDummy016 x y) (Compiler.CompactSourceSyntax.synWrex (nb054AlphaDummy017 x y) (SemanticCore.Class.cv y) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy016 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb054AlphaDummy017 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy045 x y)) (SemanticCore.Class.cab (nb054AlphaDummy016 x y) (Compiler.CompactSourceSyntax.synWrex (nb054AlphaDummy017 x y) (SemanticCore.Class.cv y) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy016 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb054AlphaDummy017 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0004.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0005 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy058, nb054AlphaDummy061 x y), (nb054AlphaDummy057, nb054AlphaDummy060 x y), (nb054AlphaDummy056, nb054AlphaDummy059 x y), (nb054AlphaDummy054, nb054AlphaDummy055 x y), (nb054AlphaDummy050, nb054AlphaDummy052 x y), (nb054AlphaDummy051, nb054AlphaDummy053 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb054AlphaDummy057) (SemanticCore.Class.cv nb054AlphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb054AlphaDummy057) (SemanticCore.Class.cv nb054AlphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb054AlphaDummy060 x y)) (SemanticCore.Class.cv (nb054AlphaDummy061 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy059 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb054AlphaDummy060 x y)) (SemanticCore.Class.cv (nb054AlphaDummy061 x y)))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0005.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0006 (x y : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy012, nb054AlphaDummy013 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy007) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb054AlphaDummy000) (SemanticCore.Class.cv nb054AlphaDummy001))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy006) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb054AlphaDummy007))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy009 x y)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv x) (SemanticCore.Class.cv y))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy008 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb054AlphaDummy009 x y)))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0006.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0007 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy058, nb054AlphaDummy061 x y), (nb054AlphaDummy057, nb054AlphaDummy060 x y), (nb054AlphaDummy056, nb054AlphaDummy059 x y), (nb054AlphaDummy054, nb054AlphaDummy055 x y), (nb054AlphaDummy050, nb054AlphaDummy052 x y), (nb054AlphaDummy051, nb054AlphaDummy053 x y), (nb054AlphaDummy076, nb054AlphaDummy077 x y), (nb054AlphaDummy074, nb054AlphaDummy075 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy072, nb054AlphaDummy073 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb054AlphaDummy057) (SemanticCore.Class.cv nb054AlphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb054AlphaDummy057) (SemanticCore.Class.cv nb054AlphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb054AlphaDummy060 x y)) (SemanticCore.Class.cv (nb054AlphaDummy061 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy059 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb054AlphaDummy060 x y)) (SemanticCore.Class.cv (nb054AlphaDummy061 x y)))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0007.

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Certificates from NAR4C054C001Part006.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0008 (x y : SemanticCore.Var) : Nominal.TAlphaClass [(nb054AlphaDummy076, nb054AlphaDummy077 x y), (nb054AlphaDummy074, nb054AlphaDummy075 x y), (nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy072, nb054AlphaDummy073 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] (SemanticCore.Class.cab nb054AlphaDummy051 (Compiler.CompactSourceSyntax.synWrex nb054AlphaDummy050 (SemanticCore.Class.cv nb054AlphaDummy007) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy051) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy050) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb054AlphaDummy050) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb054AlphaDummy050))))) (SemanticCore.Class.cab (nb054AlphaDummy053 x y) (Compiler.CompactSourceSyntax.synWrex (nb054AlphaDummy052 x y) (SemanticCore.Class.cv (nb054AlphaDummy009 x y)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy053 x y)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy052 x y)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb054AlphaDummy052 x y)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb054AlphaDummy052 x y))))))

Checked nominal proof certificate identified upstream as nb054_split_alpha_0008.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054_variable_occurrence_2 (x y : SemanticCore.Var) : Nominal.TAlphaClass [(nb054AlphaDummy007, nb054AlphaDummy009 x y), (nb054AlphaDummy006, nb054AlphaDummy008 x y), (nb054AlphaDummy072, nb054AlphaDummy073 x y), (nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] (SemanticCore.Class.cv nb054AlphaDummy002) (SemanticCore.Class.cv (nb054AlphaDummy003 x y))

Checked nominal proof certificate identified upstream as nb054_variable_occurrence_2.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0009 (x y : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(nb054AlphaDummy010, nb054AlphaDummy011 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy010) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab nb054AlphaDummy006 (Compiler.CompactSourceSyntax.synWrex nb054AlphaDummy007 (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb054AlphaDummy000) (SemanticCore.Class.cv nb054AlphaDummy001)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy006) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb054AlphaDummy007))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb054AlphaDummy010) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab nb054AlphaDummy006 (Compiler.CompactSourceSyntax.synWrex nb054AlphaDummy007 (SemanticCore.Class.cv nb054AlphaDummy002) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy006) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb054AlphaDummy007)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy011 x y)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb054AlphaDummy008 x y) (Compiler.CompactSourceSyntax.synWrex (nb054AlphaDummy009 x y) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv x) (SemanticCore.Class.cv y)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy008 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb054AlphaDummy009 x y)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb054AlphaDummy011 x y)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb054AlphaDummy008 x y) (Compiler.CompactSourceSyntax.synWrex (nb054AlphaDummy009 x y) (SemanticCore.Class.cv (nb054AlphaDummy003 x y)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy008 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb054AlphaDummy009 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0009.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb054SplitAlpha0010 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb054AlphaDummy078, nb054AlphaDummy079 x y), (nb054AlphaDummy015, nb054AlphaDummy017 x y), (nb054AlphaDummy014, nb054AlphaDummy016 x y), (nb054AlphaDummy002, nb054AlphaDummy003 x y), (nb054AlphaDummy001, y), (nb054AlphaDummy000, x), (nb054AlphaDummy004, nb054AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb054AlphaDummy015) (SemanticCore.Class.cv nb054AlphaDummy078)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb054AlphaDummy014) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb054AlphaDummy015) (SemanticCore.Class.cv nb054AlphaDummy078))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb054AlphaDummy017 x y)) (SemanticCore.Class.cv (nb054AlphaDummy079 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb054AlphaDummy016 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb054AlphaDummy017 x y)) (SemanticCore.Class.cv (nb054AlphaDummy079 x y)))).neg)

Checked nominal proof certificate identified upstream as nb054_split_alpha_0010.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nominalDfAddcfn (x y : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.NPrf (SemanticCore.Wff.classEq Compiler.CompactSourceSyntax.synCaddcfn (Compiler.CompactSourceSyntax.synCmpt2 x Compiler.CompactSourceSyntax.synCvv y Compiler.CompactSourceSyntax.synCvv (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv x) (SemanticCore.Class.cv y))))

Checked nominal proof certificate identified upstream as nominal_df_addcfn.

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