Nominal proof certificates grouped in dependency order.

Certificates from NAR4C052C001Part003.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0000 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb052AlphaDummy030, nb052AlphaDummy033 x y), (nb052AlphaDummy029, nb052AlphaDummy032 x y), (nb052AlphaDummy028, nb052AlphaDummy031 x y), (nb052AlphaDummy026, nb052AlphaDummy027 x y), (nb052AlphaDummy022, nb052AlphaDummy024 x y), (nb052AlphaDummy023, nb052AlphaDummy025 x y), (nb052AlphaDummy015, nb052AlphaDummy017 x y), (nb052AlphaDummy014, nb052AlphaDummy016 x y), (nb052AlphaDummy020, nb052AlphaDummy021 x y), (nb052AlphaDummy018, nb052AlphaDummy019 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb052AlphaDummy029) (SemanticCore.Class.cv nb052AlphaDummy030)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy028) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb052AlphaDummy029) (SemanticCore.Class.cv nb052AlphaDummy030))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb052AlphaDummy032 x y)) (SemanticCore.Class.cv (nb052AlphaDummy033 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy031 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb052AlphaDummy032 x y)) (SemanticCore.Class.cv (nb052AlphaDummy033 x y)))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0000.

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Certificates from NAR4C052C001Part004.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0001 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb052AlphaDummy015, nb052AlphaDummy017 x y), (nb052AlphaDummy014, nb052AlphaDummy016 x y), (nb052AlphaDummy020, nb052AlphaDummy021 x y), (nb052AlphaDummy018, nb052AlphaDummy019 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy014) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb052AlphaDummy015))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy016 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb052AlphaDummy017 x y))))

Checked nominal proof certificate identified upstream as nb052_split_alpha_0001.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0002 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb052AlphaDummy030, nb052AlphaDummy033 x y), (nb052AlphaDummy029, nb052AlphaDummy032 x y), (nb052AlphaDummy028, nb052AlphaDummy031 x y), (nb052AlphaDummy026, nb052AlphaDummy027 x y), (nb052AlphaDummy022, nb052AlphaDummy024 x y), (nb052AlphaDummy023, nb052AlphaDummy025 x y), (nb052AlphaDummy048, nb052AlphaDummy049 x y), (nb052AlphaDummy046, nb052AlphaDummy047 x y), (nb052AlphaDummy015, nb052AlphaDummy017 x y), (nb052AlphaDummy014, nb052AlphaDummy016 x y), (nb052AlphaDummy044, nb052AlphaDummy045 x y), (nb052AlphaDummy018, nb052AlphaDummy019 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb052AlphaDummy029) (SemanticCore.Class.cv nb052AlphaDummy030)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy028) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb052AlphaDummy029) (SemanticCore.Class.cv nb052AlphaDummy030))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb052AlphaDummy032 x y)) (SemanticCore.Class.cv (nb052AlphaDummy033 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy031 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb052AlphaDummy032 x y)) (SemanticCore.Class.cv (nb052AlphaDummy033 x y)))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0002.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0003 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb052AlphaDummy022, nb052AlphaDummy024 x y), (nb052AlphaDummy023, nb052AlphaDummy025 x y), (nb052AlphaDummy048, nb052AlphaDummy049 x y), (nb052AlphaDummy046, nb052AlphaDummy047 x y), (nb052AlphaDummy015, nb052AlphaDummy017 x y), (nb052AlphaDummy014, nb052AlphaDummy016 x y), (nb052AlphaDummy044, nb052AlphaDummy045 x y), (nb052AlphaDummy018, nb052AlphaDummy019 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy022) (SemanticCore.Class.cv nb052AlphaDummy015)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy023) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy022) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb052AlphaDummy022) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb052AlphaDummy022))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy024 x y)) (SemanticCore.Class.cv (nb052AlphaDummy017 x y))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy025 x y)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy024 x y)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb052AlphaDummy024 x y)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb052AlphaDummy024 x y)))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0003.

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Certificates from NAR4C052C001Part005.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052VariableOccurrence0 (x y : SemanticCore.Var) : Nominal.TAlphaClass [(nb052AlphaDummy015, nb052AlphaDummy017 x y), (nb052AlphaDummy014, nb052AlphaDummy016 x y), (nb052AlphaDummy044, nb052AlphaDummy045 x y), (nb052AlphaDummy018, nb052AlphaDummy019 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] (SemanticCore.Class.cv nb052AlphaDummy001) (SemanticCore.Class.cv y)

Checked nominal proof certificate identified upstream as nb052_variable_occurrence_0.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052_variable_occurrence_1 (x y : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaClass [(nb052AlphaDummy015, nb052AlphaDummy017 x y), (nb052AlphaDummy014, nb052AlphaDummy016 x y), (nb052AlphaDummy020, nb052AlphaDummy021 x y), (nb052AlphaDummy018, nb052AlphaDummy019 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] (SemanticCore.Class.cv nb052AlphaDummy000) (SemanticCore.Class.cv x)

Checked nominal proof certificate identified upstream as nb052_variable_occurrence_1.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0004 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb052AlphaDummy044, nb052AlphaDummy045 x y), (nb052AlphaDummy018, nb052AlphaDummy019 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy044) (SemanticCore.Class.cab nb052AlphaDummy014 (Compiler.CompactSourceSyntax.synWrex nb052AlphaDummy015 (SemanticCore.Class.cv nb052AlphaDummy001) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy014) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb052AlphaDummy015)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy044) (SemanticCore.Class.cab nb052AlphaDummy014 (Compiler.CompactSourceSyntax.synWrex nb052AlphaDummy015 (SemanticCore.Class.cv nb052AlphaDummy001) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy014) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb052AlphaDummy015)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy045 x y)) (SemanticCore.Class.cab (nb052AlphaDummy016 x y) (Compiler.CompactSourceSyntax.synWrex (nb052AlphaDummy017 x y) (SemanticCore.Class.cv y) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy016 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb052AlphaDummy017 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy045 x y)) (SemanticCore.Class.cab (nb052AlphaDummy016 x y) (Compiler.CompactSourceSyntax.synWrex (nb052AlphaDummy017 x y) (SemanticCore.Class.cv y) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy016 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb052AlphaDummy017 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0004.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0005 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb052AlphaDummy058, nb052AlphaDummy061 x y), (nb052AlphaDummy057, nb052AlphaDummy060 x y), (nb052AlphaDummy056, nb052AlphaDummy059 x y), (nb052AlphaDummy054, nb052AlphaDummy055 x y), (nb052AlphaDummy050, nb052AlphaDummy052 x y), (nb052AlphaDummy051, nb052AlphaDummy053 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb052AlphaDummy057) (SemanticCore.Class.cv nb052AlphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb052AlphaDummy057) (SemanticCore.Class.cv nb052AlphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb052AlphaDummy060 x y)) (SemanticCore.Class.cv (nb052AlphaDummy061 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy059 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb052AlphaDummy060 x y)) (SemanticCore.Class.cv (nb052AlphaDummy061 x y)))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0005.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0006 (x y : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy012, nb052AlphaDummy013 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy007) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb052AlphaDummy000) (SemanticCore.Class.cv nb052AlphaDummy001))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy006) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb052AlphaDummy007))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy009 x y)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv x) (SemanticCore.Class.cv y))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy008 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb052AlphaDummy009 x y)))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0006.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0007 (x y : SemanticCore.Var) : Nominal.TAlphaWff [(nb052AlphaDummy058, nb052AlphaDummy061 x y), (nb052AlphaDummy057, nb052AlphaDummy060 x y), (nb052AlphaDummy056, nb052AlphaDummy059 x y), (nb052AlphaDummy054, nb052AlphaDummy055 x y), (nb052AlphaDummy050, nb052AlphaDummy052 x y), (nb052AlphaDummy051, nb052AlphaDummy053 x y), (nb052AlphaDummy076, nb052AlphaDummy077 x y), (nb052AlphaDummy074, nb052AlphaDummy075 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy072, nb052AlphaDummy073 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb052AlphaDummy057) (SemanticCore.Class.cv nb052AlphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb052AlphaDummy057) (SemanticCore.Class.cv nb052AlphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb052AlphaDummy060 x y)) (SemanticCore.Class.cv (nb052AlphaDummy061 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy059 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb052AlphaDummy060 x y)) (SemanticCore.Class.cv (nb052AlphaDummy061 x y)))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0007.

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Certificates from NAR4C052C001Part006.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0008 (x y : SemanticCore.Var) : Nominal.TAlphaClass [(nb052AlphaDummy076, nb052AlphaDummy077 x y), (nb052AlphaDummy074, nb052AlphaDummy075 x y), (nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy072, nb052AlphaDummy073 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] (SemanticCore.Class.cab nb052AlphaDummy051 (Compiler.CompactSourceSyntax.synWrex nb052AlphaDummy050 (SemanticCore.Class.cv nb052AlphaDummy007) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy051) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy050) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb052AlphaDummy050) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb052AlphaDummy050))))) (SemanticCore.Class.cab (nb052AlphaDummy053 x y) (Compiler.CompactSourceSyntax.synWrex (nb052AlphaDummy052 x y) (SemanticCore.Class.cv (nb052AlphaDummy009 x y)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy053 x y)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy052 x y)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb052AlphaDummy052 x y)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb052AlphaDummy052 x y))))))

Checked nominal proof certificate identified upstream as nb052_split_alpha_0008.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052_variable_occurrence_2 (x y : SemanticCore.Var) : Nominal.TAlphaClass [(nb052AlphaDummy007, nb052AlphaDummy009 x y), (nb052AlphaDummy006, nb052AlphaDummy008 x y), (nb052AlphaDummy072, nb052AlphaDummy073 x y), (nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] (SemanticCore.Class.cv nb052AlphaDummy002) (SemanticCore.Class.cv (nb052AlphaDummy003 x y))

Checked nominal proof certificate identified upstream as nb052_variable_occurrence_2.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb052SplitAlpha0009 (x y : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(nb052AlphaDummy010, nb052AlphaDummy011 x y), (nb052AlphaDummy002, nb052AlphaDummy003 x y), (nb052AlphaDummy001, y), (nb052AlphaDummy000, x), (nb052AlphaDummy004, nb052AlphaDummy005 x y)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy010) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab nb052AlphaDummy006 (Compiler.CompactSourceSyntax.synWrex nb052AlphaDummy007 (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb052AlphaDummy000) (SemanticCore.Class.cv nb052AlphaDummy001)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy006) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb052AlphaDummy007))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb052AlphaDummy010) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab nb052AlphaDummy006 (Compiler.CompactSourceSyntax.synWrex nb052AlphaDummy007 (SemanticCore.Class.cv nb052AlphaDummy002) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb052AlphaDummy006) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb052AlphaDummy007)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy011 x y)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb052AlphaDummy008 x y) (Compiler.CompactSourceSyntax.synWrex (nb052AlphaDummy009 x y) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv x) (SemanticCore.Class.cv y)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy008 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb052AlphaDummy009 x y)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb052AlphaDummy011 x y)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb052AlphaDummy008 x y) (Compiler.CompactSourceSyntax.synWrex (nb052AlphaDummy009 x y) (SemanticCore.Class.cv (nb052AlphaDummy003 x y)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb052AlphaDummy008 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb052AlphaDummy009 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg)

Checked nominal proof certificate identified upstream as nb052_split_alpha_0009.

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

Checked nominal proof certificate identified upstream as nominal_df_cup.

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