Nominal proof certificates grouped in dependency order.

Certificates from NAR4C062C001Part004.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0000 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy022, nb062AlphaDummy025 r a), (nb062AlphaDummy021, nb062AlphaDummy024 r a), (nb062AlphaDummy020, nb062AlphaDummy023 r a), (nb062AlphaDummy018, nb062AlphaDummy019 r a), (nb062AlphaDummy014, nb062AlphaDummy016 r a), (nb062AlphaDummy015, nb062AlphaDummy017 r a), (nb062AlphaDummy007, nb062AlphaDummy009 r a), (nb062AlphaDummy006, nb062AlphaDummy008 r a), (nb062AlphaDummy012, nb062AlphaDummy013 r a), (nb062AlphaDummy010, nb062AlphaDummy011 r a), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb062AlphaDummy021) (SemanticCore.Class.cv nb062AlphaDummy022)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy020) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb062AlphaDummy021) (SemanticCore.Class.cv nb062AlphaDummy022))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb062AlphaDummy024 r a)) (SemanticCore.Class.cv (nb062AlphaDummy025 r a))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy023 r a)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb062AlphaDummy024 r a)) (SemanticCore.Class.cv (nb062AlphaDummy025 r a)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0000.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0001 (x y r a : SemanticCore.Var) (dv_a_r : a ≠ r) : Nominal.TAlphaWff [(nb062AlphaDummy007, nb062AlphaDummy009 r a), (nb062AlphaDummy006, nb062AlphaDummy008 r a), (nb062AlphaDummy012, nb062AlphaDummy013 r a), (nb062AlphaDummy010, nb062AlphaDummy011 r a), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy007) (SemanticCore.Class.cv nb062AlphaDummy001)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy006) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy007))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy009 r a)) (SemanticCore.Class.cv r)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy008 r a)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy009 r a)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0001.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0002 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy022, nb062AlphaDummy025 r a), (nb062AlphaDummy021, nb062AlphaDummy024 r a), (nb062AlphaDummy020, nb062AlphaDummy023 r a), (nb062AlphaDummy018, nb062AlphaDummy019 r a), (nb062AlphaDummy014, nb062AlphaDummy016 r a), (nb062AlphaDummy015, nb062AlphaDummy017 r a), (nb062AlphaDummy040, nb062AlphaDummy041 r a), (nb062AlphaDummy038, nb062AlphaDummy039 r a), (nb062AlphaDummy007, nb062AlphaDummy009 r a), (nb062AlphaDummy006, nb062AlphaDummy008 r a), (nb062AlphaDummy036, nb062AlphaDummy037 r a), (nb062AlphaDummy010, nb062AlphaDummy011 r a), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb062AlphaDummy021) (SemanticCore.Class.cv nb062AlphaDummy022)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy020) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb062AlphaDummy021) (SemanticCore.Class.cv nb062AlphaDummy022))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb062AlphaDummy024 r a)) (SemanticCore.Class.cv (nb062AlphaDummy025 r a))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy023 r a)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb062AlphaDummy024 r a)) (SemanticCore.Class.cv (nb062AlphaDummy025 r a)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0002.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0003 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy040, nb062AlphaDummy041 r a), (nb062AlphaDummy038, nb062AlphaDummy039 r a), (nb062AlphaDummy007, nb062AlphaDummy009 r a), (nb062AlphaDummy006, nb062AlphaDummy008 r a), (nb062AlphaDummy036, nb062AlphaDummy037 r a), (nb062AlphaDummy010, nb062AlphaDummy011 r a), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy040) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy007))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy040) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy007))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy041 r a)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy009 r a)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy041 r a)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy009 r a)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0003.

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Certificates from NAR4C062C001Part005.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062PairOccurrence (x y r a : SemanticCore.Var) : Nominal.TAlphaClass [(nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] (SemanticCore.Class.cv nb062AlphaDummy004) (SemanticCore.Class.cv (nb062AlphaDummy005 x y r a))

Checked nominal proof certificate identified upstream as nb062_pair_occurrence.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0004 (x y r a : SemanticCore.Var) (dv_a_r : a ≠ r) : Nominal.TAlphaWff [(nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy004) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb062AlphaDummy001) (SemanticCore.Class.cv nb062AlphaDummy000))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy005 x y r a)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv r) (SemanticCore.Class.cv a)))

Checked nominal proof certificate identified upstream as nb062_split_alpha_0004.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0005 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy058, nb062AlphaDummy061 x y), (nb062AlphaDummy057, nb062AlphaDummy060 x y), (nb062AlphaDummy056, nb062AlphaDummy059 x y), (nb062AlphaDummy054, nb062AlphaDummy055 x y), (nb062AlphaDummy050, nb062AlphaDummy052 x y), (nb062AlphaDummy051, nb062AlphaDummy053 x y), (nb062AlphaDummy043, nb062AlphaDummy045 x y), (nb062AlphaDummy042, nb062AlphaDummy044 x y), (nb062AlphaDummy048, nb062AlphaDummy049 x y), (nb062AlphaDummy046, nb062AlphaDummy047 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb062AlphaDummy057) (SemanticCore.Class.cv nb062AlphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb062AlphaDummy057) (SemanticCore.Class.cv nb062AlphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb062AlphaDummy060 x y)) (SemanticCore.Class.cv (nb062AlphaDummy061 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy059 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb062AlphaDummy060 x y)) (SemanticCore.Class.cv (nb062AlphaDummy061 x y)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0005.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0006 (x y r a : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(nb062AlphaDummy043, nb062AlphaDummy045 x y), (nb062AlphaDummy042, nb062AlphaDummy044 x y), (nb062AlphaDummy048, nb062AlphaDummy049 x y), (nb062AlphaDummy046, nb062AlphaDummy047 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy043) (SemanticCore.Class.cv nb062AlphaDummy002)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy042) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy043))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy045 x y)) (SemanticCore.Class.cv x)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy044 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy045 x y)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0006.

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Certificates from NAR4C062C001Part006.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0007 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy058, nb062AlphaDummy061 x y), (nb062AlphaDummy057, nb062AlphaDummy060 x y), (nb062AlphaDummy056, nb062AlphaDummy059 x y), (nb062AlphaDummy054, nb062AlphaDummy055 x y), (nb062AlphaDummy050, nb062AlphaDummy052 x y), (nb062AlphaDummy051, nb062AlphaDummy053 x y), (nb062AlphaDummy076, nb062AlphaDummy077 x y), (nb062AlphaDummy074, nb062AlphaDummy075 x y), (nb062AlphaDummy043, nb062AlphaDummy045 x y), (nb062AlphaDummy042, nb062AlphaDummy044 x y), (nb062AlphaDummy072, nb062AlphaDummy073 x y), (nb062AlphaDummy046, nb062AlphaDummy047 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb062AlphaDummy057) (SemanticCore.Class.cv nb062AlphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb062AlphaDummy057) (SemanticCore.Class.cv nb062AlphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb062AlphaDummy060 x y)) (SemanticCore.Class.cv (nb062AlphaDummy061 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy059 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb062AlphaDummy060 x y)) (SemanticCore.Class.cv (nb062AlphaDummy061 x y)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0007.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0008 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy051, nb062AlphaDummy053 x y), (nb062AlphaDummy076, nb062AlphaDummy077 x y), (nb062AlphaDummy074, nb062AlphaDummy075 x y), (nb062AlphaDummy043, nb062AlphaDummy045 x y), (nb062AlphaDummy042, nb062AlphaDummy044 x y), (nb062AlphaDummy072, nb062AlphaDummy073 x y), (nb062AlphaDummy046, nb062AlphaDummy047 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] (SemanticCore.Wff.all nb062AlphaDummy050 (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy050) (SemanticCore.Class.cv nb062AlphaDummy043)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy051) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy050) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb062AlphaDummy050) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb062AlphaDummy050)))).neg) (SemanticCore.Wff.all (nb062AlphaDummy052 x y) (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy052 x y)) (SemanticCore.Class.cv (nb062AlphaDummy045 x y))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy053 x y)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy052 x y)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb062AlphaDummy052 x y)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb062AlphaDummy052 x y))))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0008.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0009 (x y r a : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(nb062AlphaDummy046, nb062AlphaDummy047 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy046) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab nb062AlphaDummy042 (Compiler.CompactSourceSyntax.synWrex nb062AlphaDummy043 (SemanticCore.Class.cv nb062AlphaDummy002) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy042) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy043))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy046) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab nb062AlphaDummy042 (Compiler.CompactSourceSyntax.synWrex nb062AlphaDummy043 (SemanticCore.Class.cv nb062AlphaDummy003) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy042) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy043)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy047 x y)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb062AlphaDummy044 x y) (Compiler.CompactSourceSyntax.synWrex (nb062AlphaDummy045 x y) (SemanticCore.Class.cv x) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy044 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy045 x y)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy047 x y)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb062AlphaDummy044 x y) (Compiler.CompactSourceSyntax.synWrex (nb062AlphaDummy045 x y) (SemanticCore.Class.cv y) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy044 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy045 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0009.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0010 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy094, nb062AlphaDummy097 x y), (nb062AlphaDummy093, nb062AlphaDummy096 x y), (nb062AlphaDummy092, nb062AlphaDummy095 x y), (nb062AlphaDummy090, nb062AlphaDummy091 x y), (nb062AlphaDummy086, nb062AlphaDummy088 x y), (nb062AlphaDummy087, nb062AlphaDummy089 x y), (nb062AlphaDummy079, nb062AlphaDummy081 x y), (nb062AlphaDummy078, nb062AlphaDummy080 x y), (nb062AlphaDummy084, nb062AlphaDummy085 x y), (nb062AlphaDummy082, nb062AlphaDummy083 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb062AlphaDummy093) (SemanticCore.Class.cv nb062AlphaDummy094)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy092) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb062AlphaDummy093) (SemanticCore.Class.cv nb062AlphaDummy094))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb062AlphaDummy096 x y)) (SemanticCore.Class.cv (nb062AlphaDummy097 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy095 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb062AlphaDummy096 x y)) (SemanticCore.Class.cv (nb062AlphaDummy097 x y)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0010.

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Certificates from NAR4C062C001Part007.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0011 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy079, nb062AlphaDummy081 x y), (nb062AlphaDummy078, nb062AlphaDummy080 x y), (nb062AlphaDummy084, nb062AlphaDummy085 x y), (nb062AlphaDummy082, nb062AlphaDummy083 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy079) (SemanticCore.Class.cv nb062AlphaDummy003)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy078) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy079))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy081 x y)) (SemanticCore.Class.cv y)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy080 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy081 x y)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0011.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0012 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy094, nb062AlphaDummy097 x y), (nb062AlphaDummy093, nb062AlphaDummy096 x y), (nb062AlphaDummy092, nb062AlphaDummy095 x y), (nb062AlphaDummy090, nb062AlphaDummy091 x y), (nb062AlphaDummy086, nb062AlphaDummy088 x y), (nb062AlphaDummy087, nb062AlphaDummy089 x y), (nb062AlphaDummy112, nb062AlphaDummy113 x y), (nb062AlphaDummy110, nb062AlphaDummy111 x y), (nb062AlphaDummy079, nb062AlphaDummy081 x y), (nb062AlphaDummy078, nb062AlphaDummy080 x y), (nb062AlphaDummy108, nb062AlphaDummy109 x y), (nb062AlphaDummy082, nb062AlphaDummy083 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb062AlphaDummy093) (SemanticCore.Class.cv nb062AlphaDummy094)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy092) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb062AlphaDummy093) (SemanticCore.Class.cv nb062AlphaDummy094))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb062AlphaDummy096 x y)) (SemanticCore.Class.cv (nb062AlphaDummy097 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy095 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb062AlphaDummy096 x y)) (SemanticCore.Class.cv (nb062AlphaDummy097 x y)))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0012.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0013 (x y r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb062AlphaDummy087, nb062AlphaDummy089 x y), (nb062AlphaDummy112, nb062AlphaDummy113 x y), (nb062AlphaDummy110, nb062AlphaDummy111 x y), (nb062AlphaDummy079, nb062AlphaDummy081 x y), (nb062AlphaDummy078, nb062AlphaDummy080 x y), (nb062AlphaDummy108, nb062AlphaDummy109 x y), (nb062AlphaDummy082, nb062AlphaDummy083 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] (SemanticCore.Wff.all nb062AlphaDummy086 (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy086) (SemanticCore.Class.cv nb062AlphaDummy079)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy087) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy086) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb062AlphaDummy086) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb062AlphaDummy086)))).neg) (SemanticCore.Wff.all (nb062AlphaDummy088 x y) (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy088 x y)) (SemanticCore.Class.cv (nb062AlphaDummy081 x y))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy089 x y)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy088 x y)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb062AlphaDummy088 x y)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb062AlphaDummy088 x y))))).neg)

Checked nominal proof certificate identified upstream as nb062_split_alpha_0013.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb062SplitAlpha0014 (x y r a : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(nb062AlphaDummy082, nb062AlphaDummy083 x y), (nb062AlphaDummy003, y), (nb062AlphaDummy002, x), (nb062AlphaDummy000, a), (nb062AlphaDummy001, r), (nb062AlphaDummy004, nb062AlphaDummy005 x y r a)] (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb062AlphaDummy082) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab nb062AlphaDummy078 (Compiler.CompactSourceSyntax.synWrex nb062AlphaDummy079 (SemanticCore.Class.cv nb062AlphaDummy002) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb062AlphaDummy078) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb062AlphaDummy079)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))) (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb062AlphaDummy083 x y)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (nb062AlphaDummy080 x y) (Compiler.CompactSourceSyntax.synWrex (nb062AlphaDummy081 x y) (SemanticCore.Class.cv x) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb062AlphaDummy080 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb062AlphaDummy081 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))))

Checked nominal proof certificate identified upstream as nb062_split_alpha_0014.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nominalDfAntisym (x y r a : SemanticCore.Var) (dv_a_r : a ≠ r) (dv_a_x : a ≠ x) (dv_a_y : a ≠ y) (dv_r_x : r ≠ x) (dv_r_y : r ≠ y) (dv_x_y : x ≠ y) : Nominal.NPrf (SemanticCore.Wff.classEq Compiler.CompactSourceSyntax.synCantisym (Compiler.CompactSourceSyntax.synCopab r a (Compiler.CompactSourceSyntax.synWral x (SemanticCore.Class.cv a) (Compiler.CompactSourceSyntax.synWral y (SemanticCore.Class.cv a) ((Compiler.CompactSourceSyntax.synWa (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv x) (SemanticCore.Class.cv r) (SemanticCore.Class.cv y)) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv y) (SemanticCore.Class.cv r) (SemanticCore.Class.cv x))).imp (SemanticCore.Wff.objEq x y))))))

Checked nominal proof certificate identified upstream as nominal_df_antisym.

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