Nominal proof certificates grouped in dependency order.

Certificates from NAR4C061C001Part003.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0000 (x r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb061AlphaDummy021, nb061AlphaDummy024 r a), (nb061AlphaDummy020, nb061AlphaDummy023 r a), (nb061AlphaDummy019, nb061AlphaDummy022 r a), (nb061AlphaDummy017, nb061AlphaDummy018 r a), (nb061AlphaDummy013, nb061AlphaDummy015 r a), (nb061AlphaDummy014, nb061AlphaDummy016 r a), (nb061AlphaDummy006, nb061AlphaDummy008 r a), (nb061AlphaDummy005, nb061AlphaDummy007 r a), (nb061AlphaDummy011, nb061AlphaDummy012 r a), (nb061AlphaDummy009, nb061AlphaDummy010 r a), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb061AlphaDummy020) (SemanticCore.Class.cv nb061AlphaDummy021)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb061AlphaDummy019) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb061AlphaDummy020) (SemanticCore.Class.cv nb061AlphaDummy021))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb061AlphaDummy023 r a)) (SemanticCore.Class.cv (nb061AlphaDummy024 r a))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb061AlphaDummy022 r a)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb061AlphaDummy023 r a)) (SemanticCore.Class.cv (nb061AlphaDummy024 r a)))).neg)

Checked nominal proof certificate identified upstream as nb061_split_alpha_0000.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0001 (x r a : SemanticCore.Var) (dv_a_r : a ≠ r) : Nominal.TAlphaWff [(nb061AlphaDummy006, nb061AlphaDummy008 r a), (nb061AlphaDummy005, nb061AlphaDummy007 r a), (nb061AlphaDummy011, nb061AlphaDummy012 r a), (nb061AlphaDummy009, nb061AlphaDummy010 r a), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb061AlphaDummy006) (SemanticCore.Class.cv nb061AlphaDummy001)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb061AlphaDummy005) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb061AlphaDummy006))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb061AlphaDummy008 r a)) (SemanticCore.Class.cv r)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb061AlphaDummy007 r a)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb061AlphaDummy008 r a)))).neg)

Checked nominal proof certificate identified upstream as nb061_split_alpha_0001.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0002 (x r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb061AlphaDummy021, nb061AlphaDummy024 r a), (nb061AlphaDummy020, nb061AlphaDummy023 r a), (nb061AlphaDummy019, nb061AlphaDummy022 r a), (nb061AlphaDummy017, nb061AlphaDummy018 r a), (nb061AlphaDummy013, nb061AlphaDummy015 r a), (nb061AlphaDummy014, nb061AlphaDummy016 r a), (nb061AlphaDummy039, nb061AlphaDummy040 r a), (nb061AlphaDummy037, nb061AlphaDummy038 r a), (nb061AlphaDummy006, nb061AlphaDummy008 r a), (nb061AlphaDummy005, nb061AlphaDummy007 r a), (nb061AlphaDummy035, nb061AlphaDummy036 r a), (nb061AlphaDummy009, nb061AlphaDummy010 r a), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb061AlphaDummy020) (SemanticCore.Class.cv nb061AlphaDummy021)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb061AlphaDummy019) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb061AlphaDummy020) (SemanticCore.Class.cv nb061AlphaDummy021))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb061AlphaDummy023 r a)) (SemanticCore.Class.cv (nb061AlphaDummy024 r a))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb061AlphaDummy022 r a)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb061AlphaDummy023 r a)) (SemanticCore.Class.cv (nb061AlphaDummy024 r a)))).neg)

Checked nominal proof certificate identified upstream as nb061_split_alpha_0002.

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Certificates from NAR4C061C001Part004.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0003 (x r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb061AlphaDummy039, nb061AlphaDummy040 r a), (nb061AlphaDummy037, nb061AlphaDummy038 r a), (nb061AlphaDummy006, nb061AlphaDummy008 r a), (nb061AlphaDummy005, nb061AlphaDummy007 r a), (nb061AlphaDummy035, nb061AlphaDummy036 r a), (nb061AlphaDummy009, nb061AlphaDummy010 r a), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb061AlphaDummy039) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb061AlphaDummy006))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb061AlphaDummy039) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb061AlphaDummy006))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb061AlphaDummy040 r a)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb061AlphaDummy008 r a)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb061AlphaDummy040 r a)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb061AlphaDummy008 r a)))).neg)

Checked nominal proof certificate identified upstream as nb061_split_alpha_0003.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0004 (x r a : SemanticCore.Var) (dv_a_r : a ≠ r) : Nominal.TAlphaWff [(nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb061AlphaDummy003) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb061AlphaDummy001) (SemanticCore.Class.cv nb061AlphaDummy000))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb061AlphaDummy004 x r a)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv r) (SemanticCore.Class.cv a)))

Checked nominal proof certificate identified upstream as nb061_split_alpha_0004.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0005 (x r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb061AlphaDummy057, nb061AlphaDummy060 x), (nb061AlphaDummy056, nb061AlphaDummy059 x), (nb061AlphaDummy055, nb061AlphaDummy058 x), (nb061AlphaDummy053, nb061AlphaDummy054 x), (nb061AlphaDummy049, nb061AlphaDummy051 x), (nb061AlphaDummy050, nb061AlphaDummy052 x), (nb061AlphaDummy042, nb061AlphaDummy044 x), (nb061AlphaDummy041, nb061AlphaDummy043 x), (nb061AlphaDummy047, nb061AlphaDummy048 x), (nb061AlphaDummy045, nb061AlphaDummy046 x), (nb061AlphaDummy002, x), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb061AlphaDummy056) (SemanticCore.Class.cv nb061AlphaDummy057)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb061AlphaDummy055) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb061AlphaDummy056) (SemanticCore.Class.cv nb061AlphaDummy057))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb061AlphaDummy059 x)) (SemanticCore.Class.cv (nb061AlphaDummy060 x))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb061AlphaDummy058 x)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb061AlphaDummy059 x)) (SemanticCore.Class.cv (nb061AlphaDummy060 x)))).neg)

Checked nominal proof certificate identified upstream as nb061_split_alpha_0005.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0006 (x r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb061AlphaDummy042, nb061AlphaDummy044 x), (nb061AlphaDummy041, nb061AlphaDummy043 x), (nb061AlphaDummy047, nb061AlphaDummy048 x), (nb061AlphaDummy045, nb061AlphaDummy046 x), (nb061AlphaDummy002, x), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb061AlphaDummy042) (SemanticCore.Class.cv nb061AlphaDummy002)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb061AlphaDummy041) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb061AlphaDummy042))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb061AlphaDummy044 x)) (SemanticCore.Class.cv x)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb061AlphaDummy043 x)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb061AlphaDummy044 x)))).neg)

Checked nominal proof certificate identified upstream as nb061_split_alpha_0006.

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Certificates from NAR4C061C001Part005.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0007 (x r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb061AlphaDummy057, nb061AlphaDummy060 x), (nb061AlphaDummy056, nb061AlphaDummy059 x), (nb061AlphaDummy055, nb061AlphaDummy058 x), (nb061AlphaDummy053, nb061AlphaDummy054 x), (nb061AlphaDummy049, nb061AlphaDummy051 x), (nb061AlphaDummy050, nb061AlphaDummy052 x), (nb061AlphaDummy075, nb061AlphaDummy076 x), (nb061AlphaDummy073, nb061AlphaDummy074 x), (nb061AlphaDummy042, nb061AlphaDummy044 x), (nb061AlphaDummy041, nb061AlphaDummy043 x), (nb061AlphaDummy071, nb061AlphaDummy072 x), (nb061AlphaDummy045, nb061AlphaDummy046 x), (nb061AlphaDummy002, x), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb061AlphaDummy056) (SemanticCore.Class.cv nb061AlphaDummy057)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb061AlphaDummy055) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb061AlphaDummy056) (SemanticCore.Class.cv nb061AlphaDummy057))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb061AlphaDummy059 x)) (SemanticCore.Class.cv (nb061AlphaDummy060 x))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb061AlphaDummy058 x)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb061AlphaDummy059 x)) (SemanticCore.Class.cv (nb061AlphaDummy060 x)))).neg)

Checked nominal proof certificate identified upstream as nb061_split_alpha_0007.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0008 (x r a : SemanticCore.Var) : Nominal.TAlphaWff [(nb061AlphaDummy075, nb061AlphaDummy076 x), (nb061AlphaDummy073, nb061AlphaDummy074 x), (nb061AlphaDummy042, nb061AlphaDummy044 x), (nb061AlphaDummy041, nb061AlphaDummy043 x), (nb061AlphaDummy071, nb061AlphaDummy072 x), (nb061AlphaDummy045, nb061AlphaDummy046 x), (nb061AlphaDummy002, x), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb061AlphaDummy075) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb061AlphaDummy042))) (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb061AlphaDummy076 x)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb061AlphaDummy044 x))))

Checked nominal proof certificate identified upstream as nb061_split_alpha_0008.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb061SplitAlpha0009 (x r a : SemanticCore.Var) (dv_a_r : a ≠ r) (dv_r_x : r ≠ x) : Nominal.TAlphaWff [(nb061AlphaDummy002, x), (nb061AlphaDummy000, a), (nb061AlphaDummy001, r), (nb061AlphaDummy003, nb061AlphaDummy004 x r a)] (SemanticCore.Wff.classMem (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb061AlphaDummy002) (SemanticCore.Class.cv nb061AlphaDummy002)) (SemanticCore.Class.cv nb061AlphaDummy001)) (SemanticCore.Wff.classMem (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv x) (SemanticCore.Class.cv x)) (SemanticCore.Class.cv r))

Checked nominal proof certificate identified upstream as nb061_split_alpha_0009.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nominalDfRef (x r a : SemanticCore.Var) (dv_a_r : a ≠ r) (dv_a_x : a ≠ x) (dv_r_x : r ≠ x) : Nominal.NPrf (SemanticCore.Wff.classEq Compiler.CompactSourceSyntax.synCref (Compiler.CompactSourceSyntax.synCopab r a (Compiler.CompactSourceSyntax.synWral x (SemanticCore.Class.cv a) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv x) (SemanticCore.Class.cv r) (SemanticCore.Class.cv x)))))

Checked nominal proof certificate identified upstream as nominal_df_ref.

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