Nominal proof certificates grouped in dependency order.

Certificates from NAR4C071C001Part005.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0005 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy061, nb071AlphaDummy062 x), (nb071AlphaDummy059, nb071AlphaDummy060 x), (nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy061) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv nb071AlphaDummy042)) Compiler.CompactSourceSyntax.synC1c)).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy061) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv nb071AlphaDummy042)) Compiler.CompactSourceSyntax.synC1c)).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy062 x)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv (nb071AlphaDummy044 x))) Compiler.CompactSourceSyntax.synC1c)).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy062 x)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv (nb071AlphaDummy044 x))) Compiler.CompactSourceSyntax.synC1c)).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0005.

Equations

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0006 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy087, nb071AlphaDummy090 x), (nb071AlphaDummy086, nb071AlphaDummy089 x), (nb071AlphaDummy085, nb071AlphaDummy088 x), (nb071AlphaDummy083, nb071AlphaDummy084 x), (nb071AlphaDummy079, nb071AlphaDummy081 x), (nb071AlphaDummy080, nb071AlphaDummy082 x), (nb071AlphaDummy072, nb071AlphaDummy074 x), (nb071AlphaDummy071, nb071AlphaDummy073 x), (nb071AlphaDummy077, nb071AlphaDummy078 x), (nb071AlphaDummy075, nb071AlphaDummy076 x), (nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb071AlphaDummy086) (SemanticCore.Class.cv nb071AlphaDummy087)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy085) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb071AlphaDummy086) (SemanticCore.Class.cv nb071AlphaDummy087))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb071AlphaDummy089 x)) (SemanticCore.Class.cv (nb071AlphaDummy090 x))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy088 x)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb071AlphaDummy089 x)) (SemanticCore.Class.cv (nb071AlphaDummy090 x)))).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0006.

Equations

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0007 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy079, nb071AlphaDummy081 x), (nb071AlphaDummy080, nb071AlphaDummy082 x), (nb071AlphaDummy072, nb071AlphaDummy074 x), (nb071AlphaDummy071, nb071AlphaDummy073 x), (nb071AlphaDummy077, nb071AlphaDummy078 x), (nb071AlphaDummy075, nb071AlphaDummy076 x), (nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy079) (SemanticCore.Class.cv nb071AlphaDummy072)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy080) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy079) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb071AlphaDummy079) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb071AlphaDummy079))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy081 x)) (SemanticCore.Class.cv (nb071AlphaDummy074 x))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy082 x)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy081 x)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb071AlphaDummy081 x)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb071AlphaDummy081 x)))).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0007.

Equations

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Certificates from NAR4C071C001Part006.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0008 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy087, nb071AlphaDummy090 x), (nb071AlphaDummy086, nb071AlphaDummy089 x), (nb071AlphaDummy085, nb071AlphaDummy088 x), (nb071AlphaDummy083, nb071AlphaDummy084 x), (nb071AlphaDummy079, nb071AlphaDummy081 x), (nb071AlphaDummy080, nb071AlphaDummy082 x), (nb071AlphaDummy105, nb071AlphaDummy106 x), (nb071AlphaDummy103, nb071AlphaDummy104 x), (nb071AlphaDummy072, nb071AlphaDummy074 x), (nb071AlphaDummy071, nb071AlphaDummy073 x), (nb071AlphaDummy101, nb071AlphaDummy102 x), (nb071AlphaDummy075, nb071AlphaDummy076 x), (nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb071AlphaDummy086) (SemanticCore.Class.cv nb071AlphaDummy087)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy085) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb071AlphaDummy086) (SemanticCore.Class.cv nb071AlphaDummy087))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb071AlphaDummy089 x)) (SemanticCore.Class.cv (nb071AlphaDummy090 x))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy088 x)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb071AlphaDummy089 x)) (SemanticCore.Class.cv (nb071AlphaDummy090 x)))).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0008.

Equations

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0009 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy079, nb071AlphaDummy081 x), (nb071AlphaDummy080, nb071AlphaDummy082 x), (nb071AlphaDummy105, nb071AlphaDummy106 x), (nb071AlphaDummy103, nb071AlphaDummy104 x), (nb071AlphaDummy072, nb071AlphaDummy074 x), (nb071AlphaDummy071, nb071AlphaDummy073 x), (nb071AlphaDummy101, nb071AlphaDummy102 x), (nb071AlphaDummy075, nb071AlphaDummy076 x), (nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy080) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy079) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv nb071AlphaDummy079) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv nb071AlphaDummy079))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy082 x)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy081 x)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (nb071AlphaDummy081 x)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (nb071AlphaDummy081 x))))

Checked nominal proof certificate identified upstream as nb071_split_alpha_0009.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0010 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy101, nb071AlphaDummy102 x), (nb071AlphaDummy075, nb071AlphaDummy076 x), (nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy101) (SemanticCore.Class.cab nb071AlphaDummy071 (Compiler.CompactSourceSyntax.synWrex nb071AlphaDummy072 (SemanticCore.Class.cv nb071AlphaDummy055) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy071) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb071AlphaDummy072)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy101) (SemanticCore.Class.cab nb071AlphaDummy071 (Compiler.CompactSourceSyntax.synWrex nb071AlphaDummy072 (SemanticCore.Class.cv nb071AlphaDummy055) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy071) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb071AlphaDummy072)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy102 x)) (SemanticCore.Class.cab (nb071AlphaDummy073 x) (Compiler.CompactSourceSyntax.synWrex (nb071AlphaDummy074 x) (SemanticCore.Class.cv (nb071AlphaDummy057 x)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy073 x)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb071AlphaDummy074 x))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy102 x)) (SemanticCore.Class.cab (nb071AlphaDummy073 x) (Compiler.CompactSourceSyntax.synWrex (nb071AlphaDummy074 x) (SemanticCore.Class.cv (nb071AlphaDummy057 x)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy073 x)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb071AlphaDummy074 x))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0010.

Equations

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theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0264 : nb071AlphaDummy056 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0265 (x : SemanticCore.Var) : nb071AlphaDummy058 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0266 : nb071AlphaDummy055 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0267 (x : SemanticCore.Var) : nb071AlphaDummy057 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0268 : nb071AlphaDummy042 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0269 (x : SemanticCore.Var) : nb071AlphaDummy044 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0270 : nb071AlphaDummy041 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0271 (x : SemanticCore.Var) : nb071AlphaDummy043 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0272 : nb071AlphaDummy045 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0273 (x : SemanticCore.Var) : nb071AlphaDummy046 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0274 : nb071AlphaDummy048 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0275 (x : SemanticCore.Var) : nb071AlphaDummy050 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0276 : nb071AlphaDummy047 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0277 (x : SemanticCore.Var) : nb071AlphaDummy049 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0278 : nb071AlphaDummy001 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0279 (x : SemanticCore.Var) : nb071AlphaDummy002 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0280 : nb071AlphaDummy000 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0281 (x : SemanticCore.Var) : x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0282 : nb071AlphaDummy003 ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0283 (x : SemanticCore.Var) : nb071AlphaDummy004 x ∉ Compiler.CompactSourceSyntax.synCen.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_envfresh_0017 (x : SemanticCore.Var) : Nominal.TEnvFresh [(nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] Compiler.CompactSourceSyntax.synCen.fv

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071WppRefl0017 (x : SemanticCore.Var) : Nominal.TReflOn [(nb071AlphaDummy056, nb071AlphaDummy058 x), (nb071AlphaDummy055, nb071AlphaDummy057 x), (nb071AlphaDummy042, nb071AlphaDummy044 x), (nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] Compiler.CompactSourceSyntax.synCen.fv

Checked nominal proof certificate identified upstream as nb071_wpp_refl_0017.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071WppRefl0017 x = ⋯.reflOn