Nominal proof certificates grouped in dependency order.

Certificates from NAR4C078C001Part105.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078SplitAlpha0079 (x y g : SemanticCore.Var) : Nominal.TAlphaWff [(nb078AlphaDummy415, nb078AlphaDummy416 g), (nb078AlphaDummy413, nb078AlphaDummy414 g), (nb078AlphaDummy368, nb078AlphaDummy370 g), (nb078AlphaDummy367, nb078AlphaDummy369 g), (nb078AlphaDummy371, nb078AlphaDummy372 g), (nb078AlphaDummy571, nb078AlphaDummy574 g), (nb078AlphaDummy570, nb078AlphaDummy573 g), (nb078AlphaDummy569, nb078AlphaDummy572 g), (nb078AlphaDummy575, nb078AlphaDummy576 g), (nb078AlphaDummy567, nb078AlphaDummy568 g), (nb078AlphaDummy565, nb078AlphaDummy566 g), (nb078AlphaDummy001, g), (nb078AlphaDummy004, y), (nb078AlphaDummy003, x)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb078AlphaDummy415) (SemanticCore.Class.cab nb078AlphaDummy409 (Compiler.CompactSourceSyntax.synWrex nb078AlphaDummy410 (SemanticCore.Class.cv nb078AlphaDummy368) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb078AlphaDummy409) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb078AlphaDummy410)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb078AlphaDummy415) (SemanticCore.Class.cab nb078AlphaDummy409 (Compiler.CompactSourceSyntax.synWrex nb078AlphaDummy410 (SemanticCore.Class.cv nb078AlphaDummy368) (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb078AlphaDummy409) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb078AlphaDummy410)))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb078AlphaDummy416 g)) (SemanticCore.Class.cab (nb078AlphaDummy411 g) (Compiler.CompactSourceSyntax.synWrex (nb078AlphaDummy412 g) (SemanticCore.Class.cv (nb078AlphaDummy370 g)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb078AlphaDummy411 g)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb078AlphaDummy412 g))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb078AlphaDummy416 g)) (SemanticCore.Class.cab (nb078AlphaDummy411 g) (Compiler.CompactSourceSyntax.synWrex (nb078AlphaDummy412 g) (SemanticCore.Class.cv (nb078AlphaDummy370 g)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb078AlphaDummy411 g)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb078AlphaDummy412 g))))))).neg)

Checked nominal proof certificate identified upstream as nb078_split_alpha_0079.

Equations

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Certificates from NAR4C078C001Part106.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078SplitAlpha0080 (x y g : SemanticCore.Var) : Nominal.TAlphaWff [(nb078AlphaDummy443, nb078AlphaDummy444 g), (nb078AlphaDummy441, nb078AlphaDummy442 g), (nb078AlphaDummy410, nb078AlphaDummy412 g), (nb078AlphaDummy409, nb078AlphaDummy411 g), (nb078AlphaDummy439, nb078AlphaDummy440 g), (nb078AlphaDummy413, nb078AlphaDummy414 g), (nb078AlphaDummy368, nb078AlphaDummy370 g), (nb078AlphaDummy367, nb078AlphaDummy369 g), (nb078AlphaDummy371, nb078AlphaDummy372 g), (nb078AlphaDummy571, nb078AlphaDummy574 g), (nb078AlphaDummy570, nb078AlphaDummy573 g), (nb078AlphaDummy569, nb078AlphaDummy572 g), (nb078AlphaDummy575, nb078AlphaDummy576 g), (nb078AlphaDummy567, nb078AlphaDummy568 g), (nb078AlphaDummy565, nb078AlphaDummy566 g), (nb078AlphaDummy001, g), (nb078AlphaDummy004, y), (nb078AlphaDummy003, x)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb078AlphaDummy443) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb078AlphaDummy410))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb078AlphaDummy443) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb078AlphaDummy410))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb078AlphaDummy444 g)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb078AlphaDummy412 g)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb078AlphaDummy444 g)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb078AlphaDummy412 g)))).neg)

Checked nominal proof certificate identified upstream as nb078_split_alpha_0080.

Equations

• One or more equations did not get rendered due to their size.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078SplitAlpha0081 (x y g : SemanticCore.Var) : Nominal.TAlphaWff [(nb078AlphaDummy570, nb078AlphaDummy573 g), (nb078AlphaDummy569, nb078AlphaDummy572 g), (nb078AlphaDummy575, nb078AlphaDummy576 g), (nb078AlphaDummy567, nb078AlphaDummy568 g), (nb078AlphaDummy565, nb078AlphaDummy566 g), (nb078AlphaDummy001, g), (nb078AlphaDummy004, y), (nb078AlphaDummy003, x)] ((SemanticCore.Wff.classEq (SemanticCore.Class.cv nb078AlphaDummy575) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb078AlphaDummy569) (SemanticCore.Class.cv nb078AlphaDummy570))).imp (Compiler.CompactSourceSyntax.synWex nb078AlphaDummy571 (Compiler.CompactSourceSyntax.synWa (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv nb078AlphaDummy569) (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv nb078AlphaDummy001))) (SemanticCore.Class.cv nb078AlphaDummy571)) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv nb078AlphaDummy571) (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv nb078AlphaDummy001)) (SemanticCore.Class.cv nb078AlphaDummy570)))).neg) ((SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb078AlphaDummy576 g)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv (nb078AlphaDummy572 g)) (SemanticCore.Class.cv (nb078AlphaDummy573 g)))).imp (Compiler.CompactSourceSyntax.synWex (nb078AlphaDummy574 g) (Compiler.CompactSourceSyntax.synWa (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb078AlphaDummy572 g)) (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv g))) (SemanticCore.Class.cv (nb078AlphaDummy574 g))) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb078AlphaDummy574 g)) (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv g)) (SemanticCore.Class.cv (nb078AlphaDummy573 g))))).neg)

Checked nominal proof certificate identified upstream as nb078_split_alpha_0081.

Equations

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theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078_wpp_notmem_1930 : nb078AlphaDummy567 ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078_wpp_notmem_1931 (g : SemanticCore.Var) : nb078AlphaDummy568 g ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078_wpp_notmem_1932 : nb078AlphaDummy565 ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078_wpp_notmem_1933 (g : SemanticCore.Var) : nb078AlphaDummy566 g ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078_compact_envfresh_0273 (x y g : SemanticCore.Var) : Nominal.TEnvFresh [(nb078AlphaDummy567, nb078AlphaDummy568 g), (nb078AlphaDummy565, nb078AlphaDummy566 g), (nb078AlphaDummy001, g), (nb078AlphaDummy004, y), (nb078AlphaDummy003, x)] Compiler.CompactSourceSyntax.synCid.fv

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078WppRefl0273 (x y g : SemanticCore.Var) : Nominal.TReflOn [(nb078AlphaDummy567, nb078AlphaDummy568 g), (nb078AlphaDummy565, nb078AlphaDummy566 g), (nb078AlphaDummy001, g), (nb078AlphaDummy004, y), (nb078AlphaDummy003, x)] Compiler.CompactSourceSyntax.synCid.fv

Checked nominal proof certificate identified upstream as nb078_wpp_refl_0273.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb078WppRefl0273 x y g = ⋯.reflOn