NF weak partition development: NAR4H5C095M3Part039.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0087 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) : Nominal.TAlphaWff [(nb095AlphaDummy261 D R S_cls E, nb095AlphaDummy262 x R), (nb095AlphaDummy259 D R S_cls E, nb095AlphaDummy260 x R), (nb095AlphaDummy250 D R S_cls E, nb095AlphaDummy252 x R), (nb095AlphaDummy249 D R S_cls E, nb095AlphaDummy251 x R), (nb095AlphaDummy247 D R S_cls E, nb095AlphaDummy248 x D R), (nb095AlphaDummy245 D R S_cls E, nb095AlphaDummy246 x D R), (nb095AlphaDummy620 D R S_cls E, nb095AlphaDummy622 x D R), (nb095AlphaDummy619 D R S_cls E, nb095AlphaDummy621 x D R), (nb095AlphaDummy623 D R S_cls E, nb095AlphaDummy624 x D R), (nb095AlphaDummy617 D R S_cls E, nb095AlphaDummy618 x D R), (nb095AlphaDummy615 D R S_cls E, nb095AlphaDummy616 x D R), (nb095AlphaDummy004 D R S_cls E, nb095AlphaDummy006 x u D R S_cls f E), (nb095AlphaDummy003 D R S_cls E, nb095AlphaDummy005 x u D R S_cls f E), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy261 D R S_cls E)) (SemanticCore.Class.cab (nb095AlphaDummy255 D R S_cls E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy256 D R S_cls E) (SemanticCore.Class.cv (nb095AlphaDummy250 D R S_cls E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy255 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy256 D R S_cls E))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy261 D R S_cls E)) (SemanticCore.Class.cab (nb095AlphaDummy255 D R S_cls E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy256 D R S_cls E) (SemanticCore.Class.cv (nb095AlphaDummy250 D R S_cls E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy255 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy256 D R S_cls E))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy262 x R)) (SemanticCore.Class.cab (nb095AlphaDummy257 x R) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy258 x R) (SemanticCore.Class.cv (nb095AlphaDummy252 x R)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy257 x R)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy258 x R))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy262 x R)) (SemanticCore.Class.cab (nb095AlphaDummy257 x R) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy258 x R) (SemanticCore.Class.cv (nb095AlphaDummy252 x R)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy257 x R)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy258 x R))))))).neg)

Checked nominal proof certificate identified upstream as nb095_split_alpha_0087.

Equations

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

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0088 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) : Nominal.TAlphaWff [(nb095AlphaDummy289 D R S_cls E, nb095AlphaDummy290 x R), (nb095AlphaDummy287 D R S_cls E, nb095AlphaDummy288 x R), (nb095AlphaDummy256 D R S_cls E, nb095AlphaDummy258 x R), (nb095AlphaDummy255 D R S_cls E, nb095AlphaDummy257 x R), (nb095AlphaDummy285 D R S_cls E, nb095AlphaDummy286 x R), (nb095AlphaDummy259 D R S_cls E, nb095AlphaDummy260 x R), (nb095AlphaDummy250 D R S_cls E, nb095AlphaDummy252 x R), (nb095AlphaDummy249 D R S_cls E, nb095AlphaDummy251 x R), (nb095AlphaDummy247 D R S_cls E, nb095AlphaDummy248 x D R), (nb095AlphaDummy245 D R S_cls E, nb095AlphaDummy246 x D R), (nb095AlphaDummy620 D R S_cls E, nb095AlphaDummy622 x D R), (nb095AlphaDummy619 D R S_cls E, nb095AlphaDummy621 x D R), (nb095AlphaDummy623 D R S_cls E, nb095AlphaDummy624 x D R), (nb095AlphaDummy617 D R S_cls E, nb095AlphaDummy618 x D R), (nb095AlphaDummy615 D R S_cls E, nb095AlphaDummy616 x D R), (nb095AlphaDummy004 D R S_cls E, nb095AlphaDummy006 x u D R S_cls f E), (nb095AlphaDummy003 D R S_cls E, nb095AlphaDummy005 x u D R S_cls f E), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy289 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy256 D R S_cls E)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy289 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy256 D R S_cls E)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy290 x R)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy258 x R)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy290 x R)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy258 x R)))).neg)

Checked nominal proof certificate identified upstream as nb095_split_alpha_0088.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0066 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy620 D R S_cls E ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1716 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy620 D R S_cls E ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0067 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy622 x D R ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1717 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy622 x D R ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0068 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy619 D R S_cls E ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1718 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy619 D R S_cls E ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0069 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy621 x D R ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1719 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy621 x D R ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0070 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy623 D R S_cls E ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1720 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy623 D R S_cls E ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0071 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy624 x D R ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1721 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy624 x D R ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1722 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy617 D R S_cls E ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1723 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy618 x D R ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1724 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy615 D R S_cls E ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1725 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy616 x D R ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_compact_envfresh_0306 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) (dv_R_f : f ∉ R.fv) (dv_R_u : u ∉ R.fv) (dv_R_x : x ∉ R.fv) : Nominal.TEnvFresh [(nb095AlphaDummy250 D R S_cls E, nb095AlphaDummy252 x R), (nb095AlphaDummy249 D R S_cls E, nb095AlphaDummy251 x R), (nb095AlphaDummy247 D R S_cls E, nb095AlphaDummy248 x D R), (nb095AlphaDummy245 D R S_cls E, nb095AlphaDummy246 x D R), (nb095AlphaDummy620 D R S_cls E, nb095AlphaDummy622 x D R), (nb095AlphaDummy619 D R S_cls E, nb095AlphaDummy621 x D R), (nb095AlphaDummy623 D R S_cls E, nb095AlphaDummy624 x D R), (nb095AlphaDummy617 D R S_cls E, nb095AlphaDummy618 x D R), (nb095AlphaDummy615 D R S_cls E, nb095AlphaDummy616 x D R), (nb095AlphaDummy004 D R S_cls E, nb095AlphaDummy006 x u D R S_cls f E), (nb095AlphaDummy003 D R S_cls E, nb095AlphaDummy005 x u D R S_cls f E), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv