NF weak partition development: NAR4H5C095M3Part037.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095WppRefl0275 (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.TReflOn [(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), (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

Checked nominal proof certificate identified upstream as nb095_wpp_refl_0275.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095WppRefl0275 x u D R S_cls f E dv_R_f dv_R_u dv_R_x = ⋯.reflOn

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0083 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) : Nominal.TAlphaWff [(nb095AlphaDummy585 D R S_cls E, nb095AlphaDummy586 x u D R S_cls f E), (nb095AlphaDummy583 D R S_cls E, nb095AlphaDummy584 x u D R S_cls f E), (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 (nb095AlphaDummy585 D R S_cls E)) (SemanticCore.Class.cab (nb095AlphaDummy579 D R S_cls E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy580 D R S_cls E) (SemanticCore.Class.cv (nb095AlphaDummy003 D R S_cls E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy579 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy580 D R S_cls E))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy585 D R S_cls E)) (SemanticCore.Class.cab (nb095AlphaDummy579 D R S_cls E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy580 D R S_cls E) (SemanticCore.Class.cv (nb095AlphaDummy003 D R S_cls E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy579 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy580 D R S_cls E))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy586 x u D R S_cls f E)) (SemanticCore.Class.cab (nb095AlphaDummy581 x u D R S_cls f E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy582 x u D R S_cls f E) (SemanticCore.Class.cv (nb095AlphaDummy005 x u D R S_cls f E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy581 x u D R S_cls f E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy582 x u D R S_cls f E))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy586 x u D R S_cls f E)) (SemanticCore.Class.cab (nb095AlphaDummy581 x u D R S_cls f E) (Compiler.CompactSourceSyntax.synWrex (nb095AlphaDummy582 x u D R S_cls f E) (SemanticCore.Class.cv (nb095AlphaDummy005 x u D R S_cls f E)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy581 x u D R S_cls f E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy582 x u D R S_cls f E))))))).neg)

Checked nominal proof certificate identified upstream as nb095_split_alpha_0083.

Equations

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

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0084 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) : Nominal.TAlphaWff [(nb095AlphaDummy580 D R S_cls E, nb095AlphaDummy582 x u D R S_cls f E), (nb095AlphaDummy579 D R S_cls E, nb095AlphaDummy581 x u D R S_cls f E), (nb095AlphaDummy609 D R S_cls E, nb095AlphaDummy610 x u D R S_cls f E), (nb095AlphaDummy583 D R S_cls E, nb095AlphaDummy584 x u D R S_cls f E), (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 (nb095AlphaDummy580 D R S_cls E)) (SemanticCore.Class.cv (nb095AlphaDummy004 D R S_cls E))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy579 D R S_cls E)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy580 D R S_cls E))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy582 x u D R S_cls f E)) (SemanticCore.Class.cv (nb095AlphaDummy006 x u D R S_cls f E))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy581 x u D R S_cls f E)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy582 x u D R S_cls f E))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg)

Checked nominal proof certificate identified upstream as nb095_split_alpha_0084.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0052 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy617 D R S_cls E ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0053 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy618 x D R ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0054 (D R S_cls E : SemanticCore.Class) : nb095AlphaDummy615 D R S_cls E ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_focused_notmem_0055 (x : SemanticCore.Var) (D R : SemanticCore.Class) : nb095AlphaDummy616 x D R ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_compact_envfresh_0290 (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 [(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)] R.fv