NF weak partition development: NAR4H5C091M3BPart007.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb091SplitAlpha0010 (D R : SemanticCore.Class) (p : SemanticCore.Var) : Nominal.TAlphaWff [(nb091AlphaDummy153 D R, nb091AlphaDummy154 R p), (nb091AlphaDummy151 D R, nb091AlphaDummy152 R p), (nb091AlphaDummy120 D R, nb091AlphaDummy122 R p), (nb091AlphaDummy119 D R, nb091AlphaDummy121 R p), (nb091AlphaDummy149 D R, nb091AlphaDummy150 R p), (nb091AlphaDummy123 D R, nb091AlphaDummy124 R p), (nb091AlphaDummy106 D R, nb091AlphaDummy108 R p), (nb091AlphaDummy105 D R, nb091AlphaDummy107 R p), (nb091AlphaDummy103 D R, nb091AlphaDummy104 D R p), (nb091AlphaDummy101 D R, nb091AlphaDummy102 D R p), (nb091AlphaDummy048 D R, nb091AlphaDummy050 D R p), (nb091AlphaDummy047 D R, nb091AlphaDummy049 D R p), (nb091AlphaDummy177 D R, nb091AlphaDummy178 D R p), (nb091AlphaDummy051 D R, nb091AlphaDummy052 D R p), (nb091AlphaDummy045 D R, nb091AlphaDummy046 D R p), (nb091AlphaDummy042 D R, nb091AlphaDummy044 D R p), (nb091AlphaDummy041 D R, nb091AlphaDummy043 D R p), (nb091AlphaDummy001 D R, nb091AlphaDummy002 D R p), (nb091AlphaDummy000 D R, p), (nb091AlphaDummy003 D R, nb091AlphaDummy004 D R p)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb091AlphaDummy153 D R)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb091AlphaDummy120 D R)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb091AlphaDummy153 D R)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb091AlphaDummy120 D R)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb091AlphaDummy154 R p)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb091AlphaDummy122 R p)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb091AlphaDummy154 R p)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb091AlphaDummy122 R p)))).neg)

Checked nominal proof certificate identified upstream as nb091_split_alpha_0010.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb091_focused_notmem_0072 (D R : SemanticCore.Class) : nb091AlphaDummy177 D R ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb091_wpp_notmem_0480 (D R : SemanticCore.Class) : nb091AlphaDummy177 D R ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb091_focused_notmem_0073 (D R : SemanticCore.Class) (p : SemanticCore.Var) : nb091AlphaDummy178 D R p ∉ R.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb091_wpp_notmem_0481 (D R : SemanticCore.Class) (p : SemanticCore.Var) : nb091AlphaDummy178 D R p ∉ (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb091_compact_envfresh_0036 (D R : SemanticCore.Class) (p : SemanticCore.Var) (dv_R_p : p ∉ R.fv) : Nominal.TEnvFresh [(nb091AlphaDummy106 D R, nb091AlphaDummy108 R p), (nb091AlphaDummy105 D R, nb091AlphaDummy107 R p), (nb091AlphaDummy103 D R, nb091AlphaDummy104 D R p), (nb091AlphaDummy101 D R, nb091AlphaDummy102 D R p), (nb091AlphaDummy048 D R, nb091AlphaDummy050 D R p), (nb091AlphaDummy047 D R, nb091AlphaDummy049 D R p), (nb091AlphaDummy177 D R, nb091AlphaDummy178 D R p), (nb091AlphaDummy051 D R, nb091AlphaDummy052 D R p), (nb091AlphaDummy045 D R, nb091AlphaDummy046 D R p), (nb091AlphaDummy042 D R, nb091AlphaDummy044 D R p), (nb091AlphaDummy041 D R, nb091AlphaDummy043 D R p), (nb091AlphaDummy001 D R, nb091AlphaDummy002 D R p), (nb091AlphaDummy000 D R, p), (nb091AlphaDummy003 D R, nb091AlphaDummy004 D R p)] (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCdif R Compiler.CompactSourceSyntax.synCid)).fv