Nominal proof certificates grouped in dependency order.

Certificates from NAR4C090C001Part034.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0010 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TAlphaWff [(nb090AlphaDummy241 A, nb090AlphaDummy242 h), (nb090AlphaDummy239 A, nb090AlphaDummy240 h), (nb090AlphaDummy208 A, nb090AlphaDummy210 h), (nb090AlphaDummy207 A, nb090AlphaDummy209 h), (nb090AlphaDummy237 A, nb090AlphaDummy238 h), (nb090AlphaDummy211 A, nb090AlphaDummy212 h), (nb090AlphaDummy051 A, nb090AlphaDummy054 h), (nb090AlphaDummy050 A, nb090AlphaDummy053 h), (nb090AlphaDummy049 A, nb090AlphaDummy052 h), (nb090AlphaDummy055 A, nb090AlphaDummy056 h), (nb090AlphaDummy047 A, nb090AlphaDummy048 h), (nb090AlphaDummy045 A, nb090AlphaDummy046 h), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy241 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy208 A)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy241 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy208 A)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy242 h)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy210 h)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy242 h)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy210 h)))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0010.

Equations

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

Certificates from NAR4C090C001Part035.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0011 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TAlphaWff [(nb090AlphaDummy050 A, nb090AlphaDummy053 h), (nb090AlphaDummy049 A, nb090AlphaDummy052 h), (nb090AlphaDummy055 A, nb090AlphaDummy056 h), (nb090AlphaDummy047 A, nb090AlphaDummy048 h), (nb090AlphaDummy045 A, nb090AlphaDummy046 h), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy055 A)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv (nb090AlphaDummy049 A)) (SemanticCore.Class.cv (nb090AlphaDummy050 A)))).imp (Compiler.CompactSourceSyntax.synWex (nb090AlphaDummy051 A) (Compiler.CompactSourceSyntax.synWa (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb090AlphaDummy049 A)) (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv (nb090AlphaDummy000 A))) (SemanticCore.Class.cv (nb090AlphaDummy051 A))) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb090AlphaDummy051 A)) (SemanticCore.Class.cv (nb090AlphaDummy000 A)) (SemanticCore.Class.cv (nb090AlphaDummy050 A))))).neg) ((SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy056 h)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv (nb090AlphaDummy052 h)) (SemanticCore.Class.cv (nb090AlphaDummy053 h)))).imp (Compiler.CompactSourceSyntax.synWex (nb090AlphaDummy054 h) (Compiler.CompactSourceSyntax.synWa (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb090AlphaDummy052 h)) (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv h)) (SemanticCore.Class.cv (nb090AlphaDummy054 h))) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb090AlphaDummy054 h)) (SemanticCore.Class.cv h) (SemanticCore.Class.cv (nb090AlphaDummy053 h))))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0011.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0602 (A : SemanticCore.Class) : nb090AlphaDummy047 A ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0603 (h : SemanticCore.Var) : nb090AlphaDummy048 h ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0604 (A : SemanticCore.Class) : nb090AlphaDummy045 A ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0605 (h : SemanticCore.Var) : nb090AlphaDummy046 h ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0606 (A : SemanticCore.Class) : nb090AlphaDummy000 A ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0607 (h : SemanticCore.Var) : h ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0608 (A : SemanticCore.Class) : nb090AlphaDummy002 A ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0609 (v : SemanticCore.Var) : v ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0610 (A : SemanticCore.Class) : nb090AlphaDummy001 A ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0611 (u : SemanticCore.Var) : u ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0612 (A : SemanticCore.Class) : nb090AlphaDummy003 A ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0613 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : nb090AlphaDummy004 v u A h ∉ Compiler.CompactSourceSyntax.synCid.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_envfresh_0043 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TEnvFresh [(nb090AlphaDummy047 A, nb090AlphaDummy048 h), (nb090AlphaDummy045 A, nb090AlphaDummy046 h), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] Compiler.CompactSourceSyntax.synCid.fv

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0043 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TReflOn [(nb090AlphaDummy047 A, nb090AlphaDummy048 h), (nb090AlphaDummy045 A, nb090AlphaDummy046 h), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] Compiler.CompactSourceSyntax.synCid.fv

Checked nominal proof certificate identified upstream as nb090_wpp_refl_0043.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0043 v u A h = ⋯.reflOn