Nominal proof certificates grouped in dependency order.

Certificates from NAR4C090C001Part100.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0078 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) (dv_h_v : h ≠ v) : Nominal.TAlphaWff [(nb090AlphaDummy387 A, nb090AlphaDummy388 v), (nb090AlphaDummy385 A, nb090AlphaDummy386 v), (nb090AlphaDummy373 A, nb090AlphaDummy374 v), (nb090AlphaDummy375 A, nb090AlphaDummy376 v), (nb090AlphaDummy378 A, nb090AlphaDummy380 v), (nb090AlphaDummy377 A, nb090AlphaDummy379 v), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy387 A)) (SemanticCore.Class.cab (nb090AlphaDummy381 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy382 A) (SemanticCore.Class.cv (nb090AlphaDummy002 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy381 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy382 A))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy387 A)) (SemanticCore.Class.cab (nb090AlphaDummy381 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy382 A) (SemanticCore.Class.cv (nb090AlphaDummy002 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy381 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy382 A))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy388 v)) (SemanticCore.Class.cab (nb090AlphaDummy383 v) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy384 v) (SemanticCore.Class.cv v) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy383 v)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy384 v))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy388 v)) (SemanticCore.Class.cab (nb090AlphaDummy383 v) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy384 v) (SemanticCore.Class.cv v) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy383 v)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy384 v))))))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0078.

Equations

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

Certificates from NAR4C090C001Part101.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0079 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TAlphaWff [(nb090AlphaDummy413 A, nb090AlphaDummy414 v), (nb090AlphaDummy382 A, nb090AlphaDummy384 v), (nb090AlphaDummy381 A, nb090AlphaDummy383 v), (nb090AlphaDummy411 A, nb090AlphaDummy412 v), (nb090AlphaDummy385 A, nb090AlphaDummy386 v), (nb090AlphaDummy373 A, nb090AlphaDummy374 v), (nb090AlphaDummy375 A, nb090AlphaDummy376 v), (nb090AlphaDummy378 A, nb090AlphaDummy380 v), (nb090AlphaDummy377 A, nb090AlphaDummy379 v), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy413 A)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy382 A))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy413 A)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy414 v)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy384 v))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy414 v)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0079.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_envfresh_0267 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TEnvFresh [(nb090AlphaDummy373 A, nb090AlphaDummy374 v), (nb090AlphaDummy375 A, nb090AlphaDummy376 v), (nb090AlphaDummy378 A, nb090AlphaDummy380 v), (nb090AlphaDummy377 A, nb090AlphaDummy379 v), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] Compiler.CompactSourceSyntax.synC2nd.fv

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0267 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TReflOn [(nb090AlphaDummy373 A, nb090AlphaDummy374 v), (nb090AlphaDummy375 A, nb090AlphaDummy376 v), (nb090AlphaDummy378 A, nb090AlphaDummy380 v), (nb090AlphaDummy377 A, nb090AlphaDummy379 v), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] Compiler.CompactSourceSyntax.synC2nd.fv

Checked nominal proof certificate identified upstream as nb090_wpp_refl_0267.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0267 v u A h = ⋯.reflOn

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_fv_empty_0462 (A : SemanticCore.Class) : nb090AlphaDummy041 A ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_fv_empty_0463 (v u h : SemanticCore.Var) : nb090AlphaDummy043 v u h ∉ ∅