Nominal proof certificates grouped in dependency order.

Certificates from NAR4C090C001Part104.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0082 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) (dv_h_u : h ≠ u) (dv_u_v : u ≠ v) : Nominal.TAlphaWff [(nb090AlphaDummy297 A, nb090AlphaDummy298 u), (nb090AlphaDummy295 A, nb090AlphaDummy296 u), (nb090AlphaDummy283 A, nb090AlphaDummy284 u), (nb090AlphaDummy285 A, nb090AlphaDummy286 u), (nb090AlphaDummy288 A, nb090AlphaDummy290 u), (nb090AlphaDummy287 A, nb090AlphaDummy289 u), (nb090AlphaDummy042 A, nb090AlphaDummy044 v u h), (nb090AlphaDummy041 A, nb090AlphaDummy043 v u h), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy297 A)) (SemanticCore.Class.cab (nb090AlphaDummy291 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy292 A) (SemanticCore.Class.cv (nb090AlphaDummy001 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy291 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy292 A))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy297 A)) (SemanticCore.Class.cab (nb090AlphaDummy291 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy292 A) (SemanticCore.Class.cv (nb090AlphaDummy001 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy291 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy292 A))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy298 u)) (SemanticCore.Class.cab (nb090AlphaDummy293 u) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy294 u) (SemanticCore.Class.cv u) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy293 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy294 u))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy298 u)) (SemanticCore.Class.cab (nb090AlphaDummy293 u) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy294 u) (SemanticCore.Class.cv u) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy293 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy294 u))))))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0082.

Equations

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

Certificates from NAR4C090C001Part105.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0083 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TAlphaWff [(nb090AlphaDummy325 A, nb090AlphaDummy326 u), (nb090AlphaDummy323 A, nb090AlphaDummy324 u), (nb090AlphaDummy292 A, nb090AlphaDummy294 u), (nb090AlphaDummy291 A, nb090AlphaDummy293 u), (nb090AlphaDummy321 A, nb090AlphaDummy322 u), (nb090AlphaDummy295 A, nb090AlphaDummy296 u), (nb090AlphaDummy283 A, nb090AlphaDummy284 u), (nb090AlphaDummy285 A, nb090AlphaDummy286 u), (nb090AlphaDummy288 A, nb090AlphaDummy290 u), (nb090AlphaDummy287 A, nb090AlphaDummy289 u), (nb090AlphaDummy042 A, nb090AlphaDummy044 v u h), (nb090AlphaDummy041 A, nb090AlphaDummy043 v u h), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy325 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy292 A)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy325 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy292 A)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy326 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy294 u)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy326 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy294 u)))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0083.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1606 (A : SemanticCore.Class) : nb090AlphaDummy042 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1607 (v u h : SemanticCore.Var) : nb090AlphaDummy044 v u h ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_envfresh_0283 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TEnvFresh [(nb090AlphaDummy283 A, nb090AlphaDummy284 u), (nb090AlphaDummy285 A, nb090AlphaDummy286 u), (nb090AlphaDummy288 A, nb090AlphaDummy290 u), (nb090AlphaDummy287 A, nb090AlphaDummy289 u), (nb090AlphaDummy042 A, nb090AlphaDummy044 v u h), (nb090AlphaDummy041 A, nb090AlphaDummy043 v u h), (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.nb090WppRefl0283 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TReflOn [(nb090AlphaDummy283 A, nb090AlphaDummy284 u), (nb090AlphaDummy285 A, nb090AlphaDummy286 u), (nb090AlphaDummy288 A, nb090AlphaDummy290 u), (nb090AlphaDummy287 A, nb090AlphaDummy289 u), (nb090AlphaDummy042 A, nb090AlphaDummy044 v u h), (nb090AlphaDummy041 A, nb090AlphaDummy043 v u h), (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_0283.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0283 v u A h = ⋯.reflOn