Nominal proof certificates grouped in dependency order.

Certificates from NAR4C090C001Part052.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0029 (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), (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_0029.

Equations

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

Certificates from NAR4C090C001Part053.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0030 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TAlphaWff [(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), (nb090AlphaDummy000 A, h), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy323 A)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy292 A))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy323 A)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy324 u)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy294 u))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy324 u)) (Compiler.CompactSourceSyntax.synCcompl (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0030.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0838 (A : SemanticCore.Class) : nb090AlphaDummy283 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0839 (u : SemanticCore.Var) : nb090AlphaDummy284 u ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0840 (A : SemanticCore.Class) : nb090AlphaDummy285 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0841 (u : SemanticCore.Var) : nb090AlphaDummy286 u ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0842 (A : SemanticCore.Class) : nb090AlphaDummy288 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0843 (u : SemanticCore.Var) : nb090AlphaDummy290 u ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0844 (A : SemanticCore.Class) : nb090AlphaDummy287 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0845 (u : SemanticCore.Var) : nb090AlphaDummy289 u ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0846 (A : SemanticCore.Class) : nb090AlphaDummy000 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0847 (h : SemanticCore.Var) : h ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0848 (A : SemanticCore.Class) : nb090AlphaDummy002 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0849 (v : SemanticCore.Var) : v ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0850 (A : SemanticCore.Class) : nb090AlphaDummy001 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0851 (u : SemanticCore.Var) : u ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0852 (A : SemanticCore.Class) : nb090AlphaDummy003 A ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0853 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : nb090AlphaDummy004 v u A h ∉ Compiler.CompactSourceSyntax.synC2nd.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_envfresh_0108 (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), (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.nb090WppRefl0108 (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), (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_0108.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0108 v u A h = ⋯.reflOn

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_fv_empty_0250 (A : SemanticCore.Class) : nb090AlphaDummy331 A ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_fv_empty_0251 (v h : SemanticCore.Var) : nb090AlphaDummy332 v h ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_fv_empty_0252 (A : SemanticCore.Class) : nb090AlphaDummy329 A ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_fv_empty_0253 (v h : SemanticCore.Var) : nb090AlphaDummy330 v h ∉ ∅