NF weak partition development: NAR4C081C001Part004.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081SplitAlpha0000 (x y : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaWff [(nb081AlphaDummy034 A, nb081AlphaDummy035 x y), (nb081AlphaDummy008 A, nb081AlphaDummy009 x y), (nb081AlphaDummy001 A, y), (nb081AlphaDummy000 A, x), (nb081AlphaDummy002 A, nb081AlphaDummy003 x y A)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb081AlphaDummy034 A)) (SemanticCore.Class.cab (nb081AlphaDummy004 A) (Compiler.CompactSourceSyntax.synWrex (nb081AlphaDummy005 A) (SemanticCore.Class.cv (nb081AlphaDummy001 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb081AlphaDummy004 A)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb081AlphaDummy005 A))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb081AlphaDummy034 A)) (SemanticCore.Class.cab (nb081AlphaDummy004 A) (Compiler.CompactSourceSyntax.synWrex (nb081AlphaDummy005 A) (SemanticCore.Class.cv (nb081AlphaDummy001 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb081AlphaDummy004 A)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb081AlphaDummy005 A))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb081AlphaDummy035 x y)) (SemanticCore.Class.cab (nb081AlphaDummy006 x y) (Compiler.CompactSourceSyntax.synWrex (nb081AlphaDummy007 x y) (SemanticCore.Class.cv y) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb081AlphaDummy006 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb081AlphaDummy007 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb081AlphaDummy035 x y)) (SemanticCore.Class.cab (nb081AlphaDummy006 x y) (Compiler.CompactSourceSyntax.synWrex (nb081AlphaDummy007 x y) (SemanticCore.Class.cv y) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb081AlphaDummy006 x y)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb081AlphaDummy007 x y))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg)

Checked nominal proof certificate identified upstream as nb081_split_alpha_0000.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081_focused_notmem_0000 (A : SemanticCore.Class) : nb081AlphaDummy001 A ∉ A.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081_focused_notmem_0001 (A : SemanticCore.Class) : nb081AlphaDummy000 A ∉ A.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081_focused_notmem_0002 (A : SemanticCore.Class) : nb081AlphaDummy002 A ∉ A.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081_focused_notmem_0003 (x y : SemanticCore.Var) (A : SemanticCore.Class) : nb081AlphaDummy003 x y A ∉ A.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081_compact_envfresh_0007 (x y : SemanticCore.Var) (A : SemanticCore.Class) (dv_A_x : x ∉ A.fv) (dv_A_y : y ∉ A.fv) : Nominal.TEnvFresh [(nb081AlphaDummy001 A, y), (nb081AlphaDummy000 A, x), (nb081AlphaDummy002 A, nb081AlphaDummy003 x y A)] A.fv

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081FocusedRefl0000 (x y : SemanticCore.Var) (A : SemanticCore.Class) (dv_A_x : x ∉ A.fv) (dv_A_y : y ∉ A.fv) : Nominal.TReflOn [(nb081AlphaDummy001 A, y), (nb081AlphaDummy000 A, x), (nb081AlphaDummy002 A, nb081AlphaDummy003 x y A)] A.fv

Checked nominal proof certificate identified upstream as nb081_focused_refl_0000.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb081FocusedRefl0000 x y A dv_A_x dv_A_y = ⋯.reflOn