Nominal proof certificates grouped in dependency order.

Certificates from NAR4C071C001Part003.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0000 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy021, nb071AlphaDummy024 x), (nb071AlphaDummy020, nb071AlphaDummy023 x), (nb071AlphaDummy019, nb071AlphaDummy022 x), (nb071AlphaDummy017, nb071AlphaDummy018 x), (nb071AlphaDummy013, nb071AlphaDummy015 x), (nb071AlphaDummy014, nb071AlphaDummy016 x), (nb071AlphaDummy006, nb071AlphaDummy008 x), (nb071AlphaDummy005, nb071AlphaDummy007 x), (nb071AlphaDummy011, nb071AlphaDummy012 x), (nb071AlphaDummy009, nb071AlphaDummy010 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb071AlphaDummy020) (SemanticCore.Class.cv nb071AlphaDummy021)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy019) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb071AlphaDummy020) (SemanticCore.Class.cv nb071AlphaDummy021))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb071AlphaDummy023 x)) (SemanticCore.Class.cv (nb071AlphaDummy024 x))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy022 x)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb071AlphaDummy023 x)) (SemanticCore.Class.cv (nb071AlphaDummy024 x)))).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0000.

Equations

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

Certificates from NAR4C071C001Part004.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0001 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy006, nb071AlphaDummy008 x), (nb071AlphaDummy005, nb071AlphaDummy007 x), (nb071AlphaDummy011, nb071AlphaDummy012 x), (nb071AlphaDummy009, nb071AlphaDummy010 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy006) (SemanticCore.Class.cv nb071AlphaDummy000)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy005) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb071AlphaDummy006))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy008 x)) (SemanticCore.Class.cv x)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy007 x)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb071AlphaDummy008 x)))).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0001.

Equations

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

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0002 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy021, nb071AlphaDummy024 x), (nb071AlphaDummy020, nb071AlphaDummy023 x), (nb071AlphaDummy019, nb071AlphaDummy022 x), (nb071AlphaDummy017, nb071AlphaDummy018 x), (nb071AlphaDummy013, nb071AlphaDummy015 x), (nb071AlphaDummy014, nb071AlphaDummy016 x), (nb071AlphaDummy039, nb071AlphaDummy040 x), (nb071AlphaDummy037, nb071AlphaDummy038 x), (nb071AlphaDummy006, nb071AlphaDummy008 x), (nb071AlphaDummy005, nb071AlphaDummy007 x), (nb071AlphaDummy035, nb071AlphaDummy036 x), (nb071AlphaDummy009, nb071AlphaDummy010 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv nb071AlphaDummy020) (SemanticCore.Class.cv nb071AlphaDummy021)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy019) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv nb071AlphaDummy020) (SemanticCore.Class.cv nb071AlphaDummy021))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (nb071AlphaDummy023 x)) (SemanticCore.Class.cv (nb071AlphaDummy024 x))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy022 x)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (nb071AlphaDummy023 x)) (SemanticCore.Class.cv (nb071AlphaDummy024 x)))).neg)

Checked nominal proof certificate identified upstream as nb071_split_alpha_0002.

Equations

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

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0003 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy039, nb071AlphaDummy040 x), (nb071AlphaDummy037, nb071AlphaDummy038 x), (nb071AlphaDummy006, nb071AlphaDummy008 x), (nb071AlphaDummy005, nb071AlphaDummy007 x), (nb071AlphaDummy035, nb071AlphaDummy036 x), (nb071AlphaDummy009, nb071AlphaDummy010 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] (SemanticCore.Wff.classMem (SemanticCore.Class.cv nb071AlphaDummy039) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv nb071AlphaDummy006))) (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb071AlphaDummy040 x)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb071AlphaDummy008 x))))

Checked nominal proof certificate identified upstream as nb071_split_alpha_0003.

Equations

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

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071SplitAlpha0004 (x : SemanticCore.Var) : Nominal.TAlphaWff [(nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv nb071AlphaDummy003) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv nb071AlphaDummy000) (SemanticCore.Class.cv nb071AlphaDummy001))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb071AlphaDummy004 x)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv x) (SemanticCore.Class.cv (nb071AlphaDummy002 x))))

Checked nominal proof certificate identified upstream as nb071_split_alpha_0004.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0032 : nb071AlphaDummy041 ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0106 : nb071AlphaDummy041 ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0033 (x : SemanticCore.Var) : nb071AlphaDummy043 x ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0107 (x : SemanticCore.Var) : nb071AlphaDummy043 x ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0034 : nb071AlphaDummy045 ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0108 : nb071AlphaDummy045 ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0035 (x : SemanticCore.Var) : nb071AlphaDummy046 x ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0109 (x : SemanticCore.Var) : nb071AlphaDummy046 x ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0036 : nb071AlphaDummy048 ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0110 : nb071AlphaDummy048 ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0037 (x : SemanticCore.Var) : nb071AlphaDummy050 x ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0111 (x : SemanticCore.Var) : nb071AlphaDummy050 x ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0038 : nb071AlphaDummy047 ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0112 : nb071AlphaDummy047 ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0039 (x : SemanticCore.Var) : nb071AlphaDummy049 x ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0113 (x : SemanticCore.Var) : nb071AlphaDummy049 x ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0114 : nb071AlphaDummy001 ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0115 (x : SemanticCore.Var) : nb071AlphaDummy002 x ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0116 : nb071AlphaDummy000 ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0117 (x : SemanticCore.Var) : x ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0118 : nb071AlphaDummy003 ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_wpp_notmem_0119 (x : SemanticCore.Var) : nb071AlphaDummy004 x ∉ Compiler.CompactSourceSyntax.synCncs.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_envfresh_0008 (x : SemanticCore.Var) : Nominal.TEnvFresh [(nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] Compiler.CompactSourceSyntax.synCncs.fv

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071WppRefl0008 (x : SemanticCore.Var) : Nominal.TReflOn [(nb071AlphaDummy041, nb071AlphaDummy043 x), (nb071AlphaDummy045, nb071AlphaDummy046 x), (nb071AlphaDummy048, nb071AlphaDummy050 x), (nb071AlphaDummy047, nb071AlphaDummy049 x), (nb071AlphaDummy001, nb071AlphaDummy002 x), (nb071AlphaDummy000, x), (nb071AlphaDummy003, nb071AlphaDummy004 x)] Compiler.CompactSourceSyntax.synCncs.fv

Checked nominal proof certificate identified upstream as nb071_wpp_refl_0008.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071WppRefl0008 x = ⋯.reflOn

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0046 : nb071AlphaDummy056 ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0047 (x : SemanticCore.Var) : nb071AlphaDummy058 x ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0048 : nb071AlphaDummy055 ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0049 (x : SemanticCore.Var) : nb071AlphaDummy057 x ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0050 : nb071AlphaDummy042 ∉ ∅

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb071_compact_fv_empty_0051 (x : SemanticCore.Var) : nb071AlphaDummy044 x ∉ ∅