Nominal proof certificates grouped in dependency order.

Certificates from NAR4C090C001Part108.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0086 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) (dv_h_u : h ≠ u) (dv_u_v : u ≠ v) : Nominal.TAlphaWff [(nb090AlphaDummy667 A, nb090AlphaDummy668 u), (nb090AlphaDummy665 A, nb090AlphaDummy666 u), (nb090AlphaDummy653 A, nb090AlphaDummy654 u), (nb090AlphaDummy655 A, nb090AlphaDummy656 u), (nb090AlphaDummy658 A, nb090AlphaDummy660 u), (nb090AlphaDummy657 A, nb090AlphaDummy659 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 (nb090AlphaDummy667 A)) (SemanticCore.Class.cab (nb090AlphaDummy661 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy662 A) (SemanticCore.Class.cv (nb090AlphaDummy001 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy661 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy662 A))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy667 A)) (SemanticCore.Class.cab (nb090AlphaDummy661 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy662 A) (SemanticCore.Class.cv (nb090AlphaDummy001 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy661 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy662 A))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy668 u)) (SemanticCore.Class.cab (nb090AlphaDummy663 u) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy664 u) (SemanticCore.Class.cv u) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy663 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy664 u))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy668 u)) (SemanticCore.Class.cab (nb090AlphaDummy663 u) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy664 u) (SemanticCore.Class.cv u) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy663 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy664 u))))))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0086.

Equations

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

Certificates from NAR4C090C001Part109.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0087 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TAlphaWff [(nb090AlphaDummy695 A, nb090AlphaDummy696 u), (nb090AlphaDummy693 A, nb090AlphaDummy694 u), (nb090AlphaDummy662 A, nb090AlphaDummy664 u), (nb090AlphaDummy661 A, nb090AlphaDummy663 u), (nb090AlphaDummy691 A, nb090AlphaDummy692 u), (nb090AlphaDummy665 A, nb090AlphaDummy666 u), (nb090AlphaDummy653 A, nb090AlphaDummy654 u), (nb090AlphaDummy655 A, nb090AlphaDummy656 u), (nb090AlphaDummy658 A, nb090AlphaDummy660 u), (nb090AlphaDummy657 A, nb090AlphaDummy659 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 (nb090AlphaDummy695 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy662 A)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy695 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy662 A)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy696 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy664 u)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy696 u)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy664 u)))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0087.

Equations

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

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1804 (A : SemanticCore.Class) : nb090AlphaDummy653 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1805 (u : SemanticCore.Var) : nb090AlphaDummy654 u ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1806 (A : SemanticCore.Class) : nb090AlphaDummy655 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1807 (u : SemanticCore.Var) : nb090AlphaDummy656 u ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1808 (A : SemanticCore.Class) : nb090AlphaDummy658 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1809 (u : SemanticCore.Var) : nb090AlphaDummy660 u ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1810 (A : SemanticCore.Class) : nb090AlphaDummy657 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1811 (u : SemanticCore.Var) : nb090AlphaDummy659 u ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1812 (A : SemanticCore.Class) : nb090AlphaDummy042 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1813 (v u h : SemanticCore.Var) : nb090AlphaDummy044 v u h ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1814 (A : SemanticCore.Class) : nb090AlphaDummy041 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1815 (v u h : SemanticCore.Var) : nb090AlphaDummy043 v u h ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1816 (A : SemanticCore.Class) : nb090AlphaDummy000 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1817 (h : SemanticCore.Var) : h ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1818 (A : SemanticCore.Class) : nb090AlphaDummy002 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1819 (v : SemanticCore.Var) : v ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1820 (A : SemanticCore.Class) : nb090AlphaDummy001 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1821 (u : SemanticCore.Var) : u ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1822 (A : SemanticCore.Class) : nb090AlphaDummy003 A ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_1823 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : nb090AlphaDummy004 v u A h ∉ Compiler.CompactSourceSyntax.synC1st.fv

theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_envfresh_0298 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TEnvFresh [(nb090AlphaDummy653 A, nb090AlphaDummy654 u), (nb090AlphaDummy655 A, nb090AlphaDummy656 u), (nb090AlphaDummy658 A, nb090AlphaDummy660 u), (nb090AlphaDummy657 A, nb090AlphaDummy659 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.synC1st.fv

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0298 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) : Nominal.TReflOn [(nb090AlphaDummy653 A, nb090AlphaDummy654 u), (nb090AlphaDummy655 A, nb090AlphaDummy656 u), (nb090AlphaDummy658 A, nb090AlphaDummy660 u), (nb090AlphaDummy657 A, nb090AlphaDummy659 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.synC1st.fv

Checked nominal proof certificate identified upstream as nb090_wpp_refl_0298.

Equations

• NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0298 v u A h = ⋯.reflOn