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LeanPool.NFWeakPartition.NAR4C090C001Part024

NF weak partition development: NAR4C090C001Part024.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090SplitAlpha0000 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) :
Nominal.TAlphaWff [(nb090AlphaDummy035 A, nb090AlphaDummy036 v u), (nb090AlphaDummy009 A, nb090AlphaDummy010 v u), (nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy035 A)) (SemanticCore.Class.cab (nb090AlphaDummy005 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy006 A) (SemanticCore.Class.cv (nb090AlphaDummy002 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy005 A)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy006 A))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy035 A)) (SemanticCore.Class.cab (nb090AlphaDummy005 A) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy006 A) (SemanticCore.Class.cv (nb090AlphaDummy002 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy005 A)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy006 A))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy036 v u)) (SemanticCore.Class.cab (nb090AlphaDummy007 v u) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy008 v u) (SemanticCore.Class.cv v) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy007 v u)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy008 v u))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb090AlphaDummy036 v u)) (SemanticCore.Class.cab (nb090AlphaDummy007 v u) (Compiler.CompactSourceSyntax.synWrex (nb090AlphaDummy008 v u) (SemanticCore.Class.cv v) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb090AlphaDummy007 v u)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb090AlphaDummy008 v u))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))).neg)

Checked nominal proof certificate identified upstream as nb090_split_alpha_0000.

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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_focused_notmem_0000 (A : SemanticCore.Class) :
    nb090AlphaDummy002 A ∉ A.fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0106 (A : SemanticCore.Class) :
    nb090AlphaDummy002 A ∉ (Compiler.CompactSourceSyntax.synChwcodes A).fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0107 (v : SemanticCore.Var) (A : SemanticCore.Class) (dv_A_v : v ∉ A.fv) :
    v ∉ (Compiler.CompactSourceSyntax.synChwcodes A).fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_focused_notmem_0001 (A : SemanticCore.Class) :
    nb090AlphaDummy001 A ∉ A.fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0108 (A : SemanticCore.Class) :
    nb090AlphaDummy001 A ∉ (Compiler.CompactSourceSyntax.synChwcodes A).fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0109 (u : SemanticCore.Var) (A : SemanticCore.Class) (dv_A_u : u ∉ A.fv) :
    u ∉ (Compiler.CompactSourceSyntax.synChwcodes A).fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_focused_notmem_0002 (A : SemanticCore.Class) :
    nb090AlphaDummy003 A ∉ A.fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0110 (A : SemanticCore.Class) :
    nb090AlphaDummy003 A ∉ (Compiler.CompactSourceSyntax.synChwcodes A).fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_focused_notmem_0003 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) :
    nb090AlphaDummy004 v u A h ∉ A.fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_wpp_notmem_0111 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) :
    nb090AlphaDummy004 v u A h ∉ (Compiler.CompactSourceSyntax.synChwcodes A).fv
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    theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090_compact_envfresh_0007 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) (dv_A_u : u ∉ A.fv) (dv_A_v : v ∉ A.fv) :
    Nominal.TEnvFresh [(nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] (Compiler.CompactSourceSyntax.synChwcodes A).fv
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    noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb090WppRefl0007 (v u : SemanticCore.Var) (A : SemanticCore.Class) (h : SemanticCore.Var) (dv_A_u : u ∉ A.fv) (dv_A_v : v ∉ A.fv) :
    Nominal.TReflOn [(nb090AlphaDummy002 A, v), (nb090AlphaDummy001 A, u), (nb090AlphaDummy003 A, nb090AlphaDummy004 v u A h)] (Compiler.CompactSourceSyntax.synChwcodes A).fv

    Checked nominal proof certificate identified upstream as nb090_wpp_refl_0007.

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