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LeanPool.NFWeakPartition.NominalAlphaRepairedBase001028Tfin

NF weak partition development: NominalAlphaRepairedBase001028Tfin.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.FiniteTypeAlpha.splitAlpha0000 (n : SemanticCore.Var) (M : SemanticCore.Class) (a : SemanticCore.Var) (__dv_M_a : a ∉ M.fv) (__dv_M_n : n ∉ M.fv) (__dv_a_n : a ≠ n) :
Nominal.TAlphaWff [(alphaDummy020, alphaDummy020), (alphaDummy019, alphaDummy019), (alphaDummy018, alphaDummy018), (alphaDummy014, alphaDummy014), (alphaDummy006, alphaDummy006), (alphaDummy016, alphaDummy016), (alphaDummy015, alphaDummy015), (alphaDummy001 M, n), (alphaDummy008 M, alphaDummy009 n M a), (alphaDummy011 M, alphaDummy013 n M a), (alphaDummy010 M, alphaDummy012 n M a), (alphaDummy002 M, alphaDummy003 n M a)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy019) (SemanticCore.Class.cv alphaDummy020)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy018) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy019) (SemanticCore.Class.cv alphaDummy020))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy019) (SemanticCore.Class.cv alphaDummy020)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy018) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy019) (SemanticCore.Class.cv alphaDummy020))).neg)

Proof-translation construction identified upstream as split_alpha_0000.

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    noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.FiniteTypeAlpha.splitAlpha0001 (n : SemanticCore.Var) (M : SemanticCore.Class) (a : SemanticCore.Var) (__dv_M_a : a ∉ M.fv) (__dv_M_n : n ∉ M.fv) (__dv_a_n : a ≠ n) :
    Nominal.TAlphaWff [(alphaDummy027 M, alphaDummy028 a), (alphaDummy000 M, a), (alphaDummy001 M, n), (alphaDummy008 M, alphaDummy009 n M a), (alphaDummy011 M, alphaDummy013 n M a), (alphaDummy010 M, alphaDummy012 n M a), (alphaDummy002 M, alphaDummy003 n M a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy027 M)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv (alphaDummy000 M))) Compiler.CompactSourceSyntax.synC1c)).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy027 M)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv (alphaDummy000 M))) Compiler.CompactSourceSyntax.synC1c)).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy028 a)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv a)) Compiler.CompactSourceSyntax.synC1c)).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy028 a)) (Compiler.CompactSourceSyntax.synCnin (Compiler.CompactSourceSyntax.synCpw (SemanticCore.Class.cv a)) Compiler.CompactSourceSyntax.synC1c)).neg)

    Proof-translation construction identified upstream as split_alpha_0001.

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      noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.FiniteTypeAlpha.splitAlpha0002 (n : SemanticCore.Var) (M : SemanticCore.Class) (a : SemanticCore.Var) (dv_M_a : a ∉ M.fv) (dv_M_n : n ∉ M.fv) (dv_a_n : a ≠ n) :
      Nominal.TAlphaWff [(alphaDummy001 M, n), (alphaDummy008 M, alphaDummy009 n M a), (alphaDummy011 M, alphaDummy013 n M a), (alphaDummy010 M, alphaDummy012 n M a), (alphaDummy002 M, alphaDummy003 n M a)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy001 M)) Compiler.CompactSourceSyntax.synCnnc).imp (Compiler.CompactSourceSyntax.synWrex (alphaDummy000 M) M (SemanticCore.Wff.classMem (Compiler.CompactSourceSyntax.synCpw1 (SemanticCore.Class.cv (alphaDummy000 M))) (SemanticCore.Class.cv (alphaDummy001 M)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv n) Compiler.CompactSourceSyntax.synCnnc).imp (Compiler.CompactSourceSyntax.synWrex a M (SemanticCore.Wff.classMem (Compiler.CompactSourceSyntax.synCpw1 (SemanticCore.Class.cv a)) (SemanticCore.Class.cv n))).neg)

      Proof-translation construction identified upstream as split_alpha_0002.

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        noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.FiniteTypeAlpha.splitAlpha0003 (n : SemanticCore.Var) (M : SemanticCore.Class) (a : SemanticCore.Var) (dv_M_a : a ∉ M.fv) (dv_M_n : n ∉ M.fv) (dv_a_n : a ≠ n) :
        Nominal.TAlphaWff [(alphaDummy002 M, alphaDummy003 n M a)] ((Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy002 M)) Compiler.CompactSourceSyntax.synC0) (SemanticCore.Wff.classEq M Compiler.CompactSourceSyntax.synC0)).neg.imp (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy002 M)) (Compiler.CompactSourceSyntax.synCio (alphaDummy001 M) (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy001 M)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synWrex (alphaDummy000 M) M (SemanticCore.Wff.classMem (Compiler.CompactSourceSyntax.synCpw1 (SemanticCore.Class.cv (alphaDummy000 M))) (SemanticCore.Class.cv (alphaDummy001 M))))))) (SemanticCore.Wff.classEq M Compiler.CompactSourceSyntax.synC0).neg)) ((Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy003 n M a)) Compiler.CompactSourceSyntax.synC0) (SemanticCore.Wff.classEq M Compiler.CompactSourceSyntax.synC0)).neg.imp (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy003 n M a)) (Compiler.CompactSourceSyntax.synCio n (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv n) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synWrex a M (SemanticCore.Wff.classMem (Compiler.CompactSourceSyntax.synCpw1 (SemanticCore.Class.cv a)) (SemanticCore.Class.cv n)))))) (SemanticCore.Wff.classEq M Compiler.CompactSourceSyntax.synC0).neg))

        Proof-translation construction identified upstream as split_alpha_0003.

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          noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nominalDfTfin (n : SemanticCore.Var) (M : SemanticCore.Class) (a : SemanticCore.Var) (dv_M_a : a ∉ M.fv) (dv_M_n : n ∉ M.fv) (dv_a_n : a ≠ n) :
          Nominal.NPrf (SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCtfin M) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classEq M Compiler.CompactSourceSyntax.synC0) Compiler.CompactSourceSyntax.synC0 (Compiler.CompactSourceSyntax.synCio n (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv n) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synWrex a M (SemanticCore.Wff.classMem (Compiler.CompactSourceSyntax.synCpw1 (SemanticCore.Class.cv a)) (SemanticCore.Class.cv n)))))))

          Checked nominal proof certificate identified upstream as nominal_df_tfin.

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