NF weak partition development: NominalAlphaRepairedBase001043SiReflected001.

Shared variable, support, and alpha-certificate components.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0000 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaWff [(alphaDummy022 A, alphaDummy025 x y), (alphaDummy021 A, alphaDummy024 x y), (alphaDummy020 A, alphaDummy023 x y), (alphaDummy018 A, alphaDummy019 x y), (alphaDummy014 A, alphaDummy016 x y), (alphaDummy015 A, alphaDummy017 x y), (alphaDummy007 A, alphaDummy009 x y), (alphaDummy006 A, alphaDummy008 x y), (alphaDummy012 A, alphaDummy013 x y), (alphaDummy010 A, alphaDummy011 x y), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy021 A)) (SemanticCore.Class.cv (alphaDummy022 A))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy020 A)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy021 A)) (SemanticCore.Class.cv (alphaDummy022 A)))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy024 x y)) (SemanticCore.Class.cv (alphaDummy025 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy023 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy024 x y)) (SemanticCore.Class.cv (alphaDummy025 x y)))).neg)

Proof-translation construction identified upstream as split_alpha_0000.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0001 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(alphaDummy007 A, alphaDummy009 x y), (alphaDummy006 A, alphaDummy008 x y), (alphaDummy012 A, alphaDummy013 x y), (alphaDummy010 A, alphaDummy011 x y), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy007 A)) (SemanticCore.Class.cv (alphaDummy001 A))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy006 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy007 A)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy009 x y)) (SemanticCore.Class.cv x)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy008 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy009 x y)))).neg)

Proof-translation construction identified upstream as split_alpha_0001.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0002 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaWff [(alphaDummy022 A, alphaDummy025 x y), (alphaDummy021 A, alphaDummy024 x y), (alphaDummy020 A, alphaDummy023 x y), (alphaDummy018 A, alphaDummy019 x y), (alphaDummy014 A, alphaDummy016 x y), (alphaDummy015 A, alphaDummy017 x y), (alphaDummy040 A, alphaDummy041 x y), (alphaDummy038 A, alphaDummy039 x y), (alphaDummy007 A, alphaDummy009 x y), (alphaDummy006 A, alphaDummy008 x y), (alphaDummy036 A, alphaDummy037 x y), (alphaDummy010 A, alphaDummy011 x y), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy021 A)) (SemanticCore.Class.cv (alphaDummy022 A))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy020 A)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy021 A)) (SemanticCore.Class.cv (alphaDummy022 A)))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy024 x y)) (SemanticCore.Class.cv (alphaDummy025 x y))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy023 x y)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy024 x y)) (SemanticCore.Class.cv (alphaDummy025 x y)))).neg)

Proof-translation construction identified upstream as split_alpha_0002.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0003 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaWff [(alphaDummy040 A, alphaDummy041 x y), (alphaDummy038 A, alphaDummy039 x y), (alphaDummy007 A, alphaDummy009 x y), (alphaDummy006 A, alphaDummy008 x y), (alphaDummy036 A, alphaDummy037 x y), (alphaDummy010 A, alphaDummy011 x y), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy040 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy007 A)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy040 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy007 A)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy041 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy009 x y)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy041 x y)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy009 x y)))).neg)

Proof-translation construction identified upstream as split_alpha_0003.

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def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.swappedVariable (x y z w : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaClass [(alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] (SemanticCore.Class.cv (alphaDummy004 A)) (SemanticCore.Class.cv (alphaDummy005 x y z w A))

Proof-translation construction identified upstream as swapped_variable.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0004 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy004 A)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv (alphaDummy001 A)) (SemanticCore.Class.cv (alphaDummy002 A)))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy005 x y z w A)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv x) (SemanticCore.Class.cv y)))

Proof-translation construction identified upstream as split_alpha_0004.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0005 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaWff [(alphaDummy062 A, alphaDummy065 z w), (alphaDummy061 A, alphaDummy064 z w), (alphaDummy060 A, alphaDummy063 z w), (alphaDummy058 A, alphaDummy059 z w), (alphaDummy054 A, alphaDummy056 z w), (alphaDummy055 A, alphaDummy057 z w), (alphaDummy047 A, alphaDummy049 z w), (alphaDummy046 A, alphaDummy048 z w), (alphaDummy052 A, alphaDummy053 z w), (alphaDummy050 A, alphaDummy051 z w), (alphaDummy000 A, w), (alphaDummy003 A, z), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy061 A)) (SemanticCore.Class.cv (alphaDummy062 A))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy060 A)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy061 A)) (SemanticCore.Class.cv (alphaDummy062 A)))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy064 z w)) (SemanticCore.Class.cv (alphaDummy065 z w))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy063 z w)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy064 z w)) (SemanticCore.Class.cv (alphaDummy065 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0005.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0006 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) (dv_w_z : w ≠ z) : Nominal.TAlphaWff [(alphaDummy047 A, alphaDummy049 z w), (alphaDummy046 A, alphaDummy048 z w), (alphaDummy052 A, alphaDummy053 z w), (alphaDummy050 A, alphaDummy051 z w), (alphaDummy000 A, w), (alphaDummy003 A, z), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy047 A)) (SemanticCore.Class.cv (alphaDummy003 A))).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy046 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy047 A)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy049 z w)) (SemanticCore.Class.cv z)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy048 z w)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy049 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0006.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0007 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaWff [(alphaDummy062 A, alphaDummy065 z w), (alphaDummy061 A, alphaDummy064 z w), (alphaDummy060 A, alphaDummy063 z w), (alphaDummy058 A, alphaDummy059 z w), (alphaDummy054 A, alphaDummy056 z w), (alphaDummy055 A, alphaDummy057 z w), (alphaDummy080 A, alphaDummy081 z w), (alphaDummy078 A, alphaDummy079 z w), (alphaDummy047 A, alphaDummy049 z w), (alphaDummy046 A, alphaDummy048 z w), (alphaDummy076 A, alphaDummy077 z w), (alphaDummy050 A, alphaDummy051 z w), (alphaDummy000 A, w), (alphaDummy003 A, z), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy061 A)) (SemanticCore.Class.cv (alphaDummy062 A))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy060 A)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy061 A)) (SemanticCore.Class.cv (alphaDummy062 A)))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy064 z w)) (SemanticCore.Class.cv (alphaDummy065 z w))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy063 z w)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy064 z w)) (SemanticCore.Class.cv (alphaDummy065 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0007.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0008 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) : Nominal.TAlphaWff [(alphaDummy055 A, alphaDummy057 z w), (alphaDummy080 A, alphaDummy081 z w), (alphaDummy078 A, alphaDummy079 z w), (alphaDummy047 A, alphaDummy049 z w), (alphaDummy046 A, alphaDummy048 z w), (alphaDummy076 A, alphaDummy077 z w), (alphaDummy050 A, alphaDummy051 z w), (alphaDummy000 A, w), (alphaDummy003 A, z), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] (SemanticCore.Wff.all (alphaDummy054 A) (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy054 A)) (SemanticCore.Class.cv (alphaDummy047 A))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy055 A)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy054 A)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (alphaDummy054 A)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (alphaDummy054 A))))).neg) (SemanticCore.Wff.all (alphaDummy056 z w) (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy056 z w)) (SemanticCore.Class.cv (alphaDummy049 z w))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy057 z w)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy056 z w)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (alphaDummy056 z w)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (alphaDummy056 z w))))).neg)

Proof-translation construction identified upstream as split_alpha_0008.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.splitAlpha0009 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) (dv_w_z : w ≠ z) : Nominal.TAlphaWff [(alphaDummy050 A, alphaDummy051 z w), (alphaDummy000 A, w), (alphaDummy003 A, z), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy050 A)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (alphaDummy046 A) (Compiler.CompactSourceSyntax.synWrex (alphaDummy047 A) (SemanticCore.Class.cv (alphaDummy003 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy046 A)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy047 A)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy050 A)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (alphaDummy046 A) (Compiler.CompactSourceSyntax.synWrex (alphaDummy047 A) (SemanticCore.Class.cv (alphaDummy000 A)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy046 A)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy047 A))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy051 z w)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (alphaDummy048 z w) (Compiler.CompactSourceSyntax.synWrex (alphaDummy049 z w) (SemanticCore.Class.cv z) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy048 z w)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy049 z w)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy051 z w)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (alphaDummy048 z w) (Compiler.CompactSourceSyntax.synWrex (alphaDummy049 z w) (SemanticCore.Class.cv w) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy048 z w)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy049 z w))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg)

Proof-translation construction identified upstream as split_alpha_0009.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SingletonImageAlpha.wppRefl0014 (x y z w : SemanticCore.Var) (A : SemanticCore.Class) (dv_A_w : w ∉ A.fv) (dv_A_x : x ∉ A.fv) (dv_A_y : y ∉ A.fv) (dv_A_z : z ∉ A.fv) : Nominal.TReflOn [(alphaDummy000 A, w), (alphaDummy003 A, z), (alphaDummy002 A, y), (alphaDummy001 A, x), (alphaDummy004 A, alphaDummy005 x y z w A)] A.fv

Proof-translation construction identified upstream as wpp_refl_0014.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nominalDfSi (x y z w : SemanticCore.Var) (A : SemanticCore.Class) (dv_A_w : w ∉ A.fv) (dv_A_x : x ∉ A.fv) (dv_A_y : y ∉ A.fv) (dv_A_z : z ∉ A.fv) (dv_w_x : w ≠ x) (dv_w_y : w ≠ y) (dv_w_z : w ≠ z) (dv_x_y : x ≠ y) (dv_x_z : x ≠ z) (dv_y_z : y ≠ z) : Nominal.NPrf (SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCsi A) (Compiler.CompactSourceSyntax.synCopab x y (Compiler.CompactSourceSyntax.synWex z (Compiler.CompactSourceSyntax.synWex w (Compiler.CompactSourceSyntax.synW3a (SemanticCore.Wff.classEq (SemanticCore.Class.cv x) (Compiler.CompactSourceSyntax.synCsn (SemanticCore.Class.cv z))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv y) (Compiler.CompactSourceSyntax.synCsn (SemanticCore.Class.cv w))) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv z) A (SemanticCore.Class.cv w)))))))

Checked nominal proof certificate identified upstream as nominal_df_si.

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