NF weak partition development: NominalAlphaRepairedBase001039SwapReflected001.

Shared variable, support, and alpha-certificate components for swap.

noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0000 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy022, alphaDummy025 x y), (alphaDummy021, alphaDummy024 x y), (alphaDummy020, alphaDummy023 x y), (alphaDummy018, alphaDummy019 x y), (alphaDummy014, alphaDummy016 x y), (alphaDummy015, alphaDummy017 x y), (alphaDummy007, alphaDummy009 x y), (alphaDummy006, alphaDummy008 x y), (alphaDummy012, alphaDummy013 x y), (alphaDummy010, alphaDummy011 x y), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy021) (SemanticCore.Class.cv alphaDummy022)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy020) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy021) (SemanticCore.Class.cv alphaDummy022))).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.SwapAlpha.splitAlpha0001 (x y z w : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(alphaDummy007, alphaDummy009 x y), (alphaDummy006, alphaDummy008 x y), (alphaDummy012, alphaDummy013 x y), (alphaDummy010, alphaDummy011 x y), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy007) (SemanticCore.Class.cv alphaDummy001)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy006) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy007))).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.SwapAlpha.splitAlpha0002 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy022, alphaDummy025 x y), (alphaDummy021, alphaDummy024 x y), (alphaDummy020, alphaDummy023 x y), (alphaDummy018, alphaDummy019 x y), (alphaDummy014, alphaDummy016 x y), (alphaDummy015, alphaDummy017 x y), (alphaDummy040, alphaDummy041 x y), (alphaDummy038, alphaDummy039 x y), (alphaDummy007, alphaDummy009 x y), (alphaDummy006, alphaDummy008 x y), (alphaDummy036, alphaDummy037 x y), (alphaDummy010, alphaDummy011 x y), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy021) (SemanticCore.Class.cv alphaDummy022)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy020) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy021) (SemanticCore.Class.cv alphaDummy022))).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.SwapAlpha.splitAlpha0003 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy040, alphaDummy041 x y), (alphaDummy038, alphaDummy039 x y), (alphaDummy007, alphaDummy009 x y), (alphaDummy006, alphaDummy008 x y), (alphaDummy036, alphaDummy037 x y), (alphaDummy010, alphaDummy011 x y), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy040) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy007))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy040) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy007))).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.SwapAlpha.swappedVariable (x y z w : SemanticCore.Var) : Nominal.TAlphaClass [(alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] (SemanticCore.Class.cv alphaDummy004) (SemanticCore.Class.cv (alphaDummy005 x y z w))

Proof-translation construction identified upstream as swapped_variable.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0004 (x y z w : SemanticCore.Var) (dv_x_y : x ≠ y) : Nominal.TAlphaWff [(alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy004) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv alphaDummy001) (SemanticCore.Class.cv alphaDummy002))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy005 x y z w)) (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.SwapAlpha.splitAlpha0005 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy058, alphaDummy061 z w), (alphaDummy057, alphaDummy060 z w), (alphaDummy056, alphaDummy059 z w), (alphaDummy054, alphaDummy055 z w), (alphaDummy050, alphaDummy052 z w), (alphaDummy051, alphaDummy053 z w), (alphaDummy043, alphaDummy045 z w), (alphaDummy042, alphaDummy044 z w), (alphaDummy048, alphaDummy049 z w), (alphaDummy046, alphaDummy047 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy057) (SemanticCore.Class.cv alphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy057) (SemanticCore.Class.cv alphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy060 z w)) (SemanticCore.Class.cv (alphaDummy061 z w))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy059 z w)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy060 z w)) (SemanticCore.Class.cv (alphaDummy061 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0005.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0006 (x y z w : SemanticCore.Var) (dv_w_z : w ≠ z) : Nominal.TAlphaWff [(alphaDummy043, alphaDummy045 z w), (alphaDummy042, alphaDummy044 z w), (alphaDummy048, alphaDummy049 z w), (alphaDummy046, alphaDummy047 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy043) (SemanticCore.Class.cv alphaDummy003)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy042) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy043))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy045 z w)) (SemanticCore.Class.cv z)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy044 z w)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy045 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0006.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0007 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy058, alphaDummy061 z w), (alphaDummy057, alphaDummy060 z w), (alphaDummy056, alphaDummy059 z w), (alphaDummy054, alphaDummy055 z w), (alphaDummy050, alphaDummy052 z w), (alphaDummy051, alphaDummy053 z w), (alphaDummy076, alphaDummy077 z w), (alphaDummy074, alphaDummy075 z w), (alphaDummy043, alphaDummy045 z w), (alphaDummy042, alphaDummy044 z w), (alphaDummy072, alphaDummy073 z w), (alphaDummy046, alphaDummy047 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy057) (SemanticCore.Class.cv alphaDummy058)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy056) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy057) (SemanticCore.Class.cv alphaDummy058))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy060 z w)) (SemanticCore.Class.cv (alphaDummy061 z w))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy059 z w)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy060 z w)) (SemanticCore.Class.cv (alphaDummy061 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0007.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0008 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy051, alphaDummy053 z w), (alphaDummy076, alphaDummy077 z w), (alphaDummy074, alphaDummy075 z w), (alphaDummy043, alphaDummy045 z w), (alphaDummy042, alphaDummy044 z w), (alphaDummy072, alphaDummy073 z w), (alphaDummy046, alphaDummy047 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] (SemanticCore.Wff.all alphaDummy050 (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy050) (SemanticCore.Class.cv alphaDummy043)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy051) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy050) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv alphaDummy050) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv alphaDummy050)))).neg) (SemanticCore.Wff.all (alphaDummy052 z w) (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy052 z w)) (SemanticCore.Class.cv (alphaDummy045 z w))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy053 z w)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy052 z w)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (alphaDummy052 z w)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (alphaDummy052 z w))))).neg)

Proof-translation construction identified upstream as split_alpha_0008.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0009 (x y z w : SemanticCore.Var) (dv_w_z : w ≠ z) : Nominal.TAlphaWff [(alphaDummy046, alphaDummy047 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy046) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab alphaDummy042 (Compiler.CompactSourceSyntax.synWrex alphaDummy043 (SemanticCore.Class.cv alphaDummy003) (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy042) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy043))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy046) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab alphaDummy042 (Compiler.CompactSourceSyntax.synWrex alphaDummy043 (SemanticCore.Class.cv alphaDummy000) (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy042) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy043)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy047 z w)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (alphaDummy044 z w) (Compiler.CompactSourceSyntax.synWrex (alphaDummy045 z w) (SemanticCore.Class.cv z) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy044 z w)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy045 z w)))))))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy047 z w)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (alphaDummy044 z w) (Compiler.CompactSourceSyntax.synWrex (alphaDummy045 z w) (SemanticCore.Class.cv w) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy044 z w)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy045 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.SwapAlpha.splitAlpha0010 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy094, alphaDummy097 z w), (alphaDummy093, alphaDummy096 z w), (alphaDummy092, alphaDummy095 z w), (alphaDummy090, alphaDummy091 z w), (alphaDummy086, alphaDummy088 z w), (alphaDummy087, alphaDummy089 z w), (alphaDummy079, alphaDummy081 z w), (alphaDummy078, alphaDummy080 z w), (alphaDummy084, alphaDummy085 z w), (alphaDummy082, alphaDummy083 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy093) (SemanticCore.Class.cv alphaDummy094)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy092) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy093) (SemanticCore.Class.cv alphaDummy094))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy096 z w)) (SemanticCore.Class.cv (alphaDummy097 z w))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy095 z w)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy096 z w)) (SemanticCore.Class.cv (alphaDummy097 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0010.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0011 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy079, alphaDummy081 z w), (alphaDummy078, alphaDummy080 z w), (alphaDummy084, alphaDummy085 z w), (alphaDummy082, alphaDummy083 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy079) (SemanticCore.Class.cv alphaDummy000)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy078) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy079))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy081 z w)) (SemanticCore.Class.cv w)).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy080 z w)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy081 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0011.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0012 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy094, alphaDummy097 z w), (alphaDummy093, alphaDummy096 z w), (alphaDummy092, alphaDummy095 z w), (alphaDummy090, alphaDummy091 z w), (alphaDummy086, alphaDummy088 z w), (alphaDummy087, alphaDummy089 z w), (alphaDummy112, alphaDummy113 z w), (alphaDummy110, alphaDummy111 z w), (alphaDummy079, alphaDummy081 z w), (alphaDummy078, alphaDummy080 z w), (alphaDummy108, alphaDummy109 z w), (alphaDummy082, alphaDummy083 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv alphaDummy093) (SemanticCore.Class.cv alphaDummy094)) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy092) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv alphaDummy093) (SemanticCore.Class.cv alphaDummy094))).neg) ((SemanticCore.Wff.classEq (Compiler.CompactSourceSyntax.synCin (SemanticCore.Class.cv (alphaDummy096 z w)) (SemanticCore.Class.cv (alphaDummy097 z w))) Compiler.CompactSourceSyntax.synC0).imp (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy095 z w)) (Compiler.CompactSourceSyntax.synCun (SemanticCore.Class.cv (alphaDummy096 z w)) (SemanticCore.Class.cv (alphaDummy097 z w)))).neg)

Proof-translation construction identified upstream as split_alpha_0012.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0013 (x y z w : SemanticCore.Var) : Nominal.TAlphaWff [(alphaDummy087, alphaDummy089 z w), (alphaDummy112, alphaDummy113 z w), (alphaDummy110, alphaDummy111 z w), (alphaDummy079, alphaDummy081 z w), (alphaDummy078, alphaDummy080 z w), (alphaDummy108, alphaDummy109 z w), (alphaDummy082, alphaDummy083 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] (SemanticCore.Wff.all alphaDummy086 (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy086) (SemanticCore.Class.cv alphaDummy079)) (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy087) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy086) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv alphaDummy086) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv alphaDummy086)))).neg) (SemanticCore.Wff.all (alphaDummy088 z w) (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy088 z w)) (SemanticCore.Class.cv (alphaDummy081 z w))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy089 z w)) (Compiler.CompactSourceSyntax.synCif (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy088 z w)) Compiler.CompactSourceSyntax.synCnnc) (Compiler.CompactSourceSyntax.synCplc (SemanticCore.Class.cv (alphaDummy088 z w)) Compiler.CompactSourceSyntax.synC1c) (SemanticCore.Class.cv (alphaDummy088 z w))))).neg)

Proof-translation construction identified upstream as split_alpha_0013.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.SwapAlpha.splitAlpha0014 (x y z w : SemanticCore.Var) (dv_w_z : w ≠ z) : Nominal.TAlphaWff [(alphaDummy082, alphaDummy083 z w), (alphaDummy000, w), (alphaDummy003, z), (alphaDummy002, y), (alphaDummy001, x), (alphaDummy004, alphaDummy005 x y z w)] (SemanticCore.Wff.classMem (SemanticCore.Class.cv alphaDummy082) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab alphaDummy078 (Compiler.CompactSourceSyntax.synWrex alphaDummy079 (SemanticCore.Class.cv alphaDummy003) (SemanticCore.Wff.classEq (SemanticCore.Class.cv alphaDummy078) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv alphaDummy079)) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c))))))) (SemanticCore.Wff.classMem (SemanticCore.Class.cv (alphaDummy083 z w)) (Compiler.CompactSourceSyntax.synCcompl (SemanticCore.Class.cab (alphaDummy080 z w) (Compiler.CompactSourceSyntax.synWrex (alphaDummy081 z w) (SemanticCore.Class.cv z) (SemanticCore.Wff.classEq (SemanticCore.Class.cv (alphaDummy080 z w)) (Compiler.CompactSourceSyntax.synCun (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (alphaDummy081 z w))) (Compiler.CompactSourceSyntax.synCsn Compiler.CompactSourceSyntax.synC0c)))))))

Proof-translation construction identified upstream as split_alpha_0014.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nominalDfSwap (x y z w : SemanticCore.Var) (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.synCswap (Compiler.CompactSourceSyntax.synCopab x y (Compiler.CompactSourceSyntax.synWex z (Compiler.CompactSourceSyntax.synWex w (Compiler.CompactSourceSyntax.synWa (SemanticCore.Wff.classEq (SemanticCore.Class.cv x) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv z) (SemanticCore.Class.cv w))) (SemanticCore.Wff.classEq (SemanticCore.Class.cv y) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv w) (SemanticCore.Class.cv z))))))))

Checked nominal proof certificate identified upstream as nominal_df_swap.

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