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LeanPool.NFWeakPartition.AlphaSupport.NAR4H5C095M3Part028Stage1

NF weak partition development: NAR4H5C095M3Part028.

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noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0055 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) :
Nominal.TAlphaWff [(nb095AlphaDummy167 D R S_cls E, nb095AlphaDummy168 f), (nb095AlphaDummy165 D R S_cls E, nb095AlphaDummy166 f), (nb095AlphaDummy134 D R S_cls E, nb095AlphaDummy136 f), (nb095AlphaDummy133 D R S_cls E, nb095AlphaDummy135 f), (nb095AlphaDummy163 D R S_cls E, nb095AlphaDummy164 f), (nb095AlphaDummy137 D R S_cls E, nb095AlphaDummy138 f), (nb095AlphaDummy092 D R S_cls E, nb095AlphaDummy094 f), (nb095AlphaDummy091 D R S_cls E, nb095AlphaDummy093 f), (nb095AlphaDummy095 D R S_cls E, nb095AlphaDummy096 f), (nb095AlphaDummy387 D R S_cls E, nb095AlphaDummy390 f), (nb095AlphaDummy386 D R S_cls E, nb095AlphaDummy389 f), (nb095AlphaDummy385 D R S_cls E, nb095AlphaDummy388 f), (nb095AlphaDummy391 D R S_cls E, nb095AlphaDummy392 f), (nb095AlphaDummy383 D R S_cls E, nb095AlphaDummy384 f), (nb095AlphaDummy381 D R S_cls E, nb095AlphaDummy382 f), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy167 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy134 D R S_cls E)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy167 D R S_cls E)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy134 D R S_cls E)))).neg) ((SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy168 f)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy136 f)))).imp (SemanticCore.Wff.classMem (SemanticCore.Class.cv (nb095AlphaDummy168 f)) (Compiler.CompactSourceSyntax.synCphi (SemanticCore.Class.cv (nb095AlphaDummy136 f)))).neg)

Checked nominal proof certificate identified upstream as nb095_split_alpha_0055.

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    noncomputable def NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095SplitAlpha0056 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) (dv_f_u : f ≠ u) (dv_f_x : f ≠ x) :
    Nominal.TAlphaWff [(nb095AlphaDummy386 D R S_cls E, nb095AlphaDummy389 f), (nb095AlphaDummy385 D R S_cls E, nb095AlphaDummy388 f), (nb095AlphaDummy391 D R S_cls E, nb095AlphaDummy392 f), (nb095AlphaDummy383 D R S_cls E, nb095AlphaDummy384 f), (nb095AlphaDummy381 D R S_cls E, nb095AlphaDummy382 f), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] ((SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy391 D R S_cls E)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv (nb095AlphaDummy385 D R S_cls E)) (SemanticCore.Class.cv (nb095AlphaDummy386 D R S_cls E)))).imp (Compiler.CompactSourceSyntax.synWex (nb095AlphaDummy387 D R S_cls E) (Compiler.CompactSourceSyntax.synWa (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb095AlphaDummy385 D R S_cls E)) (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv (nb095AlphaDummy000 D R S_cls E)))) (SemanticCore.Class.cv (nb095AlphaDummy387 D R S_cls E))) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb095AlphaDummy387 D R S_cls E)) (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv (nb095AlphaDummy000 D R S_cls E))) (SemanticCore.Class.cv (nb095AlphaDummy386 D R S_cls E))))).neg) ((SemanticCore.Wff.classEq (SemanticCore.Class.cv (nb095AlphaDummy392 f)) (Compiler.CompactSourceSyntax.synCop (SemanticCore.Class.cv (nb095AlphaDummy388 f)) (SemanticCore.Class.cv (nb095AlphaDummy389 f)))).imp (Compiler.CompactSourceSyntax.synWex (nb095AlphaDummy390 f) (Compiler.CompactSourceSyntax.synWa (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb095AlphaDummy388 f)) (Compiler.CompactSourceSyntax.synCcnv (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv f))) (SemanticCore.Class.cv (nb095AlphaDummy390 f))) (Compiler.CompactSourceSyntax.synWbr (SemanticCore.Class.cv (nb095AlphaDummy390 f)) (Compiler.CompactSourceSyntax.synCcnv (SemanticCore.Class.cv f)) (SemanticCore.Class.cv (nb095AlphaDummy389 f))))).neg)

    Checked nominal proof certificate identified upstream as nb095_split_alpha_0056.

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      theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1488 (D R S_cls E : SemanticCore.Class) :
      nb095AlphaDummy383 D R S_cls E ∉ Compiler.CompactSourceSyntax.synCid.fv
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      theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1489 (f : SemanticCore.Var) :
      nb095AlphaDummy384 f ∉ Compiler.CompactSourceSyntax.synCid.fv
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      theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1490 (D R S_cls E : SemanticCore.Class) :
      nb095AlphaDummy381 D R S_cls E ∉ Compiler.CompactSourceSyntax.synCid.fv
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      theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_wpp_notmem_1491 (f : SemanticCore.Var) :
      nb095AlphaDummy382 f ∉ Compiler.CompactSourceSyntax.synCid.fv
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      theorem NFChoice.DirectNominalPrf.NominalAlphaWrappersRepaired.nb095_compact_envfresh_0192 (x u : SemanticCore.Var) (D R S_cls : SemanticCore.Class) (f : SemanticCore.Var) (E : SemanticCore.Class) :
      Nominal.TEnvFresh [(nb095AlphaDummy383 D R S_cls E, nb095AlphaDummy384 f), (nb095AlphaDummy381 D R S_cls E, nb095AlphaDummy382 f), (nb095AlphaDummy001 D R S_cls E, u), (nb095AlphaDummy002 D R S_cls E, x), (nb095AlphaDummy000 D R S_cls E, f)] Compiler.CompactSourceSyntax.synCid.fv