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Step * 5 of Lemma assert-PZF_safe


1. C : Type
⊢ ∀var:Atom. ∀body:Form(C).
    ((∀vs:Atom List. (↑(FormSafe2(body) vs) ⇐⇒ FormSafe1''(body) vs))
    ⇒ (∀vs:Atom List
          (↑((¬bvar ∈b vs) ∧b (FormSafe2(body) [var / vs])) ⇐⇒ (¬(var ∈ vs)) ∧ (FormSafe1''(body) [var / vs]))))
BY
{ (RW assert_pushdownC 0 THEN Auto) }

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Latex:

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Latex:

1.  C  :  Type
\mvdash{}  \mforall{}var:Atom.  \mforall{}body:Form(C).
        ((\mforall{}vs:Atom  List.  (\muparrow{}(FormSafe2(body)  vs)  \mLeftarrow{}{}\mRightarrow{}  FormSafe1''(body)  vs))
        {}\mRightarrow{}  (\mforall{}vs:Atom  List
                    (\muparrow{}((\mneg{}\msubb{}var  \mmember{}\msubb{}  vs)  \mwedge{}\msubb{}  (FormSafe2(body)  [var  /  vs]))
                    \mLeftarrow{}{}\mRightarrow{}  (\mneg{}(var  \mmember{}  vs))  \mwedge{}  (FormSafe1''(body)  [var  /  vs]))))


By

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Latex:
(RW  assert\_pushdownC  0  THEN  Auto)

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