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Step * 4 of Lemma FormSafe1'-iff-FormSafe1''


1. C : Type
2. left : Form(C)
3. right : Form(C)
4. ∀vs:Atom List. (FormSafe1'(left) vs ⇐⇒ FormSafe1''(left) vs)
5. ∀vs:Atom List. (FormSafe1'(right) vs ⇐⇒ FormSafe1''(right) vs)
6. vs : Atom List
7. let phi = vs-FormFvs(left) in
       (FormSafe1''(left) vs-phi) ∧ (FormSafe1''(right) phi)
⊢ ∃phi:Atom List. (l_subset(Atom;phi;vs-FormFvs(left)) ∧ (FormSafe1'(left) vs-phi) ∧ (FormSafe1'(right) phi))
BY
{ (RepUR ``let`` -1 THEN D 0 With ⌜vs-FormFvs(left)⌝  THEN Auto) }

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Latex:

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Latex:

1.  C  :  Type
2.  left  :  Form(C)
3.  right  :  Form(C)
4.  \mforall{}vs:Atom  List.  (FormSafe1'(left)  vs  \mLeftarrow{}{}\mRightarrow{}  FormSafe1''(left)  vs)
5.  \mforall{}vs:Atom  List.  (FormSafe1'(right)  vs  \mLeftarrow{}{}\mRightarrow{}  FormSafe1''(right)  vs)
6.  vs  :  Atom  List
7.  let  phi  =  vs-FormFvs(left)  in
              (FormSafe1''(left)  vs-phi)  \mwedge{}  (FormSafe1''(right)  phi)
\mvdash{}  \mexists{}phi:Atom  List
      (l\_subset(Atom;phi;vs-FormFvs(left))  \mwedge{}  (FormSafe1'(left)  vs-phi)  \mwedge{}  (FormSafe1'(right)  phi))


By

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Latex:
(RepUR  ``let``  -1  THEN  D  0  With  \mkleeneopen{}vs-FormFvs(left)\mkleeneclose{}    THEN  Auto)

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