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Step * 2 1 1 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. phi : Atom List
8. l_subset(Atom;phi;vs-FormFvs(left))
9. FormSafe1(left) vs-phi
10. FormSafe1(right) phi
11. l_subset(Atom;vs-phi;FormFvs(left))
⊢ set-equal(Atom;vs-FormFvs(left);phi)
BY
{ (D 0
   THEN Auto
   THEN (SupposeNot THENA Auto)
   THEN (D -4 With ⌜t⌝  THENA Auto)
   THEN All (RWO "member-list-diff")
   THEN Auto
   THEN D -1
   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.  phi  :  Atom  List
8.  l\_subset(Atom;phi;vs-FormFvs(left))
9.  FormSafe1(left)  vs-phi
10.  FormSafe1(right)  phi
11.  l\_subset(Atom;vs-phi;FormFvs(left))
\mvdash{}  set-equal(Atom;vs-FormFvs(left);phi)


By

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Latex:
(D  0
  THEN  Auto
  THEN  (SupposeNot  THENA  Auto)
  THEN  (D  -4  With  \mkleeneopen{}t\mkleeneclose{}    THENA  Auto)
  THEN  All  (RWO  "member-list-diff")
  THEN  Auto
  THEN  D  -1
  THEN  Auto)

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