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Step * 1 3 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. theta : Atom List
8. l_subset(Atom;theta;vs-FormFvs(right))
9. FormSafe1'(left) theta
10. set-equal(Atom;vs-FormFvs(right);theta)
11. FormSafe1''(left) vs-FormFvs(right)
⊢ l_subset(Atom;vs-vs-FormFvs(right);vs-theta)
BY
{ (MoveToConcl (-2) THEN GenConclTerm ⌜vs-FormFvs(right)⌝⋅ THEN Auto) }

1
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. theta : Atom List
8. l_subset(Atom;theta;vs-FormFvs(right))
9. FormSafe1'(left) theta
10. FormSafe1''(left) vs-FormFvs(right)
11. v : Atom List
12. vs-FormFvs(right) = v ∈ (Atom List)
13. set-equal(Atom;v;theta)
⊢ l_subset(Atom;vs-v;vs-theta)

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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.  theta  :  Atom  List
8.  l\_subset(Atom;theta;vs-FormFvs(right))
9.  FormSafe1'(left)  theta
10.  set-equal(Atom;vs-FormFvs(right);theta)
11.  FormSafe1''(left)  vs-FormFvs(right)
\mvdash{}  l\_subset(Atom;vs-vs-FormFvs(right);vs-theta)


By

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Latex:
(MoveToConcl  (-2)  THEN  GenConclTerm  \mkleeneopen{}vs-FormFvs(right)\mkleeneclose{}\mcdot{}  THEN  Auto)

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