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Step * 2 1 of Lemma member-mFOL-sequent-freevars


1. s : mFOL-sequent()@i
2. v : ℤ@i
3. (∃h∈fst(s). (v ∈ mFOL-freevars(h)))@i
4. ¬(v ∈ mFOL-freevars(snd(s)))
5. (∀h∈fst(s).¬(v ∈ mFOL-freevars(h)))
⊢ (v ∈ mFOL-sequent-freevars(s))
BY
{ (D 3 THEN With ⌜i⌝ (D (-1))⋅ THEN Auto) }

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Latex:

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Latex:

1.  s  :  mFOL-sequent()@i
2.  v  :  \mBbbZ{}@i
3.  (\mexists{}h\mmember{}fst(s).  (v  \mmember{}  mFOL-freevars(h)))@i
4.  \mneg{}(v  \mmember{}  mFOL-freevars(snd(s)))
5.  (\mforall{}h\mmember{}fst(s).\mneg{}(v  \mmember{}  mFOL-freevars(h)))
\mvdash{}  (v  \mmember{}  mFOL-sequent-freevars(s))


By

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Latex:
(D  3  THEN  With  \mkleeneopen{}i\mkleeneclose{}  (D  (-1))\mcdot{}  THEN  Auto)

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