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


1. s : mFOL-sequent()@i
2. v : ℤ@i
3. (v ∈ mFOL-sequent-freevars(s))@i
⊢ (v ∈ mFOL-freevars(snd(s))) ∨ (∃h∈fst(s). (v ∈ mFOL-freevars(h)))
BY
{ (SupposeNot THEN Assert ⌜¬(v ∈ mFOL-sequent-freevars(s))⌝⋅ THEN Auto) }

1
.....assertion..... 
1. s : mFOL-sequent()@i
2. v : ℤ@i
3. (v ∈ mFOL-sequent-freevars(s))@i
4. ¬((v ∈ mFOL-freevars(snd(s))) ∨ (∃h∈fst(s). (v ∈ mFOL-freevars(h))))
⊢ ¬(v ∈ mFOL-sequent-freevars(s))

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Latex:

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Latex:

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


By

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Latex:
(SupposeNot  THEN  Assert  \mkleeneopen{}\mneg{}(v  \mmember{}  mFOL-sequent-freevars(s))\mkleeneclose{}\mcdot{}  THEN  Auto)

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