Step
*
of Lemma
existse-between2_functionality_wrt_iff
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[P,Q:{e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ].
((∀e:{e:E| loc(e) = loc(e1) ∈ Id} . (P[e]
⇐⇒ Q[e]))
⇒ (∃e∈[e1,e2].P[e]
⇐⇒ ∃e∈[e1,e2].Q[e]))
BY
{ (Repeat ((D 0 THENA Complete (Auto)))
THEN ParallelLast
THEN ParallelLast
THEN ExRepD
THEN Auto
THEN BackThruSomeHyp
THEN Auto) }
Latex:
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[P,Q:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
((\mforall{}e:\{e:E| loc(e) = loc(e1)\} . (P[e] \mLeftarrow{}{}\mRightarrow{} Q[e])) {}\mRightarrow{} (\mexists{}e\mmember{}[e1,e2].P[e] \mLeftarrow{}{}\mRightarrow{} \mexists{}e\mmember{}[e1,e2].Q[e]))
By
(Repeat ((D 0 THENA Complete (Auto)))
THEN ParallelLast
THEN ParallelLast
THEN ExRepD
THEN Auto
THEN BackThruSomeHyp
THEN Auto)
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