Nuprl 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]))
Proof
Definitions occuring in Statement :
existse-between2: ∃e∈[e1,e2].P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-le-loc,
Id_wf,
es-loc_wf,
existse-between2_wf,
all_wf,
iff_wf,
es-E_wf,
set_wf,
event_ordering_wf
\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]))
Date html generated:
2015_07_17-AM-08_48_06
Last ObjectModification:
2015_01_27-PM-02_26_34
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