Nuprl Lemma : es-first-since_functionality_wrt_iff
∀es:EO. ∀e1:E. ∀e2:{e:E| loc(e) = loc(e1) ∈ Id} .
∀[p,p':{e:E| loc(e) = loc(e1) ∈ Id} ─→ ℙ].
((∀e:{e:E| loc(e) = loc(e1) ∈ Id} . (p[e] ⇐⇒ p'[e])) ⇒ (e2 = first e ≥ e1.p[e] ⇐⇒ e2 = first e ≥ e1.p'[e]))
Proof
Definitions occuring in Statement :
es-first-since: e2 = first e ≥ e1.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,
es-locl_wf,
es-le_wf,
es-first-since_wf,
es-E_wf,
all_wf,
iff_wf,
set_wf,
event_ordering_wf
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[p,p':\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
((\mforall{}e:\{e:E| loc(e) = loc(e1)\} . (p[e] \mLeftarrow{}{}\mRightarrow{} p'[e]))
{}\mRightarrow{} (e2 = first e \mgeq{} e1.p[e] \mLeftarrow{}{}\mRightarrow{} e2 = first e \mgeq{} e1.p'[e]))
Date html generated:
2015_07_17-AM-08_52_55
Last ObjectModification:
2015_01_27-PM-01_18_30
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