{ 
es:EO. i:Id. e:E.
[P,R:{e:E| loc(e) = i} 
].
((e:E. Dec(R[e]) supposing loc(e) = i)
(es-first-at-since(es;i;e;e.R[e];e.P[e])
(loc(e) = i)
c
((P[e] (
R[e]))
((
e'':E. ((e'' <loc e) c P[e'']))
(e':E
((e' <loc e)
c (R[e']
(e'':E
((e' <loc e'')
(e'' <loc e)
((P[e'']) (R[e'']))))))))))) }
{ Proof }
Definitions occuring in Statement :
es-first-at-since: es-first-at-since(es;i;e;e.R[e];e.P[e]),
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uimplies: b supposing a,
uall: [x:A]. B[x],
cand: A c B,
prop: ,
so_apply: x[s],
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
not: A,
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
equal: s = t
Definitions :
all: x:A. B[x],
uall: [x:A]. B[x],
prop: ,
implies: P Q,
uimplies: b supposing a,
so_apply: x[s],
iff: P Q,
cand: A c B,
and: P Q,
exists: x:A. B[x],
rev_implies: P Q,
member: t 
T,
so_lambda: 
x.t[x],
not: A,
es-le: e 
loc e' ,
or: P 
Q,
es-first-at-since: es-first-at-since(es;i;e;e.R[e];e.P[e]),
alle-lt: e<e'.P[e],
false: False,
es-locl: (e <loc e'),
trans: Trans(T;x,y.E[x; y])
Lemmas :
es-E_wf,
es-locl_wf,
Id_wf,
es-loc_wf,
es-first-at-since_wf,
not_wf,
decidable_wf,
event_ordering_wf,
previous-event-exists,
es-le_weakening,
es-le_wf,
es-le-loc,
es-locl-trans,
es-le-not-locl
\mforall{}es:EO. \mforall{}i:Id. \mforall{}e:E.
\mforall{}[P,R:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}].
((\mforall{}e:E. Dec(R[e]) supposing loc(e) = i)
{}\mRightarrow{} (es-first-at-since(es;i;e;e.R[e];e.P[e])
\mLeftarrow{}{}\mRightarrow{} (loc(e) = i)
c\mwedge{} ((P[e] \mwedge{} (\mneg{}R[e]))
\mwedge{} ((\mexists{}e'':E. ((e'' <loc e) c\mwedge{} P[e'']))
{}\mRightarrow{} (\mexists{}e':E
((e' <loc e)
c\mwedge{} (R[e']
\mwedge{} (\mforall{}e'':E
((e' <loc e'') {}\mRightarrow{} (e'' <loc e) {}\mRightarrow{} ((\mneg{}P[e'']) \mwedge{} (\mneg{}R[e''])))))))))))
Date html generated:
2011_08_16-AM-11_11_30
Last ObjectModification:
2011_06_20-AM-00_19_29
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