Nuprl Lemma : existse-before-iff
es:EO. e':E. [P:{e:E| loc(e) = loc(e')} 
]. (
e<e'.P[e] 
(
first(e')) c
(P[pred(e')] 
e<pred(e').P[e]))
Proof not projected
Definitions occuring in Statement :
existse-before: e<e'.P[e],
es-pred: pred(e),
es-first: first(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: b,
uall: [x:A]. B[x],
cand: A c B,
prop: ,
so_apply: x[s],
all: x:A. B[x],
iff: P Q,
not: A,
or: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
equal: s = t
Definitions :
so_lambda: 
x.t[x],
member: t 
T,
rev_implies: P Q,
implies: P Q,
and: P Q,
or: P Q,
cand: A c B,
so_apply: x[s],
existse-before: e<e'.P[e],
iff: P Q,
prop: ,
uall: [x:A]. B[x],
all: x:A. B[x],
false: False,
guard: {T},
exists: x:A. B[x],
not: A,
uimplies: b supposing a,
es-locl: (e <loc e')
Lemmas :
es-loc-pred,
event_ordering_wf,
es-pred_wf,
or_wf,
es-first_wf,
assert_wf,
not_wf,
es-loc_wf,
Id_wf,
es-E_wf,
existse-before_wf,
es-locl-iff,
es-locl_wf,
es-pred-locl,
es-le_weakening,
es-locl_transitivity2
\mforall{}es:EO. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]
(\mexists{}e<e'.P[e] \mLeftarrow{}{}\mRightarrow{} (\mneg{}\muparrow{}first(e')) c\mwedge{} (P[pred(e')] \mvee{} \mexists{}e<pred(e').P[e]))
Date html generated:
2012_01_23-PM-12_11_49
Last ObjectModification:
2011_12_13-AM-10_30_57
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