{ 
es:EO. i:Id.
[P:e1:{e:E| loc(e) = i} 
{e2:E| loc(e2) = i} 
]
(e1@i.e2
e1.(e:E. ((e1 <loc e) 
e 
loc e2 P[e;e2])) P[e1;e2]
e1@i.e2<e1.P[e1;e2]
(e,e':E. (P[e;e']) supposing ((loc(e') = i) and (loc(e) = i)))) }
{ Proof }
Definitions occuring in Statement :
alle-lt: e<e'.P[e],
alle-ge: e'e.P[e'],
alle-at: e@i.P[e],
es-le: e loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uimplies: b supposing a,
uall: [x:A]. B[x],
prop: ,
so_apply: x[s1;s2],
all: x:A. B[x],
implies: 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,
alle-ge: e'e.P[e'],
so_apply: x[s1;s2],
uimplies: b supposing a,
member: t 
T,
so_lambda: 
x.t[x],
and: P 
Q,
es-locl: (e <loc e'),
so_apply: x[s],
decidable: Dec(P),
or: P 
Q,
alle-at: e@i.P[e],
alle-lt: e<e'.P[e],
not: 
A,
iff: P 
Q,
false: False
Lemmas :
es-interval-induction,
Id_wf,
es-loc_wf,
es-E_wf,
alle-at_wf,
alle-lt_wf,
es-le_wf,
es-locl_wf,
event_ordering_wf,
es-le-loc,
decidable__es-le,
not_functionality_wrt_iff,
not_wf,
es-le-not-locl,
decidable__es-locl
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:e1:\{e:E| loc(e) = i\} {}\mrightarrow{} \{e2:E| loc(e2) = i\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e1@i.\mforall{}e2\mgeq{}e1.(\mforall{}e:E. ((e1 <loc e) {}\mRightarrow{} e \mleq{}loc e2 {}\mRightarrow{} P[e;e2])) {}\mRightarrow{} P[e1;e2]
{}\mRightarrow{} \mforall{}e1@i.\mforall{}e2<e1.P[e1;e2]
{}\mRightarrow{} (\mforall{}e,e':E. (P[e;e']) supposing ((loc(e') = i) and (loc(e) = i))))
Date html generated:
2011_08_16-AM-10_53_39
Last ObjectModification:
2011_06_18-AM-09_26_55
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