{ 
es:EO. i:Id.
[P:{e:E| loc(e) = i} 
]
((e:{e:E| loc(e) = i} . Dec(P[e]))
(e:E
P[e] (
e':E. (e' 
loc e 
e' is first@ i s.t. e.P[e]))
supposing loc(e) = i)) }
{ Proof }
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.P[e],
es-le: 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],
prop: ,
so_apply: x[s],
all: x:A. B[x],
exists: x:A. B[x],
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,
so_apply: x[s],
uimplies: b supposing a,
member: t 
T,
nat: 
,
guard: {T},
ge: i 
j ,
le: A B,
not: 
A,
false: False,
alle-at: e@i.P[e],
subtype: S 
T,
suptype: suptype(S; T),
and: P Q,
exists: x:A. B[x],
cand: A c B,
so_lambda: 
x.t[x],
es-le: e loc e' ,
or: P 
Q,
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: e<e'.P[e],
existse-before: e<e'.P[e],
strongwellfounded: SWellFounded(R[x; y]),
decidable: Dec(P),
es-locl: (e <loc e')
Lemmas :
es-causl-swellfnd,
nat_wf,
le_wf,
es-E_wf,
es-loc_wf,
decidable_wf,
Id_wf,
event_ordering_wf,
es-causl_wf,
nat_properties,
ge_wf,
decidable__existse-before,
es-locl_transitivity1,
es-le_weakening,
es-le_wf,
es-first-at_wf,
es-locl_wf
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}e:\{e:E| loc(e) = i\} . Dec(P[e]))
{}\mRightarrow{} (\mforall{}e:E. P[e] {}\mRightarrow{} (\mexists{}e':E. (e' \mleq{}loc e \mwedge{} e' is first@ i s.t. e.P[e])) supposing loc(e) = i))
Date html generated:
2011_08_16-AM-10_50_24
Last ObjectModification:
2011_06_18-AM-09_25_35
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