{ 
es:EO. e1:E. e2:{e:E| loc(e) = loc(e1)} .
[Q,R:{e:E| loc(e) = loc(e1)} 
].
((e:{e:E| loc(e) = loc(e1)} . Dec(Q[e]))
([e1,e2]~([a,b].b = first e 
a.Q[e] 
e
[a,b).
R[e])+
e1 
loc e2 Q[e2] e[e1,e2].R[e] Q[e])) }
{ Proof }
Definitions occuring in Statement :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
es-first-since: e2 = first e e1.P[e],
alle-between2: e[e1,e2].P[e],
alle-between1: e[e1,e2).P[e],
es-le: e loc e' ,
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: [x:A]. B[x],
prop: ,
so_apply: x[s],
all: 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,
so_apply: x[s],
iff: P Q,
and: P Q,
alle-between2: e[e1,e2].P[e],
rev_implies: P Q,
member: t T,
so_lambda: 
x y.t[x; y],
cand: A c B,
so_lambda: x.t[x],
alle-between1: e[e1,e2).P[e],
guard: {T},
not: A,
so_apply: x[s1;s2],
uimplies: b supposing a,
es-le: e loc e' ,
or: P 
Q,
false: False,
es-first-since: e2 = first e e1.P[e]
Lemmas :
es-pplus_wf,
es-loc_wf,
es-first-since_wf,
Id_wf,
es-E_wf,
alle-between1_wf,
not_wf,
es-le_wf,
decidable_wf,
event_ordering_wf,
es-le-loc,
es-pplus_functionality_wrt_implies,
es-locl_wf,
l_member_wf,
es-interval_wf,
es-pplus-first-since,
es-pplus-alle-between2,
alle-between2_wf,
member-es-interval,
es-le_transitivity,
es-locl_transitivity2,
es-le_weakening
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[Q,R:\{e:E| loc(e) = loc(e1)\} {}\mrightarrow{} \mBbbP{}].
((\mforall{}e:\{e:E| loc(e) = loc(e1)\} . Dec(Q[e]))
{}\mRightarrow{} ([e1,e2]\msim{}([a,b].b = first e \mgeq{} a.Q[e] \mwedge{} \mforall{}e\mmember{}[a,b).\mneg{}R[e])+
\mLeftarrow{}{}\mRightarrow{} e1 \mleq{}loc e2 \mwedge{} Q[e2] \mwedge{} \mforall{}e\mmember{}[e1,e2].R[e] {}\mRightarrow{} Q[e]))
Date html generated:
2011_08_16-AM-10_58_41
Last ObjectModification:
2011_06_18-AM-09_31_31
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