{ 
es:EO. e1:E. e2:{e:E| loc(e) = loc(e1)} .
[Q:{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])+ 
e1 
loc e2 
Q[e2])) }
{ Proof }
Definitions occuring in Statement :
es-pplus: [e1,e2]~([a,b].p[a; b])+,
es-first-since: e2 = first e e1.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,
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,
rev_implies: P Q,
cand: A c B,
member: t 
T,
so_lambda: 
x y.t[x; y],
so_lambda: x.t[x],
nat: 
,
le: A B,
ge: i j ,
not: 
A,
false: False,
alle-at: e@i.P[e],
top: Top,
subtype: S 
T,
es-pplus: [e1,e2]~([a,b].p[a; b])+,
es-first-since: e2 = first e e1.P[e],
so_apply: x[s1;s2],
es-pstar-q: [e1;e2]~([a,b].p[a; b])*[a,b].q[a; b],
exists: 
x:A. B[x],
decidable: Dec(P),
uimplies: b supposing a,
or: P 
Q,
existse-between1: e[e1,e2).P[e]
Lemmas :
es-pplus-le,
es-first-since_wf,
Id_wf,
es-loc_wf,
es-E_wf,
es-pplus_wf,
es-le_wf,
decidable_wf,
event_ordering_wf,
nat_properties,
ge_wf,
nat_wf,
le_wf,
length_wf1,
es-interval_wf,
decidable__existse-between1,
es-le-loc,
es-next,
es-interval-partition,
es-le-trans2,
es-pred-locl,
es-locl_wf,
append_wf,
es-interval-non-zero,
length-append,
es-interval_wf2,
top_wf,
length_wf_nat,
es-loc-pred,
es-pplus-partition,
member_wf,
es-pplus-trivial
\mforall{}es:EO. \mforall{}e1:E. \mforall{}e2:\{e:E| loc(e) = loc(e1)\} .
\mforall{}[Q:\{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])+ \mLeftarrow{}{}\mRightarrow{} e1 \mleq{}loc e2 \mwedge{} Q[e2]))
Date html generated:
2011_08_16-AM-10_58_33
Last ObjectModification:
2011_06_18-AM-09_31_25
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