{ 
es:EO. i:Id. e':E.
[P:{e:E| loc(e) = i} 
]
(e@i.Dec(P[e])
e<e'.e is first@ i s.t. e.P[e] 
e<e'.P[e]
supposing loc(e') = i) }
{ Proof }
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.P[e],
existse-before: e<e'.P[e],
alle-at: e@i.P[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],
iff: P Q,
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,
so_apply: x[s],
uimplies: b supposing a,
iff: P Q,
member: t 
T,
and: P 
Q,
rev_implies: P Q,
so_lambda: 
x.t[x],
existse-before: e<e'.P[e],
exists: x:A. B[x],
cand: A c B,
alle-lt: e<e'.P[e],
not: 
A,
false: False,
alle-at: e@i.P[e],
Id: Id,
or: P 
Q,
guard: {T},
es-first-at: e is first@ i s.t. e.P[e],
es-locl: (e <loc e'),
wellfounded: WellFnd{i}(A;x,y.R[x; y]),
sq_type: SQType(T),
decidable: Dec(P)
Lemmas :
existse-before_wf,
es-first-at_wf,
es-E_wf,
Id_wf,
es-loc_wf,
alle-at_wf,
decidable_wf,
event_ordering_wf,
es-locl_wf,
es-locl-wellfnd,
btrue_neq_bfalse,
assert_wf,
es-first_wf,
assert_elim,
es-locl-first,
decidable__existse-before,
es-pred_wf,
es-loc-pred,
subtype_base_sq,
atom2_subtype_base,
existse-before-iff,
es-pred-locl
\mforall{}es:EO. \mforall{}i:Id. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e@i.Dec(P[e]) {}\mRightarrow{} \mexists{}e<e'.e is first@ i s.t. e.P[e] \mLeftarrow{}{}\mRightarrow{} \mexists{}e<e'.P[e] supposing loc(e') = i)
Date html generated:
2011_08_16-AM-11_11_22
Last ObjectModification:
2011_06_20-AM-00_19_22
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