{ 
es:EO. i:Id.
[P:{e:E| loc(e) = i} 
]
e:E
(e is first@ i s.t. e.P[e]
{[Q:{e:E| loc(e) = i} ]
(e is first@ i s.t. e.Q[e]
Q[e] 
e'<e.e' is first@ i s.t. e.Q[e] P[e'])}) }
{ Proof }
Definitions occuring in Statement :
es-first-at: e is first@ i s.t. e.P[e],
alle-lt: e<e'.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: [x:A]. B[x],
prop: ,
guard: {T},
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,
es-first-at: e is first@ i s.t. e.P[e],
so_apply: x[s],
guard: {T},
iff: P Q,
and: P Q,
alle-lt: e<e'.P[e],
rev_implies: P Q,
not: 
A,
false: False,
member: t 
T,
so_lambda: 
x.t[x],
nat: 
,
ge: i 
j ,
le: A 
B,
Id: Id,
es-locl: (e <loc e'),
strongwellfounded: SWellFounded(R[x; y]),
exists: 
x:A. B[x],
sq_type: SQType(T),
uimplies: b supposing a
Lemmas :
es-first-at_wf,
es-locl_wf,
es-E_wf,
Id_wf,
es-loc_wf,
es-causl-swellfnd,
nat_wf,
le_wf,
alle-lt_wf,
event_ordering_wf,
es-causl_wf,
es-locl_transitivity2,
es-le_weakening,
nat_properties,
ge_wf,
subtype_base_sq,
atom2_subtype_base
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
\mforall{}e:E
(e is first@ i s.t. e.P[e]
{}\mRightarrow{} \{\mforall{}[Q:\{e:E| loc(e) = i\} {}\mrightarrow{} \mBbbP{}]
(e is first@ i s.t. e.Q[e] \mLeftarrow{}{}\mRightarrow{} Q[e] \mwedge{} \mforall{}e'<e.e' is first@ i s.t. e.Q[e] {}\mRightarrow{} P[e'])\})
Date html generated:
2011_08_16-AM-10_50_56
Last ObjectModification:
2011_06_18-AM-09_26_02
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