Nuprl Lemma : es-direct-prior-member-iff
es:EO. e,e':E.
(e' 
es-direct-prior(es;e) 
(e' < e) 
(e'':E. ((loc(e'') = loc(e')) (e'' < e) e'' 
loc e' )))
Proof not projected
Definitions occuring in Statement :
es-direct-prior: es-direct-prior(es;e),
es-le: e loc e' ,
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
all: x:A. B[x],
iff: P Q,
implies: P Q,
and: P Q,
equal: s = t,
bag-member: x bs
Definitions :
all: x:A. B[x],
iff: P Q,
and: P Q,
implies: P Q,
rev_implies: P Q,
member: t T,
so_lambda: 
x.t[x],
es-le: e loc e' ,
uiff: uiff(P;Q),
guard: {T},
or: P 
Q,
es-direct-prior: es-direct-prior(es;e),
bag-maximals: bag-maximals(bg;R),
not: 
A,
uall: [x:A]. B[x],
so_apply: x[s],
uimplies: b supposing a,
false: False,
rev_uimplies: rev_uimplies(P;Q),
es-locl: (e <loc e'),
prop: 
,
subtype: S 
T
Lemmas :
es-direct-prior-member,
es-causl_wf,
equal_wf,
Id_wf,
es-loc_wf,
bag-member_wf,
es-direct-prior_wf,
and_wf,
all_wf,
implies-wf,
es-le_wf,
es-E_wf,
event_ordering_wf,
bag-member-remove-repeats,
bag-maximals_wf,
es-pred-list_wf,
bag_qinc,
bnot_wf,
es-blocl_wf,
es-eq_wf,
bag-member-filter,
bag-maximal?_wf,
bag-maximal?-max,
bag-member-list,
decidable__es-E-equal,
member-es-pred-list,
assert_of_bnot,
not_functionality_wrt_iff,
assert_wf,
es-locl_wf,
es-blocl-iff,
es-locl-trichotomy,
subtype_rel_self,
bag-maximal?-iff,
es-locl_transitivity2,
es-locl_irreflexivity
\mforall{}es:EO. \mforall{}e,e':E.
(e' \mdownarrow{}\mmember{} es-direct-prior(es;e)
\mLeftarrow{}{}\mRightarrow{} (e' < e) \mwedge{} (\mforall{}e'':E. ((loc(e'') = loc(e')) {}\mRightarrow{} (e'' < e) {}\mRightarrow{} e'' \mleq{}loc e' )))
Date html generated:
2012_01_23-PM-12_08_56
Last ObjectModification:
2011_11_29-PM-09_15_19
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