Nuprl Lemma : last-event
∀es:EO. ∀e:E.
∀[P:{a:E| loc(a) = loc(e) ∈ Id} ─→ ℙ]
((∀a:{a:E| loc(a) = loc(e) ∈ Id} . Dec(P[a]))
⇒ (∀e'≤e.¬P[e'] ∨ (∃e':E. (e' ≤loc e c∧ (P[e'] ∧ (∀e'':E. ((e' <loc e'') ⇒ e'' ≤loc e ⇒ (¬P[e'']))))))))
Proof
Definitions occuring in Statement :
alle-le: ∀e≤e'.P[e],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
cand: A c∧ B,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
previous-event-exists,
decidable__existse-le,
Id_wf,
es-loc_wf,
equal_wf,
all_wf,
es-E_wf,
decidable_wf,
event_ordering_wf,
alle-le_wf,
not_wf,
exists_wf,
es-le_wf,
es-le-loc,
es-locl_wf
\mforall{}es:EO. \mforall{}e:E.
\mforall{}[P:\{a:E| loc(a) = loc(e)\} {}\mrightarrow{} \mBbbP{}]
((\mforall{}a:\{a:E| loc(a) = loc(e)\} . Dec(P[a]))
{}\mRightarrow{} (\mforall{}e'\mleq{}e.\mneg{}P[e']
\mvee{} (\mexists{}e':E. (e' \mleq{}loc e c\mwedge{} (P[e'] \mwedge{} (\mforall{}e'':E. ((e' <loc e'') {}\mRightarrow{} e'' \mleq{}loc e {}\mRightarrow{} (\mneg{}P[e'']))))))))
Date html generated:
2015_07_17-AM-08_50_45
Last ObjectModification:
2015_01_27-PM-01_20_03
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