Nuprl Lemma : existse-before-iff
∀es:EO. ∀e':E.
∀[P:{e:E| loc(e) = loc(e') ∈ Id} ─→ ℙ]. (∃e<e'.P[e] ⇐⇒ (¬↑first(e')) c∧ (P[pred(e')] ∨ ∃e<pred(e').P[e]))
Proof
Definitions occuring in Statement :
existse-before: ∃e<e'.P[e],
es-first: first(e),
es-pred: pred(e),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
assert_wf,
es-first_wf2,
existse-before_wf,
Id_wf,
es-loc_wf,
es-E_wf,
not_wf,
or_wf,
es-pred-loc-base,
iff_weakening_equal,
es-pred_wf,
event_ordering_wf,
es-locl-iff,
and_wf,
equal_wf,
es-loc-pred,
exists_wf,
es-locl_wf,
es-pred-locl,
es-locl_transitivity2,
es-le_weakening
\mforall{}es:EO. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]
(\mexists{}e<e'.P[e] \mLeftarrow{}{}\mRightarrow{} (\mneg{}\muparrow{}first(e')) c\mwedge{} (P[pred(e')] \mvee{} \mexists{}e<pred(e').P[e]))
Date html generated:
2015_07_17-AM-08_45_56
Last ObjectModification:
2015_02_04-PM-05_55_45
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