Nuprl Lemma : es-first-before2
∀es:EO. ∀e':E.
∀[P:{e:E| loc(e) = loc(e') ∈ Id} ─→ ℙ]
(∀e@loc(e').Dec(P[e]) ⇒ (∃e<e'.e is first@ loc(e') s.t. e.P[e] ⇐⇒ ∃e<e'.P[e]))
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),
uall: ∀[x:A]. B[x],
prop: ℙ,
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 ∈ T
Lemmas :
es-first-before,
alle-at_wf,
es-loc_wf,
Id_wf,
es-E_wf,
decidable_wf,
event_ordering_wf
\mforall{}es:EO. \mforall{}e':E.
\mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e@loc(e').Dec(P[e]) {}\mRightarrow{} (\mexists{}e<e'.e is first@ loc(e') s.t. e.P[e] \mLeftarrow{}{}\mRightarrow{} \mexists{}e<e'.P[e]))
Date html generated:
2015_07_17-AM-09_05_44
Last ObjectModification:
2015_01_27-PM-00_48_41
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