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
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\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:
2016_05_16-AM-10_25_13
Last ObjectModification:
2015_12_28-PM-09_18_49
Theory : new!event-ordering
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