Nuprl Lemma : existse-le-iff
∀es:EO. ∀e':E. ∀[P:{e:E| loc(e) = loc(e') ∈ Id} ─→ ℙ]. (∃e≤e'.P[e] ⇐⇒ P[e'] ∨ ∃e<e'.P[e])
Proof
Definitions occuring in Statement :
existse-before: ∃e<e'.P[e],
existse-le: ∃e≤e'.P[e],
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
existse-le_wf,
Id_wf,
es-loc_wf,
es-E_wf,
or_wf,
existse-before_wf,
event_ordering_wf,
es-locl_wf,
and_wf,
equal_wf,
es-le-self,
es-le_wf,
es-le-loc,
es-le_weakening
\mforall{}es:EO. \mforall{}e':E. \mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]. (\mexists{}e\mleq{}e'.P[e] \mLeftarrow{}{}\mRightarrow{} P[e'] \mvee{} \mexists{}e<e'.P[e])
Date html generated:
2015_07_17-AM-08_46_07
Last ObjectModification:
2015_01_27-PM-02_29_09
Home
Index