Nuprl Lemma : alle-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 :
alle-le: ∀e≤e'.P[e],
alle-lt: ∀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,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
es-le-self,
es-le_weakening,
es-locl_wf,
es-E_wf,
all_wf,
es-le_wf,
es-le-loc,
Id_wf,
es-loc_wf,
equal_wf,
and_wf,
member_wf
\mforall{}es:EO. \mforall{}e':E. \mforall{}[P:\{e:E| loc(e) = loc(e')\} {}\mrightarrow{} \mBbbP{}]. (\mforall{}e\mleq{}e'.P[e] \mLeftarrow{}{}\mRightarrow{} P[e'] \mwedge{} \mforall{}e<e'.P[e])
Date html generated:
2015_07_17-AM-08_46_41
Last ObjectModification:
2015_01_27-PM-02_28_10
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