Nuprl Lemma : member-es-closed-open-interval
∀es:EO. ∀e,e',ev:E. ((ev ∈ [e;e')) ⇐⇒ e ≤loc ev ∧ (ev <loc e'))
Proof
Definitions occuring in Statement :
es-closed-open-interval: [e;e'),
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
event_ordering: EO,
l_member: (x ∈ l),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
es-closed-open-interval: [e;e'),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q
Latex:
\mforall{}es:EO. \mforall{}e,e',ev:E. ((ev \mmember{} [e;e')) \mLeftarrow{}{}\mRightarrow{} e \mleq{}loc ev \mwedge{} (ev <loc e'))
Date html generated:
2016_05_16-AM-09_31_58
Last ObjectModification:
2015_12_28-PM-09_47_59
Theory : new!event-ordering
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