Nuprl Lemma : es-locl-iff
∀the_es:EO. ∀e,e':E. ((e <loc e') ⇐⇒ (¬↑first(e')) ∧ ((e = pred(e') ∈ E) ∨ (e <loc pred(e'))))
Proof
Definitions occuring in Statement :
es-locl: (e <loc e'),
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
es-E: E,
es-base-E: es-base-E(es),
uimplies: b supposing a,
or: P ∨ Q,
not: ¬A,
false: False,
guard: {T},
trans: Trans(T;x,y.E[x; y])
Latex:
\mforall{}the$_{es}$:EO. \mforall{}e,e':E. ((e <loc e') \mLeftarrow{}{}\mRightarrow{} (\mneg{}\muparrow{}first(e')) \mwedge{} ((e = pred(e')) \mvee{} (e \000C<loc pred(e'))))
Date html generated:
2016_05_16-AM-09_18_27
Last ObjectModification:
2015_12_28-PM-09_56_36
Theory : new!event-ordering
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