Nuprl Lemma : es-le-iff
∀the_es:EO. ∀e,e':E. (e ≤loc e' ⇐⇒ ((¬↑first(e')) c∧ e ≤loc pred(e') ) ∨ (e = e' ∈ E))
Proof
Definitions occuring in Statement :
es-le: e ≤loc e' ,
es-first: first(e),
es-pred: pred(e),
es-E: E,
event_ordering: EO,
assert: ↑b,
cand: A c∧ B,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
or: P ∨ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
es-le: e ≤loc e' ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
or: P ∨ Q,
cand: A c∧ B,
guard: {T},
prop: ℙ,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
rev_implies: P ⇐ Q
Latex:
\mforall{}the$_{es}$:EO. \mforall{}e,e':E. (e \mleq{}loc e' \mLeftarrow{}{}\mRightarrow{} ((\mneg{}\muparrow{}first(e')) c\mwedge{} e \mleq{}loc pred(e') ) \mvee{} \000C(e = e'))
Date html generated:
2016_05_16-AM-09_22_51
Last ObjectModification:
2015_12_28-PM-09_53_34
Theory : new!event-ordering
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