Nuprl Lemma : es-base-pred-properties
∀es:EO. ∀e:es-base-E(es).
((loc(pred1(e)) = loc(e) ∈ Id)
∧ (¬(e < pred1(e)))
∧ (∀x:es-base-E(es). ((x < e) ⇒ (loc(x) = loc(e) ∈ Id) ⇒ ((pred1(e) < e) ∧ (¬(pred1(e) < x))))))
Proof
Definitions occuring in Statement :
es-causl: (e < e'),
es-base-pred: pred1(e),
es-loc: loc(e),
es-base-E: es-base-E(es),
event_ordering: EO,
Id: Id,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
uall: ∀[x:A]. B[x]
Latex:
\mforall{}es:EO. \mforall{}e:es-base-E(es).
((loc(pred1(e)) = loc(e))
\mwedge{} (\mneg{}(e < pred1(e)))
\mwedge{} (\mforall{}x:es-base-E(es). ((x < e) {}\mRightarrow{} (loc(x) = loc(e)) {}\mRightarrow{} ((pred1(e) < e) \mwedge{} (\mneg{}(pred1(e) < x))))))
Date html generated:
2016_05_16-AM-09_14_35
Last ObjectModification:
2015_12_28-PM-09_58_19
Theory : new!event-ordering
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