Nuprl Lemma : es-locless-property
∀es:EO. ∀x,y:es-base-E(es).
((loc(x) = loc(y) ∈ Id)
⇒ (((x < y) ⇐⇒ ↑es-locless(es;x;y))
∧ ((¬↑es-locless(es;x;y)) ⇒ (¬↑es-locless(es;y;x)) ⇒ (x = y ∈ es-base-E(es)))))
Proof
Definitions occuring in Statement :
es-locless: es-locless(es;e1;e2),
es-causl: (e < e'),
es-loc: loc(e),
es-base-E: es-base-E(es),
event_ordering: EO,
Id: Id,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Lemmas :
event_ordering_properties,
es-loc-wf-base,
es-locless-wf-base,
es-causl-wf-base,
not_wf,
assert_wf,
equal_wf,
Id_wf,
es-base-E_wf,
event_ordering_wf
\mforall{}es:EO. \mforall{}x,y:es-base-E(es).
((loc(x) = loc(y))
{}\mRightarrow{} (((x < y) \mLeftarrow{}{}\mRightarrow{} \muparrow{}es-locless(es;x;y))
\mwedge{} ((\mneg{}\muparrow{}es-locless(es;x;y)) {}\mRightarrow{} (\mneg{}\muparrow{}es-locless(es;y;x)) {}\mRightarrow{} (x = y))))
Date html generated:
2015_07_17-AM-08_34_25
Last ObjectModification:
2015_01_27-PM-02_59_08
Home
Index