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
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
not: ¬A,
iff: P ⇐⇒ Q,
false: False,
prop: ℙ,
guard: {T}
Latex:
\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:
2016_05_16-AM-09_14_38
Last ObjectModification:
2015_12_28-PM-09_57_53
Theory : new!event-ordering
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