Nuprl Lemma : thread-ordered
∀es:EO. ∀p:E ⟶ (E + Top).
((causal-predecessor(es;p) ∧ p-inject(E;E;p))
⇒ (∀e,e':E. ((e < e') ∨ (e = e' ∈ E)) ∨ (e' < e) supposing same-thread(es;p;e;e')))
Proof
Definitions occuring in Statement :
same-thread: same-thread(es;p;e;e'),
causal-predecessor: causal-predecessor(es;p),
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
union: left + right,
equal: s = t ∈ T,
p-inject: p-inject(A;B;f)
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
same-thread: same-thread(es;p;e;e'),
and: P ∧ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
or: P ∨ Q,
guard: {T}
Latex:
\mforall{}es:EO. \mforall{}p:E {}\mrightarrow{} (E + Top).
((causal-predecessor(es;p) \mwedge{} p-inject(E;E;p))
{}\mRightarrow{} (\mforall{}e,e':E. ((e < e') \mvee{} (e = e')) \mvee{} (e' < e) supposing same-thread(es;p;e;e')))
Date html generated:
2016_05_16-AM-10_33_44
Last ObjectModification:
2015_12_28-PM-09_17_30
Theory : new!event-ordering
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