Nuprl Lemma : es-pred_property
∀es:EO. ∀e:E.
{(loc(pred(e)) = loc(e) ∈ Id)
∧ (pred(e) < e)
∧ (∀e':E. (e' < e) ⇒ ((e' = pred(e) ∈ E) ∨ (e' < pred(e))) supposing loc(e') = loc(e) ∈ Id)}
supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-first: first(e),
es-pred: pred(e),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
guard: {T},
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
es-E: E,
es-base-E: es-base-E(es),
guard: {T},
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
or: P ∨ Q,
es-first: first(e),
btrue: tt,
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
assert: ↑b,
true: True,
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
es-dom: es-dom(es),
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}es:EO. \mforall{}e:E.
\{(loc(pred(e)) = loc(e))
\mwedge{} (pred(e) < e)
\mwedge{} (\mforall{}e':E. (e' < e) {}\mRightarrow{} ((e' = pred(e)) \mvee{} (e' < pred(e))) supposing loc(e') = loc(e))\}
supposing \mneg{}\muparrow{}first(e)
Date html generated:
2016_05_16-AM-09_16_44
Last ObjectModification:
2016_01_17-PM-01_31_04
Theory : new!event-ordering
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