Nuprl Lemma : es-pred_property_base
∀es:EO. ∀e:es-base-E(es).
((loc(pred(e)) = loc(e) ∈ Id)
∧ ((pred(e) < e) ∨ (pred(e) = e ∈ es-base-E(es)))
∧ (∀e':E. (e' < e) ⇒ ((e' = pred(e) ∈ es-base-E(es)) ∨ (e' < pred(e))) supposing loc(e') = loc(e) ∈ Id))
Proof
Definitions occuring in Statement :
es-pred: pred(e),
es-causl: (e < e'),
es-loc: loc(e),
es-E: E,
es-base-E: es-base-E(es),
event_ordering: EO,
Id: Id,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
prop: ℙ,
implies: P ⇒ Q,
es-E: E,
es-base-E: es-base-E(es),
uimplies: b supposing a,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
false: False,
not: ¬A
Latex:
\mforall{}es:EO. \mforall{}e:es-base-E(es).
((loc(pred(e)) = loc(e))
\mwedge{} ((pred(e) < e) \mvee{} (pred(e) = e))
\mwedge{} (\mforall{}e':E. (e' < e) {}\mRightarrow{} ((e' = pred(e)) \mvee{} (e' < pred(e))) supposing loc(e') = loc(e)))
Date html generated:
2016_05_16-AM-09_16_38
Last ObjectModification:
2015_12_28-PM-09_56_44
Theory : new!event-ordering
Home
Index