Nuprl Lemma : member-rcvs-on
∀tg:Id. ∀links:IdLnk List. ∀k:Knd. ((k ∈ Rcvs(tg) on links) ⇐⇒ (↑isrcv(k)) ∧ (tag(k) = tg ∈ Id) ∧ (lnk(k) ∈ links))
Proof
Definitions occuring in Statement :
rcvs-on: Rcvs(tg) on links,
tagof: tag(k),
lnk: lnk(k),
isrcv: isrcv(k),
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
rcvs-on: Rcvs(tg) on links,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
exists: ∃x:A. B[x],
Knd: Knd,
IdLnk: IdLnk,
Id: Id,
sq_type: SQType(T),
guard: {T},
top: Top,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
cand: A c∧ B,
rcv: rcv(l,tg),
isrcv: isrcv(k),
isl: isl(x),
bfalse: ff,
false: False
Latex:
\mforall{}tg:Id. \mforall{}links:IdLnk List. \mforall{}k:Knd.
((k \mmember{} Rcvs(tg) on links) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}isrcv(k)) \mwedge{} (tag(k) = tg) \mwedge{} (lnk(k) \mmember{} links))
Date html generated:
2016_05_16-AM-10_56_28
Last ObjectModification:
2015_12_29-AM-09_09_15
Theory : event-ordering
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