Nuprl Lemma : rcvs-on-links-from-to
∀tg1,tg2:Id. ∀srclocs,dstlocs:Id List.
(∀d∈dstlocs.(∀s∈srclocs.(∃k∈Rcvs(tg1) on links(tg2) from srclocs to dstlocs. (source(lnk(k)) = s ∈ Id)
∧ (destination(lnk(k)) = d ∈ Id))))
Proof
Definitions occuring in Statement :
rcvs-on: Rcvs(tg) on links,
links-from-to: links(tg) from srclocs to dstlocs,
ldst: destination(l),
lsrc: source(l),
lnk: lnk(k),
Id: Id,
l_exists: (∃x∈L. P[x]),
l_all: (∀x∈L.P[x]),
list: T List,
all: ∀x:A. B[x],
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
assert: ↑b,
ifthenelse: if b then t else f fi ,
isrcv: isrcv(k),
isl: isl(x),
rcv: rcv(l,tg),
btrue: tt,
true: True,
uall: ∀[x:A]. B[x],
prop: ℙ,
and: P ∧ Q,
cand: A c∧ B,
lsrc: source(l),
pi1: fst(t),
lnk: lnk(k),
outl: outl(x),
mk_lnk: (link(n) from i to j),
ldst: destination(l),
pi2: snd(t),
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
top: Top
Latex:
\mforall{}tg1,tg2:Id. \mforall{}srclocs,dstlocs:Id List.
(\mforall{}d\mmember{}dstlocs.(\mforall{}s\mmember{}srclocs.(\mexists{}k\mmember{}Rcvs(tg1) on links(tg2) from srclocs to dstlocs. (source(lnk(k)) = s)
\mwedge{} (destination(lnk(k)) = d))))
Date html generated:
2016_05_16-AM-10_56_32
Last ObjectModification:
2015_12_29-AM-09_11_34
Theory : event-ordering
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