Nuprl Lemma : member-links-from-to
∀tg:Id. ∀srclocs,dstlocs:Id List. ∀l:IdLnk.
((l ∈ links(tg) from srclocs to dstlocs)
⇐⇒ {(source(l) ∈ srclocs) ∧ (destination(l) ∈ dstlocs) ∧ (lname(l) = tg ∈ Id)})
Proof
Definitions occuring in Statement :
links-from-to: links(tg) from srclocs to dstlocs,
lname: lname(l),
ldst: destination(l),
lsrc: source(l),
IdLnk: IdLnk,
Id: Id,
l_member: (x ∈ l),
list: T List,
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
links-from-to: links(tg) from srclocs to dstlocs,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
guard: {T},
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
uimplies: b supposing a,
IdLnk: IdLnk,
Id: Id,
sq_type: SQType(T),
top: Top,
cand: A c∧ B,
lsrc: source(l),
pi1: fst(t),
ldst: destination(l),
pi2: snd(t),
lname: lname(l),
mk_lnk: (link(n) from i to j),
squash: ↓T,
true: True
Latex:
\mforall{}tg:Id. \mforall{}srclocs,dstlocs:Id List. \mforall{}l:IdLnk.
((l \mmember{} links(tg) from srclocs to dstlocs)
\mLeftarrow{}{}\mRightarrow{} \{(source(l) \mmember{} srclocs) \mwedge{} (destination(l) \mmember{} dstlocs) \mwedge{} (lname(l) = tg)\})
Date html generated:
2016_05_16-AM-10_56_18
Last ObjectModification:
2016_01_17-PM-03_49_09
Theory : event-ordering
Home
Index