Nuprl Lemma : assert-graph-rcvset
∀a:Id ⟶ Id ⟶ Id. ∀b:Id. ∀S:Id List. ∀G:Graph(S). ∀k:Knd.
(↑graph-rcvset(a;b;S;G;k) ⇐⇒ ∃i,j:Id. ((i ∈ S) ∧ (j ∈ S) ∧ (i⟶j)∈G ∧ (k = rcv((link(a i j) from i to j),b) ∈ Knd)))
Proof
Definitions occuring in Statement :
graph-rcvset: graph-rcvset(a;b;S;G;k),
rcv: rcv(l,tg),
Knd: Knd,
mk_lnk: (link(n) from i to j),
id-graph-edge: (i⟶j)∈G,
id-graph: Graph(S),
Id: Id,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
id-graph: Graph(S),
Knd: Knd,
IdLnk: IdLnk,
graph-rcvset: graph-rcvset(a;b;S;G;k),
lnk: lnk(k),
tagof: tag(k),
isrcv: isrcv(k),
isl: isl(x),
outl: outl(x),
band: p ∧b q,
ifthenelse: if b then t else f fi ,
btrue: tt,
pi2: snd(t),
pi1: fst(t),
lname: lname(l),
lsrc: source(l),
ldst: destination(l),
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
uimplies: b supposing a,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
subtype_rel: A ⊆r B,
id-graph-edge: (i⟶j)∈G,
mk_lnk: (link(n) from i to j),
rcv: rcv(l,tg),
cand: A c∧ B,
Id: Id,
top: Top,
l_member: (x ∈ l)
Latex:
\mforall{}a:Id {}\mrightarrow{} Id {}\mrightarrow{} Id. \mforall{}b:Id. \mforall{}S:Id List. \mforall{}G:Graph(S). \mforall{}k:Knd.
(\muparrow{}graph-rcvset(a;b;S;G;k)
\mLeftarrow{}{}\mRightarrow{} \mexists{}i,j:Id. ((i \mmember{} S) \mwedge{} (j \mmember{} S) \mwedge{} (i{}\mrightarrow{}j)\mmember{}G \mwedge{} (k = rcv((link(a i j) from i to j),b))))
Date html generated:
2016_05_16-AM-10_59_04
Last ObjectModification:
2015_12_29-AM-09_18_05
Theory : event-ordering
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