Nuprl Lemma : assert-cs-is-committed
∀[V:Type]. ∀x:consensus-state3(V). (↑cs-is-committed(x) ⇐⇒ ∃v:V. (x = COMMITED[v] ∈ consensus-state3(V)))
Proof
Definitions occuring in Statement :
cs-is-committed: cs-is-committed(x),
cs-commited: COMMITED[v],
consensus-state3: consensus-state3(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
cs-commited: COMMITED[v],
consensus-state3: consensus-state3(T),
cs-is-committed: cs-is-committed(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
uimplies: b supposing a,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
outl: outl(x),
bfalse: ff,
false: False,
true: True
Latex:
\mforall{}[V:Type]. \mforall{}x:consensus-state3(V). (\muparrow{}cs-is-committed(x) \mLeftarrow{}{}\mRightarrow{} \mexists{}v:V. (x = COMMITED[v]))
Date html generated:
2016_05_16-AM-11_50_06
Last ObjectModification:
2015_12_29-PM-01_17_07
Theory : event-ordering
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