Nuprl Lemma : cs-archived-listable
∀[V:Type]
∀A:Id List. ∀s:ConsensusState.
∃L:V List
∀b:{a:Id| (a ∈ A)} . ∀v:V. ∀j:ℤ. ((v ∈ L)) supposing ((Estimate(s;b)(j) = v ∈ V) and (↑j ∈ dom(Estimate(s;b))))
Proof
Definitions occuring in Statement :
cs-estimate: Estimate(s;a),
consensus-state4: ConsensusState,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
Id: Id,
l_member: (x ∈ l),
list: T List,
int-deq: IntDeq,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
fpf-domain: fpf-domain(f),
exists: ∃x:A. B[x],
cand: A c∧ B,
sq_stable: SqStable(P),
squash: ↓T
Latex:
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}s:ConsensusState.
\mexists{}L:V List
\mforall{}b:\{a:Id| (a \mmember{} A)\} . \mforall{}v:V. \mforall{}j:\mBbbZ{}.
((v \mmember{} L)) supposing ((Estimate(s;b)(j) = v) and (\muparrow{}j \mmember{} dom(Estimate(s;b))))
Date html generated:
2016_05_16-PM-00_02_29
Last ObjectModification:
2016_01_17-PM-03_55_45
Theory : event-ordering
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