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,
int-deq: IntDeq,
l_member: (x ∈ l),
list: T List,
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
Lemmas :
consensus-state4_wf,
list_wf,
Id_wf,
set_wf,
l_member_wf,
map-wf2,
fpf-domain_wf,
cs-estimate_wf,
top_wf,
consensus-state4-subtype,
fpf-ap_wf,
int-deq_wf,
member-fpf-dom,
map_wf,
list-subtype,
concat_wf,
assert_witness,
fpf-dom_wf,
equal_wf,
assert_wf,
all_wf,
isect_wf,
member-concat,
member_map,
l_member-set,
sq_stable__l_member,
decidable__equal_Id,
member_map2,
member-fpf-domain
\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:
2015_07_17-AM-11_29_28
Last ObjectModification:
2015_01_28-AM-01_34_27
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