Nuprl Lemma : cs-inning-committed-single-stable
∀[V:Type]. ∀[A:Id List]. ∀[W:{a:Id| (a ∈ A)} List List]. ∀[s,s2:ConsensusState].
∀[i:ℤ]. ∀[v,v2:V].
(v = v2 ∈ V) supposing
(in state s, inning i has committed v2 and
in state s2, inning i could commit v and
two-intersection(A;W))
supposing s ts-rel(consensus-ts4(V;A;W)) s2
Proof
Definitions occuring in Statement :
two-intersection: two-intersection(A;W),
cs-inning-committable: in state s, inning i could commit v ,
cs-inning-committed: in state s, inning i has committed v,
consensus-ts4: consensus-ts4(V;A;W),
consensus-state4: ConsensusState,
Id: Id,
l_member: (x ∈ l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
set: {x:A| B[x]} ,
int: ℤ,
universe: Type,
equal: s = t ∈ T,
ts-rel: ts-rel(ts)
Lemmas :
cs-inning-committed-single,
cs-inning-committed_wf,
cs-inning-committable_wf,
two-intersection_wf,
infix_ap_wf,
consensus-state4_wf,
ts-rel_wf,
consensus-ts4_wf,
subtype_rel_dep_function,
ts-type_wf,
subtype_rel_self,
Id_wf,
l_member_wf,
fpf_wf,
list_wf,
consensus-ts4-inning-committed-stable
\mforall{}[V:Type]. \mforall{}[A:Id List]. \mforall{}[W:\{a:Id| (a \mmember{} A)\} List List]. \mforall{}[s,s2:ConsensusState].
\mforall{}[i:\mBbbZ{}]. \mforall{}[v,v2:V].
(v = v2) supposing
(in state s, inning i has committed v2 and
in state s2, inning i could commit v and
two-intersection(A;W))
supposing s ts-rel(consensus-ts4(V;A;W)) s2
Date html generated:
2015_07_17-AM-11_30_49
Last ObjectModification:
2015_01_28-AM-01_32_51
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