{ 
[V:Type]
eq:EqDecider(V). A:Id List. t:
. f:V List 
V.
((vs:V List. (f vs 
vs) supposing ||vs|| 
1 )
(v:V. s:ts-reachable(three-consensus-ts(V;A;t;f)).
(three-cs-decided(V;A;t;f;s;v)
(
aA. (||s a|| 1 ) 
(hd(s a) = Init[v]))))) }
{ Proof }
Definitions occuring in Statement :
three-cs-decided: three-cs-decided(V;A;t;f;s;v),
three-consensus-ts: three-consensus-ts(V;A;t;f),
cs-initial-rcv: Init[v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
hd: hd(l),
length: ||as||,
nat_plus: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
ge: i j ,
all: x:A. B[x],
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A B[x],
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
l_exists: (xL. P[x]),
l_member: (x l),
deq: EqDecider(T),
ts-reachable: ts-reachable(ts)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
implies: P Q,
uimplies: b supposing a,
member: t T,
prop: 
,
or: P 
Q,
ts-reachable: ts-reachable(ts),
three-consensus-ts: three-consensus-ts(V;A;t;f),
three-cs-decided: three-cs-decided(V;A;t;f;s;v),
and: P Q,
exists: x:A. B[x],
ts-type: ts-type(ts),
pi1: fst(t),
length: ||as||,
l_all: (xL.P[x]),
ycomb: Y,
iff: P 
Q,
rev_implies: P Q,
subtype: S 
T
Lemmas :
three-cs-archive-invariant,
three-cs-decided_wf,
ts-reachable_wf,
three-consensus-ts_wf,
nat_plus_inc,
ts-type_wf,
ge_wf,
length_wf1,
l_member_wf,
nat_plus_wf,
Id_wf,
deq_wf,
cons_member
\mforall{}[V:Type]
\mforall{}eq:EqDecider(V). \mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:V List {}\mrightarrow{} V.
((\mforall{}vs:V List. (f vs \mmember{} vs) supposing ||vs|| \mgeq{} 1 )
{}\mRightarrow{} (\mforall{}v:V. \mforall{}s:ts-reachable(three-consensus-ts(V;A;t;f)).
(three-cs-decided(V;A;t;f;s;v) {}\mRightarrow{} (\mexists{}a\mmember{}A. (||s a|| \mgeq{} 1 ) \mwedge{} (hd(s a) = Init[v])))))
Date html generated:
2011_08_16-AM-10_17_57
Last ObjectModification:
2011_06_18-AM-09_07_10
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