{ 
V:Type. A:Id List. t:
. f:V List 
V.
s:ts-type(three-consensus-ts(V;A;t;f)).
((ts-init(three-consensus-ts(V;A;t;f))
(ts-rel(three-consensus-ts(V;A;t;f))^*)
s)
(a:{a:Id| (a 
A)} . n:. b:{a:Id| (a A)} . v1:V.
((Vote[b;n;v1] s a)
(
L:consensus-rcv(V;A) List
(L 
s b 
archive-condition(V;A;t;f;n;v1;L)))))) }
{ Proof }
Definitions occuring in Statement :
three-consensus-ts: three-consensus-ts(V;A;t;f),
archive-condition: archive-condition(V;A;t;f;n;v;L),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
nat_plus: ,
nat: ,
infix_ap: x f y,
all: x:A. B[x],
exists: 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,
universe: Type,
iseg: l1 l2,
l_member: (x l),
rel_star: R^*,
ts-rel: ts-rel(ts),
ts-init: ts-init(ts),
ts-type: ts-type(ts)
Definitions :
member: t T,
rev_implies: P 
Q,
iff: P Q,
implies: P Q,
true: True,
squash: 
T,
and: P Q,
or: P 
Q,
prop: 
,
cand: A c B,
exists: x:A. B[x],
consensus-rcv: consensus-rcv(V;A),
all: x:A. B[x],
decidable: Dec(P),
nat: ,
guard: {T},
sq_type: SQType(T),
subtype: S 
T
Lemmas :
decidable__equal_Id,
member_singleton,
or_functionality_wrt_iff,
member_append,
iff_transitivity,
cs-rcv-vote_wf,
consensus-rcv_wf,
l_member_wf,
Id_wf,
member_wf,
nat_plus_inc,
archive-condition_wf,
iseg_wf,
Id_sq,
nat_wf,
iseg_append
\mforall{}V:Type. \mforall{}A:Id List. \mforall{}t:\mBbbN{}\msupplus{}. \mforall{}f:V List {}\mrightarrow{} V. \mforall{}s:ts-type(three-consensus-ts(V;A;t;f)).
((ts-init(three-consensus-ts(V;A;t;f)) (ts-rel(three-consensus-ts(V;A;t;f))\^{}*) s)
{}\mRightarrow{} (\mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}n:\mBbbN{}. \mforall{}b:\{a:Id| (a \mmember{} A)\} . \mforall{}v1:V.
((Vote[b;n;v1] \mmember{} s a)
{}\mRightarrow{} (\mexists{}L:consensus-rcv(V;A) List. (L \mleq{} s b \mwedge{} archive-condition(V;A;t;f;n;v1;L))))))
Date html generated:
2011_08_16-AM-10_16_58
Last ObjectModification:
2011_01_03-PM-03_09_41
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