{ 
[V:Type]
eq:EqDecider(V). A:Id List. t:
. f:V List 
V.
((vs:V List. (f vs 
vs) supposing ||vs|| 
1 )
(s:ts-reachable(three-consensus-ts(V;A;t;f)). v:V.
a:{a:Id| (a A)} . n:
. L:consensus-rcv(V;A) List.
(L 
s a
archive-condition(V;A;t;f;n;v;L)
(
aA. (||s a|| 1 ) 
(hd(s a) = Init[v]))))) }
{ 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-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,
int: ,
universe: Type,
equal: s = t,
l_exists: (xL. P[x]),
iseg: l1 l2,
l_member: (x l),
deq: EqDecider(T),
ts-reachable: ts-reachable(ts)
Definitions :
cand: A c B,
so_lambda: 
x.t[x],
prop: 
,
member: t T,
implies: P Q,
and: P Q,
ge: i j ,
all: x:A. B[x],
exists: x:A. B[x],
l_exists: (xL. P[x]),
Id: Id,
false: False,
le: A B,
ycomb: Y,
append: as @ bs,
not: 
A,
hd: hd(l),
length: ||as||,
subtype: S 
T,
top: Top,
rev_implies: P 
Q,
iff: P Q,
or: P 
Q,
nat: ,
true: True,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
isl: isl(x),
bnot: 
b,
outr: outr(x),
assert: 
b,
so_apply: x[s],
uall: [x:A]. B[x],
pi1: fst(t),
ts-type: ts-type(ts),
three-consensus-ts: three-consensus-ts(V;A;t;f),
ts-reachable: ts-reachable(ts),
uimplies: b supposing a,
decidable: Dec(P),
guard: {T},
sq_type: SQType(T),
nat_plus: ,
pi2: snd(t),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A)
Lemmas :
sq_stable_from_decidable,
sq_stable__all,
cs-initial-rcv_wf,
hd_wf,
length_wf1,
ge_wf,
list-subtype,
l_exists_wf,
archive-condition_wf,
iseg_wf,
consensus-rcv_wf,
l_member_wf,
Id_wf,
ts-type_wf,
nat_plus_inc,
three-consensus-ts_wf,
ts-reachable_wf,
decidable__equal_Id,
atom2_subtype_base,
subtype_base_sq,
archive-condition-append-vote,
cs-rcv-vote_wf,
pos_length,
votes-from-inning_wf,
strong-subtype-self,
strong-subtype-set3,
strong-subtype-deq-subtype,
id-deq_wf,
values-for-distinct_wf,
nat_plus_properties,
le_wf,
member_wf,
nat_wf,
top_wf,
length_wf_nat,
member-values-for-distinct2,
member_singleton,
or_functionality_wrt_iff,
member_append,
iff_transitivity,
member-votes-from-inning,
pi2_wf,
pi1_wf_top,
isl_wf,
bnot_wf,
assert_wf,
outr_wf,
three-cs-vote-invariant
\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{}s:ts-reachable(three-consensus-ts(V;A;t;f)). \mforall{}v:V. \mforall{}a:\{a:Id| (a \mmember{} A)\} . \mforall{}n:\mBbbZ{}.
\mforall{}L:consensus-rcv(V;A) List.
(L \mleq{} s a
{}\mRightarrow{} archive-condition(V;A;t;f;n;v;L)
{}\mRightarrow{} (\mexists{}a\mmember{}A. (||s a|| \mgeq{} 1 ) \mwedge{} (hd(s a) = Init[v])))))
Date html generated:
2011_08_16-AM-10_17_21
Last ObjectModification:
2011_06_18-AM-09_07_02
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