{ 
V:Type
((v1,v2:V. Dec(v1 = v2))
{
v,v':V. (
(v = v'))}
(L:V List. Dec(v:V. ((v 
L))))
(A:Id List. W:{a:Id| (a A)} List List.
((||W|| 
1 )
two-intersection(A;W)
(s1,s2:ts-reachable(consensus-ts4(V;A;W)).
((s1 (ts-rel(consensus-ts4(V;A;W))^*) s2)
(v1,v2:V.
((i:
. in state s1, inning i has committed v1)
(j:. in state s2, inning j has committed v2)
(v1 = v2)))))))) }
{ Proof }
Definitions occuring in Statement :
two-intersection: two-intersection(A;W),
cs-inning-committed: in state s, inning i has committed v,
consensus-ts4: consensus-ts4(V;A;W),
Id: Id,
length: ||as||,
nat: ,
decidable: Dec(P),
guard: {T},
infix_ap: x f y,
ge: i j ,
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
set: {x:A| B[x]} ,
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
l_member: (x l),
rel_star: R^*,
ts-reachable: ts-reachable(ts),
ts-rel: ts-rel(ts),
ts-type: ts-type(ts)
Definitions :
prop: 
,
member: t T,
exists: x:A. B[x],
pi1: fst(t),
suptype: suptype(S; T),
subtype: S 
T,
ts-type: ts-type(ts),
consensus-ts1: consensus-ts1(T),
consensus-ts4: consensus-ts4(V;A;W),
all: x:A. B[x],
infix_ap: x f y,
and: P 
Q,
implies: P Q,
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
isl: isl(x),
assert: 
b,
outl: outl(x),
rev_implies: P 
Q,
iff: P Q,
ts-reachable: ts-reachable(ts),
pi2: snd(t),
ts-rel: ts-rel(ts),
rel_star: R^*,
guard: {T},
sq_type: SQType(T),
bfalse: ff,
or: P 
Q,
ycomb: Y,
rel_exp: R^n,
nat: ,
cs-decided: Decided[v],
consensus-state1: consensus-state1(V)
Lemmas :
cs-inning-committed_wf,
ts-type_wf,
consensus-state1_wf,
consensus-state4_wf,
consensus-ts4_wf,
consensus-ts1_wf,
ts-refinement-reachable2,
ts-rel_wf,
rel_star_wf,
cs-decided_wf,
cs-undecided_wf,
not_functionality_wrt_iff,
assert_of_bnot,
eqff_to_assert,
assert_of_eq_int,
eqtt_to_assert,
iff_transitivity,
bool_sq,
bool_cases,
not_wf,
bnot_wf,
assert_wf,
bool_wf,
eq_int_wf,
isl_wf,
outl_wf,
top_wf
\mforall{}V:Type
((\mforall{}v1,v2:V. Dec(v1 = v2))
{}\mRightarrow{} \{\mexists{}v,v':V. (\mneg{}(v = v'))\}
{}\mRightarrow{} (\mforall{}L:V List. Dec(\mexists{}v:V. (\mneg{}(v \mmember{} L))))
{}\mRightarrow{} (\mforall{}A:Id List. \mforall{}W:\{a:Id| (a \mmember{} A)\} List List.
((||W|| \mgeq{} 1 )
{}\mRightarrow{} two-intersection(A;W)
{}\mRightarrow{} (\mforall{}s1,s2:ts-reachable(consensus-ts4(V;A;W)).
((s1 rel\_star(ts-type(consensus-ts4(V;A;W)); ts-rel(consensus-ts4(V;A;W))) s2)
{}\mRightarrow{} (\mforall{}v1,v2:V.
((\mexists{}i:\mBbbN{}. in state s1, inning i has committed v1)
{}\mRightarrow{} (\mexists{}j:\mBbbN{}. in state s2, inning j has committed v2)
{}\mRightarrow{} (v1 = v2))))))))
Date html generated:
2011_08_16-AM-10_06_50
Last ObjectModification:
2011_01_03-PM-03_08_24
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