{ 
[V:Type]
A:Id List. r:consensus-rcv(V;A). i:
.
(
i <z inning(r)
a:{b:Id| (b 
A)} . v:V. j:
. ((i < j) 
(r = Vote[a;j;v]))) }
{ Proof }
Definitions occuring in Statement :
rcvd-inning-gt: i <z inning(r),
cs-rcv-vote: Vote[a;i;v],
consensus-rcv: consensus-rcv(V;A),
Id: Id,
assert: b,
nat: ,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
iff: P Q,
and: P Q,
less_than: a < b,
set: {x:A| B[x]} ,
list: type List,
int: ,
universe: Type,
equal: s = t,
l_member: (x l)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
consensus-rcv: consensus-rcv(V;A),
iff: P Q,
assert: b,
rcvd-inning-gt: i <z inning(r),
exists: x:A. B[x],
and: P Q,
band: p 
q,
rcv-vote?: rcv-vote?(x),
spreadn: spread3,
rcvd-vote: rcvd-vote(x),
bfalse: ff,
btrue: tt,
outr: outr(x),
ifthenelse: if b then t else f fi ,
implies: P Q,
rev_implies: P Q,
member: t T,
prop: 
,
cand: A c B,
false: False,
bnot: 
b,
isl: isl(x),
true: True,
top: Top,
subtype: S 
T,
so_lambda: 
x.t[x],
squash: 
T,
nat: ,
cs-rcv-vote: Vote[a;i;v],
uimplies: b supposing a,
pi1: fst(t),
pi2: snd(t),
so_apply: x[s],
le: A 
B,
not: A
Lemmas :
Id_wf,
l_member_wf,
nat_wf,
nat_properties,
consensus-rcv_wf,
cs-rcv-vote_wf,
iff_weakening_uiff,
assert_of_lt_int,
assert_wf,
lt_int_wf,
outr_wf,
bnot_wf,
isl_wf,
pi1_wf_top,
pi2_wf,
le_wf
\mforall{}[V:Type]
\mforall{}A:Id List. \mforall{}r:consensus-rcv(V;A). \mforall{}i:\mBbbZ{}.
(\muparrow{}i <z inning(r) \mLeftarrow{}{}\mRightarrow{} \mexists{}a:\{b:Id| (b \mmember{} A)\} . \mexists{}v:V. \mexists{}j:\mBbbN{}. ((i < j) \mwedge{} (r = Vote[a;j;v])))
Date html generated:
2011_08_16-AM-10_10_59
Last ObjectModification:
2011_06_18-AM-09_03_51
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