{ 
[V:Type]
((
v,v':V. (
(v = v')))
(v,v':V. Dec(v = v'))
(L:V List. Dec(v:V. ((v 
L))))
(A:Id List. W:{a:Id| (a A)} List List.
(one-intersection(A;W)
(i:
. x,y:ConsensusState.
Dec(v:V
(in state x, inning i could commit v
(in state y, inning i could commit v ))))))) }
{ Proof }
Definitions occuring in Statement :
one-intersection: one-intersection(A;W),
cs-inning-committable: in state s, inning i could commit v ,
consensus-state4: ConsensusState,
Id: Id,
decidable: Dec(P),
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
not: A,
implies: P Q,
and: P Q,
set: {x:A| B[x]} ,
list: type List,
int: ,
universe: Type,
equal: s = t,
l_member: (x l)
Definitions :
uall: [x:A]. B[x],
implies: P Q,
exists: x:A. B[x],
all: x:A. B[x],
member: t T,
prop: 
,
and: P Q,
so_lambda: 
x.t[x],
not: A,
decidable: Dec(P),
or: P 
Q,
false: False,
iff: P 
Q,
rev_implies: P Q,
guard: {T},
cand: A c B,
l_exists: (xL. P[x]),
so_apply: x[s],
uimplies: b supposing a
Lemmas :
cs-inning-committable-some2,
consensus-state4_wf,
one-intersection_wf,
Id_wf,
l_member_wf,
decidable_wf,
not_wf,
cs-inning-committable_wf,
decidable__l_exists_better-extract,
decidable__cand,
decidable__cs-inning-committable,
decidable__not,
cs-not-completed_wf,
decidable__all-list,
decidable__equal_Id,
decidable__implies_better,
decidable__l_member,
decidable__equal_set,
decidable__cs-not-completed,
decidable_functionality,
l_exists_wf,
iff_functionality_wrt_iff,
and_functionality_wrt_iff,
exists_functionality_wrt_iff,
not_functionality_wrt_iff
\mforall{}[V:Type]
((\mexists{}v,v':V. (\mneg{}(v = v')))
{}\mRightarrow{} (\mforall{}v,v':V. Dec(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.
(one-intersection(A;W)
{}\mRightarrow{} (\mforall{}i:\mBbbZ{}. \mforall{}x,y:ConsensusState.
Dec(\mexists{}v:V
(in state x, inning i could commit v
\mwedge{} (\mneg{}in state y, inning i could commit v )))))))
Date html generated:
2011_08_16-AM-10_06_08
Last ObjectModification:
2011_06_18-AM-09_01_19
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