{ 
[V:Type]
L:ts-reachable(consensus-ts3(V)). v:V.
((v':V. (
(COMMITED[v'] 
L))) 
(CONSIDERING[v] L)
cs-ref-map3(L) = PREDECIDED[v]) }
{ Proof }
Definitions occuring in Statement :
cs-ref-map3: cs-ref-map3(L),
consensus-ts3: consensus-ts3(T),
cs-commited: COMMITED[v],
cs-considering: CONSIDERING[v],
consensus-state3: consensus-state3(T),
cs-predecided: PREDECIDED[v],
consensus-state2: consensus-state2(T),
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
not: A,
and: P Q,
universe: Type,
equal: s = t,
l_member: (x l),
ts-reachable: ts-reachable(ts)
Definitions :
uall: [x:A]. B[x],
all: x:A. B[x],
member: t T,
iff: P Q,
and: P Q,
not: A,
implies: P Q,
rev_implies: P Q,
prop: 
,
false: False,
cs-ref-map3: cs-ref-map3(L),
let: let,
ifthenelse: if b then t else f fi ,
assert: 
b,
btrue: tt,
bfalse: ff,
true: True,
so_lambda: 
x.t[x],
le: A 
B,
int_seg: {i..j
},
lelt: i j < k,
exists: 
x:A. B[x],
squash: 
T,
hd: hd(l),
subtype: S 
T,
or: P 
Q,
outr: outr(x),
bnot: 
b,
isl: isl(x),
outl: outl(x),
ts-reachable: ts-reachable(ts),
consensus-ts3: consensus-ts3(T),
ts-type: ts-type(ts),
pi1: fst(t),
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
so_apply: x[s],
l_member: (x l),
nat: 
,
cand: A c B,
consensus-state2: consensus-state2(T),
cs-decided: Decided[v],
cs-predecided: PREDECIDED[v],
sq_type: SQType(T),
guard: {T},
cs-ambivalent: AMBIVALENT,
it: 
Lemmas :
consensus-ts3-invariant1,
cs-ref-map3-decided,
ts-reachable_wf,
consensus-ts3_wf,
ts-type_wf,
not_wf,
l_member_wf,
consensus-state3_wf,
cs-commited_wf,
cs-considering_wf,
consensus-state2_wf,
cs-ref-map3_wf,
cs-predecided_wf,
filter_is_empty,
cs-is-committed_wf,
null_wf3,
filter_wf_top,
bool_wf,
filter_wf,
assert_wf,
bnot_wf,
iff_weakening_uiff,
uiff_transitivity,
eqtt_to_assert,
assert_of_null,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
cs-is-considering_wf,
uiff_wf,
true_wf,
uall_wf,
int_seg_wf,
length_wf1,
select_wf,
le_wf,
assert-cs-is-considering,
squash_wf,
false_wf,
filter_type,
cs-considered-val_wf,
cons_member,
member_filter,
cs-is-considering-implies,
assert-cs-is-committed,
select_member,
top_wf,
bool_cases,
subtype_base_sq,
bool_subtype_base,
outr_wf,
isl_wf,
outl_wf
\mforall{}[V:Type]
\mforall{}L:ts-reachable(consensus-ts3(V)). \mforall{}v:V.
((\mforall{}v':V. (\mneg{}(COMMITED[v'] \mmember{} L))) \mwedge{} (CONSIDERING[v] \mmember{} L) \mLeftarrow{}{}\mRightarrow{} cs-ref-map3(L) = PREDECIDED[v])
Date html generated:
2011_08_16-AM-09_56_59
Last ObjectModification:
2011_06_18-AM-08_56_23
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