Nuprl Lemma : RSC-agreement-property
[Cmd:ValueAllType]. [eq:EqDecider(Cmd)]. [locs,clients:bag(Id)]. [f:
]. [es:EO'].
((RSC_SimpleConsensus_stdma{mark-simple-consensus-V2.esh:o, i:l}(Cmd; clients; eq; f; locs) es)
bag-no-repeats(Id;locs)
(bag-size(locs) = ((3 * f) + 1))
RSC_agreement(Cmd;es))
Proof not projected
Definitions occuring in Statement :
RSC_agreement: RSC_agreement(Cmd;es),
Message: Message,
event-ordering+: EO+(Info),
Id: Id,
uall: [x:A]. B[x],
implies: P Q,
apply: f a,
multiply: n * m,
add: n + m,
natural_number: $n,
int: ,
equal: s = t,
deq: EqDecider(T),
bag-no-repeats: bag-no-repeats(T;bs),
bag-size: bag-size(bs),
bag: bag(T),
vatype: ValueAllType
Definitions :
uall: [x:A]. B[x],
vatype: ValueAllType,
implies: P Q,
RSC_agreement: RSC_agreement(Cmd;es),
member: t 
T,
all: x:A. B[x],
pi2: snd(t),
prop: 
,
top: Top,
subtype: S 
T,
so_lambda: 
x.t[x],
and: P 
Q,
exists: 
x:A. B[x],
cand: A c B,
bag-size: bag-size(bs),
bag-no-repeats: bag-no-repeats(T;bs),
squash: 
T,
true: True,
guard: {T},
not: 
A,
l_exists: (xL. P[x]),
l_disjoint: l_disjoint(T;l1;l2),
nat: 
,
ge: i 
j ,
le: A 
B,
false: False,
l_all: (xL.P[x]),
int_seg: {i..j
},
lelt: i j < k,
bag-append: as + bs,
bag-member: x bs,
Id: Id,
iff: P 
Q,
rev_implies: P Q,
assert: 
b,
null: null(as),
btrue: tt,
bfalse: ff,
ifthenelse: if b then t else f fi ,
pi1: fst(t),
sq_type: SQType(T),
uimplies: b supposing a,
decidable: Dec(P),
or: P 
Q,
so_apply: x[s],
uiff: uiff(P;Q),
sq_or: a b,
sq_stable: SqStable(P),
deq: EqDecider(T),
possible-majority: possible-majority(T;eq;L;x),
rev_uimplies: rev_uimplies(P;Q),
l_member: (x l),
length: ||as||,
ycomb: Y,
RSC_Retry: Error :RSC_Retry
Lemmas :
subtype_base_sq,
int_subtype_base,
RSC-decided-property,
pi1_wf_top,
classrel_wf,
Error :RSC_Decided_wf,
es-E_wf,
event-ordering+_inc,
bag-size_wf,
Id_wf,
nat_wf,
bag-no-repeats_wf,
Error :RSC_SimpleConsensus_stdma_wf,
Message_wf,
event-ordering+_wf,
bag_wf,
deq_wf,
valueall-type_wf,
decidable__equal_int,
decidable__l_exists_better-extract,
l_member_wf,
decidable__l_member,
decidable__equal_Id,
append_wf,
bag_qinc,
bag-member_wf,
bag-size-append,
no_repeats_wf,
no_repeats-append,
bag-member-list,
member_append,
bag-no-repeats-le-bag-size,
non_neg_length,
length_wf_nat,
top_wf,
RSC-votes-consistent,
decidable__lt,
nat_properties,
ge_wf,
RSC_vote,
sq_stable__valueall-type,
RSC-retry-property,
Error :RSC_SimpleConsensus_main_wf,
make-Msg_wf,
product-valueall-type,
int-valueall-type,
Id-valueall-type,
le_wf,
poss-maj-property,
hd_wf,
count-all,
assert-deq,
select_wf,
filter-split-length,
deq-member_wf,
id-deq_wf,
bag-append_wf,
filter_wf,
bnot_wf,
no_repeats_filter,
member_filter,
assert_wf,
not_wf,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
not_functionality_wrt_iff,
assert-deq-member,
bag-member-append,
member_filter_2,
atom2_subtype_base,
squash_wf,
true_wf,
length_append,
length_wf,
count_wf,
count-as-filter,
filter-upto-length,
length-map,
int_seg_wf,
upto_wf,
length-filter-le,
false_wf,
pos_length3,
hd_member
\mforall{}[Cmd:ValueAllType]. \mforall{}[eq:EqDecider(Cmd)]. \mforall{}[locs,clients:bag(Id)]. \mforall{}[f:\mBbbZ{}]. \mforall{}[es:EO'].
((RSC\_SimpleConsensus\_stdma\{mark-simple-consensus-V2.esh:o, i:l\}(Cmd; clients; eq; f; locs) es)
{}\mRightarrow{} bag-no-repeats(Id;locs)
{}\mRightarrow{} (bag-size(locs) = ((3 * f) + 1))
{}\mRightarrow{} RSC\_agreement(Cmd;es))
Date html generated:
2012_02_20-PM-04_04_37
Last ObjectModification:
2012_02_02-PM-01_59_53
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