Nuprl Lemma : ler_leader_max
es:EO'. nodes:bag(Id). client:Id. uid:Id 
.
(((ler_leader_ring_message-constraint{i:l}(client;nodes;uid) es)
ler_consistent_configuration(es)
ler_non_dummy_configuration+(es;nodes)
ler_non_dummy_request(es)
Inj(Id;;uid)
ler_ring_setup(es;nodes))
(e:E. l:Id. epoch:. (<epoch, l> 
ler_Leader()(e) (l':Id. (l' 
nodes ((uid l) 
(uid l') ))))))
Proof not projected
Definitions occuring in Statement :
ler_ring_setup: ler_ring_setup(es;nodes),
ler_non_dummy_request: ler_non_dummy_request(es),
ler_consistent_configuration: ler_consistent_configuration(es),
ler_non_dummy_configuration+: ler_non_dummy_configuration+(es;nodes),
ler_Leader: ler_Leader(),
ler_leader_ring_message-constraint: ler_leader_ring_message-constraint{i:l}(client;nodes;uid),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
inject: Inj(A;B;f),
ge: i j ,
all: x:A. B[x],
implies: P Q,
and: P Q,
apply: f a,
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
int: ,
bag-member: x bs,
bag: bag(T)
Definitions :
all: x:A. B[x],
implies: P Q,
and: P Q,
ge: i j ,
squash: T,
member: t T,
true: True,
le: A 
B,
prop: 
,
ler_non_dummy_configuration: ler_non_dummy_configuration(es;nodes),
es-locl: (e <loc e'),
int_seg: {i..j
},
cand: A c B,
gt: i > j,
subtype: S 
T,
or: P 
Q,
not: 
A,
false: False,
so_lambda: 
x.t[x],
top: Top,
lelt: i j < k,
Id: Id,
so_apply: x[s1;s2],
so_lambda: x y.t[x; y],
nat: 
,
name: Name,
length: ||as||,
ycomb: Y,
bag: bag(T),
iff: P 
Q,
rev_implies: P Q,
pi2: snd(t),
pi1: fst(t),
exists: 
x:A. B[x],
l_member: (x l),
ler_ring_setup: ler_ring_setup(es;nodes),
sq_stable: SqStable(P),
uall: [x:A]. B[x],
listp: A List
,
last: last(L),
sq_type: SQType(T),
uimplies: b supposing a,
guard: {T},
so_apply: x[s],
ler_non_dummy_configuration+: ler_non_dummy_configuration+(es;nodes),
ler_consistent_configuration: ler_consistent_configuration(es),
no_repeats: no_repeats(T;l),
ler_Propose: ler_Propose(),
single-valued-classrel: single-valued-classrel(es;X;T),
inject: Inj(A;B;f),
uiff: uiff(P;Q),
l_all: (xL.P[x])
Lemmas :
ler_Leader_from_Propose,
sq_stable_from_decidable,
le_wf,
decidable__le,
ler_Propose_from_Choose,
id_in_bag_in_list,
l_member_wf,
ler_list_Propose,
classrel_wf,
Message_wf,
ler_Config_wf,
es-E_wf,
event-ordering+_inc,
es-locl_wf,
decidable__es-locl,
es-causl_transitivity2,
es-causle_weakening,
Id_wf,
listp_properties,
length_wf,
subtype_base_sq,
int_subtype_base,
Error :pi2_wf,
pi1_wf_top,
es-loc_wf,
select_wf,
ma-ring-property2,
top_wf,
bag-member_wf,
ler_Leader_wf,
ler_leader_ring_message-constraint_wf,
ler_consistent_configuration_wf,
ler_non_dummy_configuration+_wf,
ler_non_dummy_request_wf,
inject_wf,
ler_ring_setup_wf,
bag_wf,
event-ordering+_wf,
atom2_subtype_base,
int_seg_wf,
nat_properties,
gt_wf,
nat_wf,
natrec_wf,
length-map,
length_wf_nat,
select-map,
select0,
single-valued-classrel-base,
base-headers-msg-val_wf,
squash_wf,
true_wf,
Error :eclass_wf,
imax-list_wf,
firstn_wf,
map_wf,
non_neg_length,
length_firstn,
map_length,
length_cons,
imax-list-eq-implies,
cons_member,
member_firstn,
bag-member-list-member,
decidable__equal_Id,
bag-member-l_eqset,
ler_Propose_wf,
imax-list-lb,
select_cons_tl,
select_firstn,
add_functionality_wrt_eq
\mforall{}es:EO'. \mforall{}nodes:bag(Id). \mforall{}client:Id. \mforall{}uid:Id {}\mrightarrow{} \mBbbZ{}.
(((ler\_leader\_ring\_message-constraint\{i:l\}(client;nodes;uid) es)
\mwedge{} ler\_consistent\_configuration(es)
\mwedge{} ler\_non\_dummy\_configuration+(es;nodes)
\mwedge{} ler\_non\_dummy\_request(es)
\mwedge{} Inj(Id;\mBbbZ{};uid)
\mwedge{} ler\_ring\_setup(es;nodes))
{}\mRightarrow{} (\mforall{}e:E. \mforall{}l:Id. \mforall{}epoch:\mBbbZ{}.
(<epoch, l> \mmember{} ler\_Leader()(e) {}\mRightarrow{} (\mforall{}l':Id. (l' \mdownarrow{}\mmember{} nodes {}\mRightarrow{} ((uid l) \mgeq{} (uid l') ))))))
Date html generated:
2012_02_20-PM-06_06_55
Last ObjectModification:
2012_02_02-PM-02_40_10
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