Nuprl Lemma : SpLeaderRing-ilf
(
[es:EO']. [e:E]. [v:
Id].
{v 
ler_Nbr()(e)
v 
zb,za.
let epoch,succ = za
in z.let epoch',succ' = z
in if epoch' <z epoch
then {<epoch, succ>}
else {<epoch', succ'>}
fi @Loc|Loc, ler_Config(), Prior(self)?l.{<ler_dumEpoch(), l>}|(e)})
([client:Id]. [nodes:bag(Id)]. [uid:Id 
]. [es:EO']. [e:E]. [i:Id]. [m:Message].
{<i, m> ler_leader_ring_main(client;nodes;uid)(e)
loc(e) 
nodes
((
a:
a1:Id
(<a, a1> Prior(ler_Nbr())(e)
(b1:
(<a, b1> Base([propose]; )(e)
(((b1 = (uid loc(e))) (i = client) (m = make-Msg([leader]; Id;<a, loc(e)>)))
((
(b1 = (uid loc(e))))
(i = a1)
(m = make-Msg([propose]; ;<a, imax(b1;uid loc(e))>))))))))
(a:
(a Base([choose];)(e)
(m = make-Msg([propose]; ;<a, uid loc(e)>))
<a, i> Prior(ler_Nbr())(e))))})
Proof not projected
Definitions occuring in Statement :
ler_leader_ring_main: ler_leader_ring_main(client;nodes;uid),
ler_Nbr: ler_Nbr(),
ler_dumEpoch: ler_dumEpoch(),
ler_Config: ler_Config(),
concat-lifting-loc-2: f@Loc,
make-Msg: make-Msg(hdr;typ;val),
base-headers-msg-val: Base(hdr;typ),
Message: Message,
rec-combined-loc-class-opt-1: F|Loc, X, Prior(self)?init|,
primed-class: Prior(X),
classrel: v X(e),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
imax: imax(a;b),
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
sq_or: a b,
uall: [x:A]. B[x],
guard: {T},
exists: x:A. B[x],
iff: P Q,
not: A,
or: P Q,
and: P Q,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
spread: spread def,
pair: <a, b>,
product: x:A B[x],
cons: [car / cdr],
nil: [],
int: ,
token: "$token",
equal: s = t,
bag-member: x bs,
single-bag: {x},
bag: bag(T)
Definitions :
not: A,
cand: A c B,
top: Top,
bfalse: ff,
subtype: S 
T,
btrue: tt,
false: False,
ler_Choose: ler_Choose(),
ler_Propose: ler_Propose(),
ler_send_propose: ler_send_propose(),
ler_send_leader: ler_send_leader(),
ifthenelse: if b then t else f fi ,
ler_ChooseReply: ler_ChooseReply(uid),
ler_ProposeReply: ler_ProposeReply(client;uid),
ler_leader_ring_main: ler_leader_ring_main(client;nodes;uid),
Id: Id,
so_lambda: 
x.t[x],
name: Name,
all: x:A. B[x],
prop: 
,
or: P Q,
exists: x:A. B[x],
sq_or: a b,
let: let,
ler_Nbr: ler_Nbr(),
true: True,
squash: T,
bag-member: x bs,
rev_implies: P Q,
implies: P Q,
member: t T,
classrel: v X(e),
iff: P Q,
guard: {T},
uall: [x:A]. B[x],
and: P Q,
pi2: snd(t),
pi1: fst(t),
sq_type: SQType(T),
unit: Unit,
bool: 
,
uimplies: b supposing a,
uiff: uiff(P;Q),
so_apply: x[s],
it: 
Lemmas :
or_functionality_wrt_iff,
atom2_subtype_base,
Error :pi2_wf,
pi1_wf_top,
int_subtype_base,
subtype_base_sq,
iff_weakening_uiff,
not_functionality_wrt_uiff,
assert_of_bnot,
eqff_to_assert,
bnot_wf,
assert_of_eq_int,
eqtt_to_assert,
assert_wf,
uiff_transitivity,
bool_wf,
bag-member-single-weak,
bag-member-empty-weak,
ifthenelse_functionality_wrt_iff,
bag-member-ifthenelse,
and_functionality_wrt_uiff2,
exists_functionality_wrt_iff,
sq_or_squash,
and_functionality_wrt_uiff3,
simple-loc-comb-2-concat-classrel-weak,
sq_or_functionality_wrt_iff,
parallel-classrel-weak,
and_functionality_wrt_iff,
classrel-at,
iff_transitivity,
false_wf,
squash_wf,
ler_Choose_wf,
ler_Propose_wf,
empty-bag_wf,
ler_send_propose_wf,
ler_send_leader_wf,
eq_int_wf,
simple-loc-comb-2_wf,
ler_ChooseReply_wf,
ler_ProposeReply_wf,
parallel-class_wf,
class-at_wf,
imax_wf,
not_wf,
valueall-type_wf,
Id-valueall-type,
int-valueall-type,
product-valueall-type,
make-Msg_wf,
base-headers-msg-val_wf,
primed-class_wf,
sq_or_wf,
es-loc_wf,
bag-member_wf,
ler_leader_ring_main_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
ler_dumEpoch_wf,
ler_Config_wf,
single-bag_wf,
bag_wf,
lt_int_wf,
ifthenelse_wf,
concat-lifting-loc-2_wf,
rec-combined-loc-class-opt-1_wf,
ler_Nbr_wf,
Id_wf,
Message_wf,
classrel_wf
(\mforall{}[es:EO']. \mforall{}[e:E]. \mforall{}[v:\mBbbZ{} \mtimes{} Id].
\{v \mmember{} ler\_Nbr()(e)
\mLeftarrow{}{}\mRightarrow{} v \mmember{} \mlambda{}zb,za.
let epoch,succ = za
in \mlambda{}z.let epoch',succ' = z
in if epoch' <z epoch
then \{<epoch, succ>\}
else \{<epoch', succ'>\}
fi @Loc|Loc, ler\_Config(), Prior(self)?\mlambda{}l.\{<ler\_dumEpoch(), l>\}|(e)\})
\mwedge{} (\mforall{}[client:Id]. \mforall{}[nodes:bag(Id)]. \mforall{}[uid:Id {}\mrightarrow{} \mBbbZ{}]. \mforall{}[es:EO']. \mforall{}[e:E]. \mforall{}[i:Id]. \mforall{}[m:Message].
\{<i, m> \mmember{} ler\_leader\_ring\_main(client;nodes;uid)(e)
\mLeftarrow{}{}\mRightarrow{} loc(e) \mdownarrow{}\mmember{} nodes
\mwedge{} ((\mexists{}a:\mBbbZ{}
\mexists{}a1:Id
(<a, a1> \mmember{} Prior(ler\_Nbr())(e)
\mwedge{} (\mexists{}b1:\mBbbZ{}
(<a, b1> \mmember{} Base([propose];\mBbbZ{} \mtimes{} \mBbbZ{})(e)
\mwedge{} (((b1 = (uid loc(e)))
\mwedge{} (i = client)
\mwedge{} (m = make-Msg([leader];\mBbbZ{} \mtimes{} Id;<a, loc(e)>)))
\mvee{} ((\mneg{}(b1 = (uid loc(e))))
\mwedge{} (i = a1)
\mwedge{} (m = make-Msg([propose];\mBbbZ{} \mtimes{} \mBbbZ{};<a, imax(b1;uid loc(e))>))))))))
\mdownarrow{}\mvee{} (\mexists{}a:\mBbbZ{}
(a \mmember{} Base([choose];\mBbbZ{})(e)
\mwedge{} (m = make-Msg([propose];\mBbbZ{} \mtimes{} \mBbbZ{};<a, uid loc(e)>))
\mwedge{} <a, i> \mmember{} Prior(ler\_Nbr())(e))))\})
Date html generated:
2012_02_20-PM-06_02_47
Last ObjectModification:
2012_02_02-PM-02_38_38
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