Nuprl Lemma : rsc5_quorum_progress
es:EO'. e1,e2:E. Cmd:ValueAllType. cmdeq:EqDecider(Cmd). ni:
. zh,z: Cmd? (Id List).
((
zi: Cmd Id
z: Cmd? (Id List)
e:E
(e1 
loc e
(e <loc e2)
zi 
rsc5_vote'base(Cmd)(e)
z rsc5_QuorumState(Cmd;cmdeq) ni(e)
let zj,sndr = zi
in let ni',c = zj
in let pmaj,z = z
in 
(eqof(product-deq(;;IntDeq;IntDeq)) ni ni')))
(e1 <loc e2)
zh rsc5_QuorumState(Cmd;cmdeq) ni(e1)
z rsc5_QuorumState(Cmd;cmdeq) ni(e2)
let pmaj1,locs1 = zh
in let pmaj2,locs2 = z
in isl(pmaj2))
Proof not projected
Definitions occuring in Statement :
rsc5_QuorumState: rsc5_QuorumState(Cmd;cmdeq),
rsc5_vote'base: rsc5_vote'base(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-E: E,
Id: Id,
isl: isl(x),
assert: b,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
unit: Unit,
apply: f a,
spread: spread def,
product: x:A B[x],
union: left + right,
list: type List,
int: ,
product-deq: product-deq(A;B;a;b),
int-deq: IntDeq,
eqof: eqof(d),
deq: EqDecider(T),
vatype: ValueAllType
Definitions :
name: Name,
rev_implies: P 
Q,
guard: {T},
iff: P Q,
rsc5_addvote: rsc5_addvote(Cmd;cmdeq),
rsc5_newvote: rsc5_newvote(Cmd),
cand: A c B,
bfalse: ff,
btrue: tt,
true: True,
ifthenelse: if b then t else f fi ,
so_lambda: 
x.t[x],
member: t T,
not: 
A,
trans: Trans(T;x,y.E[x; y]),
prop: 
,
rsc5_init: rsc5_init(),
rsc5_add_to_quorum: rsc5_add_to_quorum(Cmd;cmdeq),
isl: isl(x),
assert: b,
rsc5_vote'base: rsc5_vote'base(Cmd),
and: P Q,
exists: x:A. B[x],
implies: P Q,
Id: Id,
vatype: ValueAllType,
all: x:A. B[x],
sq_type: SQType(T),
so_apply: x[s],
or: P 
Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
false: False,
bool: 
,
so_apply: x[s1;s2],
decidable: Dec(P),
uall: [x:A]. B[x],
rsc5_QuorumState: rsc5_QuorumState(Cmd;cmdeq),
unit: Unit,
subtype: S 
T,
it: 
Lemmas :
event-ordering+_wf,
valueall-type_wf,
deq_wf,
es-E_wf,
rsc5_QuorumState_wf,
exists_wf,
single-valued-bag-single,
single-valued-classrel-base,
es-le_wf,
Message_wf,
event-ordering+_inc,
es-locl_wf,
Memory-class_wf,
classrel_wf,
or_functionality_wrt_iff,
assert_of_bor,
bnot_thru_band,
assert_functionality_wrt_uiff,
or_wf,
bor_wf,
implies_functionality_wrt_iff,
not_functionality_wrt_uiff,
nil_member,
false_wf,
atom2_subtype_base,
list_subtype_base,
assert_of_null,
decidable__assert,
rsc5_quorum_inv,
int_subtype_base,
product_subtype_base,
subtype_base_sq,
decidable__equal_product,
not_over_and,
assert-deq-member,
and_functionality_wrt_iff,
assert_of_band,
iff_weakening_uiff,
iff_transitivity,
l_member_wf,
and_wf,
not_functionality_wrt_iff,
assert_of_bnot,
eqff_to_assert,
not_wf,
equal_wf,
uiff_transitivity,
eqtt_to_assert,
id-deq_wf,
deq-member_wf,
bnot_wf,
band_wf,
safe-assert-deq,
sq_stable__assert,
unit_wf2,
decidable__false,
decidable__equal_int,
bool_wf,
rsc5_vote'base_wf,
it_wf,
bag_wf,
Id_wf,
rsc5_init_wf,
rsc5_add_to_quorum_wf,
int-deq_wf,
product-deq_wf,
eqof_wf,
isl_wf,
assert_wf,
Memory-class-progress
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}cmdeq:EqDecider(Cmd). \mforall{}ni:\mBbbZ{} \mtimes{} \mBbbZ{}. \mforall{}zh,z:\mBbbZ{} \mtimes{} Cmd? \mtimes{} (Id List).
((\mexists{}zi:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd \mtimes{} Id
\mexists{}z:\mBbbZ{} \mtimes{} Cmd? \mtimes{} (Id List)
\mexists{}e:E
(e1 \mleq{}loc e
\mwedge{} (e <loc e2)
\mwedge{} zi \mmember{} rsc5\_vote'base(Cmd)(e)
\mwedge{} z \mmember{} rsc5\_QuorumState(Cmd;cmdeq) ni(e)
\mwedge{} let zj,sndr = zi
in let ni',c = zj
in let pmaj,z = z
in \muparrow{}(eqof(product-deq(\mBbbZ{};\mBbbZ{};IntDeq;IntDeq)) ni ni')))
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} zh \mmember{} rsc5\_QuorumState(Cmd;cmdeq) ni(e1)
{}\mRightarrow{} z \mmember{} rsc5\_QuorumState(Cmd;cmdeq) ni(e2)
{}\mRightarrow{} let pmaj1,locs1 = zh
in let pmaj2,locs2 = z
in \muparrow{}isl(pmaj2))
Date html generated:
2012_02_20-PM-05_06_32
Last ObjectModification:
2012_02_02-PM-02_18_27
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