Nuprl Lemma : rsc5_quorum_inv
es:EO'. e1:E. Cmd:ValueAllType. cmdeq:EqDecider(Cmd). ni:
. z: Cmd? (Id List).
(z 
rsc5_QuorumState(Cmd;cmdeq) ni(e1) 
let pmaj,z = z in no_repeats(Id;z) 
(
isl(pmaj) 
null(z)))
Proof not projected
Definitions occuring in Statement :
rsc5_QuorumState: rsc5_QuorumState(Cmd;cmdeq),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
null: null(as),
isl: isl(x),
assert: b,
all: x:A. B[x],
iff: P Q,
not: A,
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: ,
no_repeats: no_repeats(T;l),
deq: EqDecider(T),
vatype: ValueAllType
Definitions :
rsc5_addvote: rsc5_addvote(Cmd;cmdeq),
rsc5_newvote: rsc5_newvote(Cmd),
false: False,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
true: True,
squash: 
T,
rev_implies: P Q,
subtype: S 
T,
top: Top,
cand: A c B,
so_lambda: 
x.t[x],
member: t T,
prop: 
,
rsc5_init: rsc5_init(),
rsc5_add_to_quorum: rsc5_add_to_quorum(Cmd;cmdeq),
null: null(as),
isl: isl(x),
assert: b,
not: A,
iff: P Q,
and: P Q,
implies: P Q,
Id: Id,
vatype: ValueAllType,
all: x:A. B[x],
ycomb: Y,
length: ||as||,
sq_type: SQType(T),
guard: {T},
uimplies: b supposing a,
uiff: uiff(P;Q),
bool: 
,
so_apply: x[s],
sq_stable: SqStable(P),
uall: [x:A]. B[x],
rsc5_QuorumState: rsc5_QuorumState(Cmd;cmdeq),
unit: Unit,
it: 
Lemmas :
event-ordering+_wf,
es-E_wf,
deq_wf,
rsc5_QuorumState_wf,
classrel_wf,
single-bag_wf,
bag-member_wf,
no_repeats_nil,
bag-member-single,
event-ordering+_inc,
es-locl_wf,
length_wf,
atom2_subtype_base,
list_subtype_base,
subtype_base_sq,
eqff_to_assert,
uiff_transitivity,
assert-deq-member,
not_functionality_wrt_iff,
assert_of_bnot,
safe-assert-deq,
assert_of_band,
l_member_wf,
iff_transitivity,
no_repeats_cons,
eqtt_to_assert,
bool_wf,
id-deq_wf,
deq-member_wf,
bnot_wf,
int-deq_wf,
product-deq_wf,
eqof_wf,
band_wf,
assert_of_null,
iff_weakening_uiff,
iff_functionality_wrt_iff,
equal_wf,
false_wf,
true_wf,
and_functionality_wrt_iff,
sq_stable__assert,
sq_stable__not,
sq_stable__iff,
sq_stable__no_repeats,
sq_stable__and,
rsc5_vote'base_wf,
it_wf,
bag_wf,
rsc5_init_wf,
valueall-type_wf,
sq_stable__valueall-type,
rsc5_add_to_quorum_wf,
top_wf,
null_wf3,
isl_wf,
assert_wf,
not_wf,
iff_wf,
no_repeats_wf,
Id_wf,
unit_wf2,
Message_wf,
Memory-class-invariant
\mforall{}es:EO'. \mforall{}e1:E. \mforall{}Cmd:ValueAllType. \mforall{}cmdeq:EqDecider(Cmd). \mforall{}ni:\mBbbZ{} \mtimes{} \mBbbZ{}. \mforall{}z:\mBbbZ{} \mtimes{} Cmd? \mtimes{} (Id List).
(z \mmember{} rsc5\_QuorumState(Cmd;cmdeq) ni(e1)
{}\mRightarrow{} let pmaj,z = z
in no\_repeats(Id;z) \mwedge{} (\mneg{}\muparrow{}isl(pmaj) \mLeftarrow{}{}\mRightarrow{} \muparrow{}null(z)))
Date html generated:
2012_02_20-PM-05_06_23
Last ObjectModification:
2012_02_02-PM-02_18_25
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