Nuprl Lemma : rsc5_rounds_progress
es:EO'. e1,e2:E. Cmd:ValueAllType. n,round1,round2:
.
((
z: 
Cmd
round:
e:E
(e1 
loc e
(e <loc e2)
z 
rsc5_RoundInfo(Cmd)(e)
round rsc5_NewRoundsState(Cmd) n(e)
let z,c = z
in let m,i = z
in (
(eqof(IntDeq) m n)) (round < i)))
(e1 <loc e2)
round1 rsc5_NewRoundsState(Cmd) n(e1)
round2 rsc5_NewRoundsState(Cmd) n(e2)
(round1 < round2))
Proof not projected
Definitions occuring in Statement :
rsc5_NewRoundsState: rsc5_NewRoundsState(Cmd),
rsc5_RoundInfo: rsc5_RoundInfo(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-E: E,
assert: b,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
less_than: a < b,
apply: f a,
spread: spread def,
product: x:A B[x],
int: ,
int-deq: IntDeq,
eqof: eqof(d),
vatype: ValueAllType
Definitions :
eq_atom: x =a y,
atom-deq: AtomDeq,
list-deq: list-deq(eq),
name-deq: NameDeq,
name_eq: name_eq(x;y),
name: Name,
rsc5_vote'base: rsc5_vote'base(Cmd),
rsc5_vote2retry: rsc5_vote2retry(Cmd),
rsc5_retry'base: rsc5_retry'base(Cmd),
false: False,
bfalse: ff,
btrue: tt,
band: p 
q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
guard: {T},
cand: A c B,
so_lambda: 
x.t[x],
member: t T,
not: 
A,
trans: Trans(T;x,y.E[x; y]),
prop: 
,
rsc5_init: rsc5_init(),
rsc5_update_round: rsc5_update_round(Cmd),
assert: b,
rsc5_RoundInfo: rsc5_RoundInfo(Cmd),
and: P Q,
exists: x:A. B[x],
implies: P Q,
vatype: ValueAllType,
all: x:A. B[x],
so_apply: x[s],
or: P 
Q,
uimplies: b supposing a,
unit: Unit,
iff: P 
Q,
bool: 
,
so_apply: x[s1;s2],
uall: [x:A]. B[x],
rsc5_NewRoundsState: rsc5_NewRoundsState(Cmd),
subtype: S 
T,
it: 
Lemmas :
event-ordering+_wf,
valueall-type_wf,
rsc5_NewRoundsState_wf,
exists_wf,
es-E_wf,
single-valued-bag-single,
single-valued-classrel-base,
simple-loc-comb-1-concat-single-val,
name_wf,
assert-name_eq,
base-disjoint-classrel,
simple-loc-comb-1-concat-disjoint-classrel,
disjoint-classrel-symm,
rsc5_vote'base_wf,
rsc5_vote2retry_wf,
concat-lifting-loc-1_wf,
simple-loc-comb-1_wf,
rsc5_retry'base_wf,
parallel-class-single-val,
es-le_wf,
Message_wf,
event-ordering+_inc,
es-locl_wf,
Memory-class_wf,
classrel_wf,
and_functionality_wrt_uiff3,
eqtt_to_assert,
decidable__equal_int,
not_over_and,
assert_of_lt_int,
and_functionality_wrt_uiff,
assert_of_band,
not_functionality_wrt_uiff,
assert_of_bnot,
not_wf,
bnot_wf,
uiff_transitivity,
eqff_to_assert,
bool_wf,
lt_int_wf,
band_wf,
safe-assert-deq,
equal_wf,
and_functionality_wrt_uiff2,
sq_stable_from_decidable,
decidable__lt,
decidable__assert,
decidable__cand,
rsc5_RoundInfo_wf,
bag_wf,
Id_wf,
rsc5_init_wf,
rsc5_update_round_wf,
less_than_wf,
int-deq_wf,
eqof_wf,
assert_wf,
and_wf,
Memory-class-progress
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}n,round1,round2:\mBbbZ{}.
((\mexists{}z:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd
\mexists{}round:\mBbbZ{}
\mexists{}e:E
(e1 \mleq{}loc e
\mwedge{} (e <loc e2)
\mwedge{} z \mmember{} rsc5\_RoundInfo(Cmd)(e)
\mwedge{} round \mmember{} rsc5\_NewRoundsState(Cmd) n(e)
\mwedge{} let z,c = z
in let m,i = z
in (\muparrow{}(eqof(IntDeq) m n)) \mwedge{} (round < i)))
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} round1 \mmember{} rsc5\_NewRoundsState(Cmd) n(e1)
{}\mRightarrow{} round2 \mmember{} rsc5\_NewRoundsState(Cmd) n(e2)
{}\mRightarrow{} (round1 < round2))
Date html generated:
2012_02_20-PM-05_08_02
Last ObjectModification:
2012_02_02-PM-02_19_08
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