Nuprl Lemma : rsc4_strict_inc_rounds
es:EO'. e1,e2:E. Cmd:ValueAllType. n,round1,round2:
.
((
x: 
Cmd
e:E
round:
(e1 
loc e
(e <loc e2)
x 
rsc4_RoundInfo(Cmd)(e)
round rsc4_NewRoundsState(Cmd) n(e)
let ni,c = x
in let a1,a2 = ni
in (round < a2) (n = a1)))
(e1 <loc e2)
round1 rsc4_NewRoundsState(Cmd) n(e1)
round2 rsc4_NewRoundsState(Cmd) n(e2)
(
round1 <z round2))
Proof
Definitions occuring in Statement :
rsc4_NewRoundsState: rsc4_NewRoundsState(Cmd),
rsc4_RoundInfo: rsc4_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,
lt_int: i <z j,
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: ,
equal: s = t,
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,
rsc4_vote'base: rsc4_vote'base(Cmd),
rsc4_vote2retry: rsc4_vote2retry(Cmd),
rsc4_retry'base: rsc4_retry'base(Cmd),
false: False,
rev_implies: P 
Q,
true: True,
squash: 
T,
iff: P Q,
bfalse: ff,
guard: {T},
btrue: tt,
band: p 
q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
cand: A c B,
so_lambda: 
x.t[x],
member: t T,
not: 
A,
trans: Trans(T;x,y.E[x; y]),
prop: 
,
rsc4_init: rsc4_init(),
rsc4_update_round: rsc4_update_round(Cmd),
assert: b,
rsc4_RoundInfo: rsc4_RoundInfo(Cmd),
and: P Q,
exists: x:A. B[x],
implies: P Q,
vatype: ValueAllType,
all: x:A. B[x],
so_apply: x[s],
sq_type: SQType(T),
or: P 
Q,
unit: Unit,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
bool: 
,
so_apply: x[s1;s2],
uall: [x:A]. B[x],
rsc4_NewRoundsState: rsc4_NewRoundsState(Cmd),
subtype: S 
T,
it: 
Lemmas :
event-ordering+_wf,
valueall-type_wf,
rsc4_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,
rsc4_vote'base_wf,
rsc4_vote2retry_wf,
concat-lifting-loc-1_wf,
simple-loc-comb-1_wf,
rsc4_retry'base_wf,
parallel-class-single-val,
es-le_wf,
Message_wf,
event-ordering+_inc,
es-locl_wf,
Memory-class_wf,
classrel_wf,
int_subtype_base,
subtype_base_sq,
not_over_and,
implies_functionality_wrt_iff,
assert_of_le_int,
not_functionality_wrt_uiff,
assert_of_bnot,
or_functionality_wrt_uiff,
assert_of_bor,
bnot_of_lt_int,
true_wf,
squash_wf,
bnot_thru_band,
assert_functionality_wrt_uiff,
eqff_to_assert,
iff_weakening_uiff,
le_wf,
not_wf,
or_wf,
le_int_wf,
bnot_wf,
bor_wf,
iff_transitivity,
assert_of_eq_int,
and_functionality_wrt_uiff,
assert_of_band,
eqtt_to_assert,
uiff_transitivity,
bool_wf,
eq_int_wf,
band_wf,
ifthenelse_wf,
sq_stable__assert,
assert_of_lt_int,
decidable__equal_int,
decidable__lt,
decidable__cand,
rsc4_RoundInfo_wf,
bag_wf,
Id_wf,
rsc4_init_wf,
rsc4_update_round_wf,
equal_wf,
less_than_wf,
and_wf,
lt_int_wf,
assert_wf,
Memory-class-progress
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}n,round1,round2:\mBbbZ{}.
((\mexists{}x:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd
\mexists{}e:E
\mexists{}round:\mBbbZ{}
(e1 \mleq{}loc e
\mwedge{} (e <loc e2)
\mwedge{} x \mmember{} rsc4\_RoundInfo(Cmd)(e)
\mwedge{} round \mmember{} rsc4\_NewRoundsState(Cmd) n(e)
\mwedge{} let ni,c = x
in let a1,a2 = ni
in (round < a2) \mwedge{} (n = a1)))
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} round1 \mmember{} rsc4\_NewRoundsState(Cmd) n(e1)
{}\mRightarrow{} round2 \mmember{} rsc4\_NewRoundsState(Cmd) n(e2)
{}\mRightarrow{} (\muparrow{}round1 <z round2))
Date html generated:
2012_02_20-PM-04_57_53
Last ObjectModification:
2012_02_02-PM-02_16_26
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