Nuprl Lemma : ohc_v2_mem_rounds
es:EO'. e1,e2:E. Cmd:ValueAllType. n,round1,round2:
. z: 
Cmd.
((e1 <loc e2)
z 
ohc_v2_RoundInfo(Cmd)(e1)
round1 ohc_v2_NewRoundsState(Cmd) n(e1)
round2 ohc_v2_NewRoundsState(Cmd) n(e2)
let z,c = z
in let m,i = z
in (n = m) (i 
round2))
Proof not projected
Definitions occuring in Statement :
ohc_v2_NewRoundsState: ohc_v2_NewRoundsState(Cmd),
ohc_v2_RoundInfo: ohc_v2_RoundInfo(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
le: A B,
all: x:A. B[x],
implies: P Q,
apply: f a,
spread: spread def,
product: x:A B[x],
int: ,
equal: s = t,
vatype: ValueAllType
Definitions :
all: x:A. B[x],
vatype: ValueAllType,
implies: P Q,
ohc_v2_RoundInfo: ohc_v2_RoundInfo(Cmd),
le: A B,
ohc_v2_update_round: ohc_v2_update_round(Cmd),
ohc_v2_init: ohc_v2_init(),
prop: 
,
member: t T,
so_lambda: 
x.t[x],
ifthenelse: if b then t else f fi ,
band: p 
q,
btrue: tt,
and: P Q,
uiff: uiff(P;Q),
assert: 
b,
guard: {T},
not: 
A,
false: False,
bfalse: ff,
squash: 
T,
true: True,
ohc_v2_retry'base: ohc_v2_retry'base(Cmd),
ohc_v2_prop2retry: ohc_v2_prop2retry(Cmd),
ohc_v2_proposal'base: ohc_v2_proposal'base(Cmd),
name: Name,
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
atom-deq: AtomDeq,
eq_atom: x =a y,
ohc_v2_NewRoundsState: ohc_v2_NewRoundsState(Cmd),
uall: [x:A]. B[x],
so_apply: x[s1;s2;s3],
bool: 
,
unit: Unit,
uimplies: b supposing a,
iff: P 
Q,
so_apply: x[s],
it: 
,
subtype: S 
T
Lemmas :
Memory-class-mem,
le_wf,
ohc_v2_update_round_wf,
ohc_v2_init_wf,
Id_wf,
bag_wf,
ohc_v2_RoundInfo_wf,
band_wf,
eq_int_wf,
lt_int_wf,
bool_wf,
uiff_transitivity,
equal_wf,
assert_wf,
and_wf,
less_than_wf,
eqtt_to_assert,
assert_of_band,
and_functionality_wrt_uiff,
assert_of_eq_int,
assert_of_lt_int,
iff_transitivity,
bor_wf,
bnot_wf,
le_int_wf,
or_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_thru_band,
squash_wf,
true_wf,
bnot_of_lt_int,
assert_of_bor,
or_functionality_wrt_uiff,
assert_of_bnot,
not_functionality_wrt_uiff,
assert_of_le_int,
es-locl_wf,
event-ordering+_inc,
Message_wf,
es-le_wf,
sq_stable__all,
sq_stable_from_decidable,
decidable__le,
parallel-class-single-val,
ohc_v2_retry'base_wf,
simple-loc-comb-1_wf,
concat-lifting-loc-1_wf,
ohc_v2_prop2retry_wf,
ohc_v2_proposal'base_wf,
disjoint-classrel-symm,
simple-loc-comb-1-concat-disjoint-classrel,
base-disjoint-classrel,
assert-name_eq,
name_wf,
simple-loc-comb-1-concat-single-val,
single-valued-classrel-base,
single-valued-bag-single,
classrel_wf,
es-E_wf,
ohc_v2_NewRoundsState_wf,
valueall-type_wf,
event-ordering+_wf
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}n,round1,round2:\mBbbZ{}. \mforall{}z:\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd.
((e1 <loc e2)
{}\mRightarrow{} z \mmember{} ohc\_v2\_RoundInfo(Cmd)(e1)
{}\mRightarrow{} round1 \mmember{} ohc\_v2\_NewRoundsState(Cmd) n(e1)
{}\mRightarrow{} round2 \mmember{} ohc\_v2\_NewRoundsState(Cmd) n(e2)
{}\mRightarrow{} let z,c = z
in let m,i = z
in (n = m) {}\mRightarrow{} (i \mleq{} round2))
Date html generated:
2012_02_20-PM-05_50_28
Last ObjectModification:
2012_02_17-PM-10_29_21
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