Nuprl Lemma : rsc5_replica_mem
es:EO'. e1,e2:E. Cmd:ValueAllType. zo,z:
( List). zp: Cmd.
((e1 <loc e2)
zp 
rsc5_Proposal(Cmd)(e1)
zo rsc5_ReplicaState(Cmd)(e1)
z rsc5_ReplicaState(Cmd)(e2)
let n,c = zp
in let max1,missing1 = zo
in let max2,missing2 = z
in (max1 
max2)
(x:. ((x missing2) ((x missing1) 
(max1 < x))))
(n max2)
(
(n missing2)))
Proof not projected
Definitions occuring in Statement :
rsc5_ReplicaState: rsc5_ReplicaState(Cmd),
rsc5_Proposal: rsc5_Proposal(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],
not: A,
implies: P Q,
or: P Q,
and: P Q,
less_than: a < b,
spread: spread def,
product: x:A B[x],
list: type List,
int: ,
l_member: (x l),
vatype: ValueAllType
Definitions :
eq_atom: x =a y,
atom-deq: AtomDeq,
band: p 
q,
list-deq: list-deq(eq),
name-deq: NameDeq,
name_eq: name_eq(x;y),
name: Name,
rsc5_vote'base: rsc5_vote'base(Cmd),
rsc5_vote2prop: rsc5_vote2prop(Cmd),
rsc5_propose'base: rsc5_propose'base(Cmd),
bfalse: ff,
subtype: S 
T,
guard: {T},
false: False,
cand: A c B,
assert: 
b,
uiff: uiff(P;Q),
btrue: tt,
ifthenelse: if b then t else f fi ,
so_lambda: 
x.t[x],
member: t T,
prop: 
,
rsc5_init: rsc5_init(),
rsc5_update_replica: rsc5_update_replica(Cmd),
not: A,
or: P Q,
le: A B,
and: P Q,
rsc5_Proposal: rsc5_Proposal(Cmd),
implies: P Q,
vatype: ValueAllType,
all: x:A. B[x],
rev_implies: P 
Q,
iff: P Q,
decidable: Dec(P),
uimplies: b supposing a,
unit: Unit,
bool: 
,
so_apply: x[s],
so_apply: x[s1;s2;s3],
uall: [x:A]. B[x],
rsc5_ReplicaState: rsc5_ReplicaState(Cmd),
it: 
Lemmas :
event-ordering+_wf,
valueall-type_wf,
rsc5_ReplicaState_wf,
es-E_wf,
classrel_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_vote2prop_wf,
concat-lifting-loc-1_wf,
simple-loc-comb-1_wf,
rsc5_propose'base_wf,
parallel-class-single-val,
sq_stable__not,
decidable__lt,
decidable__or,
sq_stable__all,
decidable__le,
sq_stable_from_decidable,
sq_stable__and,
es-le_wf,
Message_wf,
event-ordering+_inc,
es-locl_wf,
not_functionality_wrt_iff,
assert_of_bnot,
cons_member,
list-diff_wf,
member-list-diff,
assert-deq-member,
iff_weakening_uiff,
iff_transitivity,
int-deq_wf,
deq-member_wf,
assert_of_le_int,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
bnot_wf,
le_int_wf,
rsc5_pos_max_missing,
from-upto_wf,
append_wf,
from-upto-member,
member_append,
decidable__equal_int,
decidable__l_member,
assert_of_lt_int,
eqtt_to_assert,
assert_wf,
equal_wf,
uiff_transitivity,
bool_wf,
lt_int_wf,
rsc5_Proposal_wf,
bag_wf,
Id_wf,
rsc5_init_wf,
rsc5_update_replica_wf,
not_wf,
less_than_wf,
or_wf,
l_member_wf,
all_wf,
le_wf,
and_wf,
Memory-class-mem
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}zo,z:\mBbbZ{} \mtimes{} (\mBbbZ{} List). \mforall{}zp:\mBbbZ{} \mtimes{} Cmd.
((e1 <loc e2)
{}\mRightarrow{} zp \mmember{} rsc5\_Proposal(Cmd)(e1)
{}\mRightarrow{} zo \mmember{} rsc5\_ReplicaState(Cmd)(e1)
{}\mRightarrow{} z \mmember{} rsc5\_ReplicaState(Cmd)(e2)
{}\mRightarrow{} let n,c = zp
in let max1,missing1 = zo
in let max2,missing2 = z
in (max1 \mleq{} max2)
\mwedge{} (\mforall{}x:\mBbbZ{}. ((x \mmember{} missing2) {}\mRightarrow{} ((x \mmember{} missing1) \mvee{} (max1 < x))))
\mwedge{} (n \mleq{} max2)
\mwedge{} (\mneg{}(n \mmember{} missing2)))
Date html generated:
2012_02_20-PM-05_09_57
Last ObjectModification:
2012_02_02-PM-02_19_58
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