Nuprl Lemma : rsc4_replica_state_mem
es:EO'. e1,e2:E. Cmd:ValueAllType. z1,z2:
( List). v: Cmd.
((e1 <loc e2)
v 
rsc4_Proposal(Cmd)(e1)
z1 rsc4_ReplicaState(Cmd)(e1)
z2 rsc4_ReplicaState(Cmd)(e2)
let num,c = v
in let max1,missing1 = z1
in let max2,missing2 = z2
in (num 
max2)
(
int-list-member(num;missing2))
(max1 z max2)
(x:. ((int-list-member(x;missing2)) ((int-list-member(x;missing1)) 
(max1 <z x)))))
Proof
Definitions occuring in Statement :
rsc4_ReplicaState: rsc4_ReplicaState(Cmd),
rsc4_Proposal: rsc4_Proposal(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-E: E,
le_int: i z j,
lt_int: i <z j,
assert: b,
le: A B,
all: x:A. B[x],
not: A,
implies: P Q,
or: P Q,
and: P Q,
spread: spread def,
product: x:A B[x],
list: type List,
int: ,
int-list-member: int-list-member(i;xs),
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_vote2prop: rsc4_vote2prop(Cmd),
rsc4_propose'base: rsc4_propose'base(Cmd),
true: True,
squash: 
T,
band: p 
q,
bfalse: ff,
subtype: S 
T,
false: False,
cand: A c B,
guard: {T},
uiff: uiff(P;Q),
btrue: tt,
rsc4_onnewpropose: rsc4_onnewpropose(Cmd),
ifthenelse: if b then t else f fi ,
so_lambda: 
x.t[x],
member: t T,
prop: 
,
rsc4_init: rsc4_init(),
rsc4_update_replica: rsc4_update_replica(Cmd),
or: P Q,
assert: b,
not: A,
le: A B,
and: P Q,
rsc4_Proposal: rsc4_Proposal(Cmd),
implies: P Q,
vatype: ValueAllType,
all: x:A. B[x],
sq_type: SQType(T),
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P),
uimplies: b supposing a,
rev_implies: P 
Q,
iff: P Q,
unit: Unit,
so_apply: x[s],
bool: 
,
so_apply: x[s1;s2;s3],
uall: [x:A]. B[x],
rsc4_ReplicaState: rsc4_ReplicaState(Cmd),
it: 
Lemmas :
assert_elim,
event-ordering+_wf,
valueall-type_wf,
rsc4_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,
rsc4_vote'base_wf,
rsc4_vote2prop_wf,
concat-lifting-loc-1_wf,
simple-loc-comb-1_wf,
rsc4_propose'base_wf,
parallel-class-single-val,
decidable__or,
sq_stable__all,
sq_stable__assert,
sq_stable__not,
decidable__le,
sq_stable_from_decidable,
sq_stable__and,
imax_wf,
imax-right,
es-le_wf,
Message_wf,
event-ordering+_inc,
es-locl_wf,
bool_subtype_base,
subtype_base_sq,
assert_of_bnot,
and_functionality_wrt_iff,
assert_of_band,
true_wf,
squash_wf,
bnot_thru_bor,
band_wf,
list-diff_wf,
cons_member,
member-list-diff,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
bnot_wf,
decidable__assert,
from-upto_wf,
append_wf,
from-upto-member,
assert_of_le_int,
and_functionality_wrt_uiff,
implies_functionality_wrt_iff,
all_functionality_wrt_iff,
decidable__false,
rsc4_pos_max_missing,
member_append,
assert-int-list-member,
not_functionality_wrt_iff,
uiff_transitivity,
assert-deq-member,
assert_of_lt_int,
or_functionality_wrt_iff,
assert_of_bor,
eqtt_to_assert,
iff_weakening_uiff,
l_member_wf,
less_than_wf,
equal_wf,
iff_transitivity,
bool_wf,
int-deq_wf,
deq-member_wf,
bor_wf,
rsc4_Proposal_wf,
bag_wf,
Id_wf,
rsc4_init_wf,
rsc4_update_replica_wf,
lt_int_wf,
or_wf,
all_wf,
le_int_wf,
int-list-member_wf,
assert_wf,
not_wf,
le_wf,
and_wf,
Memory-class-mem
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}z1,z2:\mBbbZ{} \mtimes{} (\mBbbZ{} List). \mforall{}v:\mBbbZ{} \mtimes{} Cmd.
((e1 <loc e2)
{}\mRightarrow{} v \mmember{} rsc4\_Proposal(Cmd)(e1)
{}\mRightarrow{} z1 \mmember{} rsc4\_ReplicaState(Cmd)(e1)
{}\mRightarrow{} z2 \mmember{} rsc4\_ReplicaState(Cmd)(e2)
{}\mRightarrow{} let num,c = v
in let max1,missing1 = z1
in let max2,missing2 = z2
in (num \mleq{} max2)
\mwedge{} (\mneg{}\muparrow{}int-list-member(num;missing2))
\mwedge{} (\muparrow{}max1 \mleq{}z max2)
\mwedge{} (\mforall{}x:\mBbbZ{}
((\muparrow{}int-list-member(x;missing2))
{}\mRightarrow{} ((\muparrow{}int-list-member(x;missing1)) \mvee{} (\muparrow{}max1 <z x)))))
Date html generated:
2012_02_20-PM-04_58_40
Last ObjectModification:
2012_02_02-PM-02_16_35
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