Nuprl Lemma : ohc_v1_mem_rep
es:EO'. e1,e2:E. Cmd:ValueAllType. zq,z:
( List). zr: Cmd.
((e1 <loc e2)
zr 
ohc_v1_Initial(Cmd)(e1)
zq ohc_v1_ReplicaState(Cmd)(e1)
z ohc_v1_ReplicaState(Cmd)(e2)
let n,c = zr
in let max1,missing1 = zq
in let max2,missing2 = z
in (n 
max2)
(
(n missing2))
(max1 max2)
(x:. ((x missing2) ((x missing1) 
(max1 < x)))))
Proof not projected
Definitions occuring in Statement :
ohc_v1_ReplicaState: ohc_v1_ReplicaState(Cmd),
ohc_v1_Initial: ohc_v1_Initial(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 :
all: x:A. B[x],
vatype: ValueAllType,
implies: P Q,
ohc_v1_Initial: ohc_v1_Initial(Cmd),
and: P Q,
le: A B,
not: A,
or: P Q,
ohc_v1_update_replica: ohc_v1_update_replica(Cmd),
ohc_v1_init: ohc_v1_init(),
prop: 
,
member: t T,
so_lambda: 
x.t[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
assert: 
b,
cand: A c B,
false: False,
guard: {T},
subtype: S 
T,
bfalse: ff,
ohc_v1_initial'base: ohc_v1_initial'base(Cmd),
ohc_v1_prop2init: ohc_v1_prop2init(Cmd),
ohc_v1_proposal'base: ohc_v1_proposal'base(Cmd),
name: Name,
name_eq: name_eq(x;y),
name-deq: NameDeq,
list-deq: list-deq(eq),
band: p 
q,
atom-deq: AtomDeq,
eq_atom: x =a y,
ohc_v1_ReplicaState: ohc_v1_ReplicaState(Cmd),
uall: [x:A]. B[x],
so_apply: x[s1;s2;s3],
so_apply: x[s],
bool: 
,
unit: Unit,
uimplies: b supposing a,
iff: P 
Q,
rev_implies: P Q,
decidable: Dec(P),
it: 
Lemmas :
Memory-class-mem,
and_wf,
le_wf,
not_wf,
l_member_wf,
all_wf,
or_wf,
less_than_wf,
ohc_v1_update_replica_wf,
ohc_v1_init_wf,
Id_wf,
bag_wf,
ohc_v1_Initial_wf,
lt_int_wf,
bool_wf,
uiff_transitivity,
equal_wf,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
member_append,
ohc_v1_pos_max,
decidable__false,
from-upto-member,
decidable__l_member,
decidable__equal_int,
append_wf,
from-upto_wf,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
deq-member_wf,
int-deq_wf,
iff_transitivity,
iff_weakening_uiff,
assert-deq-member,
member-list-diff,
cons_member,
list-diff_wf,
assert_of_bnot,
not_functionality_wrt_iff,
es-locl_wf,
event-ordering+_inc,
Message_wf,
es-le_wf,
sq_stable__and,
sq_stable_from_decidable,
decidable__le,
sq_stable__not,
sq_stable__all,
decidable__or,
decidable__lt,
parallel-class-single-val,
ohc_v1_initial'base_wf,
simple-loc-comb-1_wf,
concat-lifting-loc-1_wf,
ohc_v1_prop2init_wf,
ohc_v1_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_v1_ReplicaState_wf,
valueall-type_wf,
event-ordering+_wf
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}Cmd:ValueAllType. \mforall{}zq,z:\mBbbZ{} \mtimes{} (\mBbbZ{} List). \mforall{}zr:\mBbbZ{} \mtimes{} Cmd.
((e1 <loc e2)
{}\mRightarrow{} zr \mmember{} ohc\_v1\_Initial(Cmd)(e1)
{}\mRightarrow{} zq \mmember{} ohc\_v1\_ReplicaState(Cmd)(e1)
{}\mRightarrow{} z \mmember{} ohc\_v1\_ReplicaState(Cmd)(e2)
{}\mRightarrow{} let n,c = zr
in let max1,missing1 = zq
in let max2,missing2 = z
in (n \mleq{} max2)
\mwedge{} (\mneg{}(n \mmember{} missing2))
\mwedge{} (max1 \mleq{} max2)
\mwedge{} (\mforall{}x:\mBbbZ{}. ((x \mmember{} missing2) {}\mRightarrow{} ((x \mmember{} missing1) \mvee{} (max1 < x)))))
Date html generated:
2012_02_20-PM-05_27_55
Last ObjectModification:
2012_02_13-PM-01_03_37
Home
Index