Nuprl Lemma : rsc4_positive_max
es:EO'. e1:E. Cmd:ValueAllType. v1:
( List).
(v1 
rsc4_ReplicaState(Cmd)(e1)
let max,missing = v1
in (
0 
z max) 
(x:. ((int-list-member(x;missing)) ((0 <z x) (x <z max)))))
Proof
Definitions occuring in Statement :
rsc4_ReplicaState: rsc4_ReplicaState(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-E: E,
le_int: i z j,
lt_int: i <z j,
assert: b,
all: x:A. B[x],
implies: P Q,
and: P Q,
spread: spread def,
product: x:A B[x],
list: type List,
natural_number: $n,
int: ,
int-list-member: int-list-member(i;xs),
vatype: ValueAllType
Definitions :
bnot: 
b,
bfalse: ff,
subtype: S 
T,
false: False,
not: A,
btrue: tt,
rsc4_onnewpropose: rsc4_onnewpropose(Cmd),
ifthenelse: if b then t else f fi ,
guard: {T},
le: A B,
true: True,
squash: 
T,
cand: A c B,
so_lambda: 
x.t[x],
member: t T,
prop: 
,
rsc4_init: rsc4_init(),
rsc4_update_replica: rsc4_update_replica(Cmd),
lt_int: i <z j,
le_int: i z j,
assert: b,
and: P Q,
implies: P Q,
vatype: ValueAllType,
all: x:A. B[x],
sq_type: SQType(T),
rev_uimplies: rev_uimplies(P;Q),
or: P 
Q,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
iff: P 
Q,
bool: 
,
so_apply: x[s],
sq_stable: SqStable(P),
uall: [x:A]. B[x],
rsc4_ReplicaState: rsc4_ReplicaState(Cmd),
it: 
Lemmas :
event-ordering+_wf,
rsc4_ReplicaState_wf,
classrel_wf,
single-bag_wf,
bag-member_wf,
nil_member,
list_subtype_base,
int_subtype_base,
product_subtype_base,
subtype_base_sq,
bag-member-single,
event-ordering+_inc,
es-E_wf,
not_functionality_wrt_iff,
assert_of_bnot,
assert_of_band,
true_wf,
squash_wf,
bnot_thru_bor,
not_wf,
band_wf,
member-list-diff,
list-diff_wf,
bnot_of_lt_int,
assert_functionality_wrt_uiff,
eqff_to_assert,
bnot_wf,
from-upto-member,
member_append,
from-upto_wf,
append_wf,
uiff_transitivity,
assert-deq-member,
or_functionality_wrt_iff,
assert_of_bor,
eqtt_to_assert,
or_wf,
equal_wf,
iff_transitivity,
bool_wf,
int-deq_wf,
deq-member_wf,
bor_wf,
assert_of_lt_int,
less_than_wf,
and_functionality_wrt_uiff,
assert-int-list-member,
implies_functionality_wrt_iff,
all_functionality_wrt_iff,
assert_of_le_int,
iff_weakening_uiff,
l_member_wf,
le_wf,
and_functionality_wrt_iff,
sq_stable__all,
sq_stable__assert,
and_wf,
sq_stable__and,
valueall-type_wf,
sq_stable__valueall-type,
rsc4_Proposal_wf,
bag_wf,
Id_wf,
rsc4_init_wf,
rsc4_update_replica_wf,
lt_int_wf,
int-list-member_wf,
all_wf,
le_int_wf,
assert_wf,
Message_wf,
Memory-class-invariant
\mforall{}es:EO'. \mforall{}e1:E. \mforall{}Cmd:ValueAllType. \mforall{}v1:\mBbbZ{} \mtimes{} (\mBbbZ{} List).
(v1 \mmember{} rsc4\_ReplicaState(Cmd)(e1)
{}\mRightarrow{} let max,missing = v1
in (\muparrow{}0 \mleq{}z max) \mwedge{} (\mforall{}x:\mBbbZ{}. ((\muparrow{}int-list-member(x;missing)) {}\mRightarrow{} ((\muparrow{}0 <z x) \mwedge{} (\muparrow{}x <z max)))))
Date html generated:
2012_02_20-PM-04_54_32
Last ObjectModification:
2012_02_02-PM-02_09_54
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