Nuprl Lemma : rsc5_pos_max_missing
es:EO'. e1:E. Cmd:ValueAllType. z:
( List).
(z 
rsc5_ReplicaState(Cmd)(e1)
let max,missing = z
in (0 
max) 
no_repeats(;missing) (x:. ((x missing) ((0 < x) (x < max)))))
Proof not projected
Definitions occuring in Statement :
rsc5_ReplicaState: rsc5_ReplicaState(Cmd),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-E: E,
le: A B,
all: x:A. B[x],
implies: P Q,
and: P Q,
less_than: a < b,
spread: spread def,
product: x:A B[x],
list: type List,
natural_number: $n,
int: ,
no_repeats: no_repeats(T;l),
l_member: (x l),
vatype: ValueAllType
Definitions :
bfalse: ff,
guard: {T},
ge: i 
j ,
or: P 
Q,
subtype: S 
T,
false: False,
not: 
A,
uiff: uiff(P;Q),
btrue: tt,
ifthenelse: if b then t else f fi ,
true: True,
squash: 
T,
cand: A c B,
so_lambda: 
x.t[x],
member: t T,
prop: 
,
rsc5_init: rsc5_init(),
rsc5_update_replica: rsc5_update_replica(Cmd),
le: A B,
and: P Q,
implies: P Q,
vatype: ValueAllType,
all: x:A. B[x],
sq_type: SQType(T),
iff: P 
Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
unit: Unit,
bool: 
,
decidable: Dec(P),
so_apply: x[s],
sq_stable: SqStable(P),
uall: [x:A]. B[x],
rsc5_ReplicaState: rsc5_ReplicaState(Cmd),
it: 
Lemmas :
event-ordering+_wf,
es-E_wf,
rsc5_ReplicaState_wf,
classrel_wf,
single-bag_wf,
bag-member_wf,
nil_member,
no_repeats_nil,
list_subtype_base,
int_subtype_base,
product_subtype_base,
subtype_base_sq,
bag-member-single,
event-ordering+_inc,
es-locl_wf,
not_functionality_wrt_iff,
assert_of_bnot,
not_wf,
list-diff_wf,
member-list-diff,
no_repeats_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,
append_wf,
from-upto-member,
member_append,
no_repeats_from-upto,
ge_wf,
l_disjoint_from-upto,
from-upto_wf,
no_repeats_append_iff,
assert_of_lt_int,
eqtt_to_assert,
assert_wf,
equal_wf,
uiff_transitivity,
bool_wf,
lt_int_wf,
decidable__lt,
sq_stable__all,
sq_stable__no_repeats,
decidable__le,
sq_stable_from_decidable,
less_than_wf,
and_wf,
sq_stable__and,
valueall-type_wf,
sq_stable__valueall-type,
rsc5_Proposal_wf,
bag_wf,
Id_wf,
rsc5_init_wf,
rsc5_update_replica_wf,
l_member_wf,
all_wf,
no_repeats_wf,
le_wf,
Message_wf,
Memory-class-invariant
\mforall{}es:EO'. \mforall{}e1:E. \mforall{}Cmd:ValueAllType. \mforall{}z:\mBbbZ{} \mtimes{} (\mBbbZ{} List).
(z \mmember{} rsc5\_ReplicaState(Cmd)(e1)
{}\mRightarrow{} let max,missing = z
in (0 \mleq{} max) \mwedge{} no\_repeats(\mBbbZ{};missing) \mwedge{} (\mforall{}x:\mBbbZ{}. ((x \mmember{} missing) {}\mRightarrow{} ((0 < x) \mwedge{} (x < max)))))
Date html generated:
2012_02_20-PM-05_09_40
Last ObjectModification:
2012_02_02-PM-02_19_54
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