Nuprl Lemma : ohc_v2_pos_max
es:EO'. e1:E. Cmd:ValueAllType. z:
( List).
(z 
ohc_v2_ReplicaState(Cmd)(e1)
let max,missing = z
in (0 
max) 
(x:. ((x missing) ((0 < x) (x < max)))))
Proof not projected
Definitions occuring in Statement :
ohc_v2_ReplicaState: ohc_v2_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: ,
l_member: (x l),
vatype: ValueAllType
Definitions :
all: x:A. B[x],
vatype: ValueAllType,
implies: P Q,
and: P Q,
le: A B,
ohc_v2_update_replica: ohc_v2_update_replica(Cmd),
ohc_v2_init: ohc_v2_init(),
prop: 
,
member: t T,
so_lambda: 
x.t[x],
cand: A c B,
squash: 
T,
true: True,
ifthenelse: if b then t else f fi ,
btrue: tt,
not: 
A,
false: False,
subtype: S 
T,
bfalse: ff,
ohc_v2_ReplicaState: ohc_v2_ReplicaState(Cmd),
uall: [x:A]. B[x],
sq_stable: SqStable(P),
so_apply: x[s],
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
or: P 
Q,
iff: P 
Q,
guard: {T},
sq_type: SQType(T),
it: 
Lemmas :
Memory-class-invariant,
Message_wf,
le_wf,
all_wf,
l_member_wf,
ohc_v2_update_replica_wf,
ohc_v2_init_wf,
Id_wf,
bag_wf,
ohc_v2_Initial_wf,
sq_stable__valueall-type,
valueall-type_wf,
sq_stable__and,
and_wf,
less_than_wf,
sq_stable_from_decidable,
decidable__le,
sq_stable__all,
decidable__lt,
lt_int_wf,
bool_wf,
uiff_transitivity,
equal_wf,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
member_append,
from-upto-member,
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,
list-diff_wf,
not_wf,
assert_of_bnot,
not_functionality_wrt_iff,
es-locl_wf,
event-ordering+_inc,
bag-member-single,
subtype_base_sq,
product_subtype_base,
int_subtype_base,
list_subtype_base,
nil_member,
bag-member_wf,
single-bag_wf,
classrel_wf,
ohc_v2_ReplicaState_wf,
es-E_wf,
event-ordering+_wf
\mforall{}es:EO'. \mforall{}e1:E. \mforall{}Cmd:ValueAllType. \mforall{}z:\mBbbZ{} \mtimes{} (\mBbbZ{} List).
(z \mmember{} ohc\_v2\_ReplicaState(Cmd)(e1)
{}\mRightarrow{} let max,missing = z
in (0 \mleq{} max) \mwedge{} (\mforall{}x:\mBbbZ{}. ((x \mmember{} missing) {}\mRightarrow{} ((0 < x) \mwedge{} (x < max)))))
Date html generated:
2012_02_20-PM-05_52_17
Last ObjectModification:
2012_02_17-PM-10_28_27
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