Nuprl Lemma : max_exch_inc_nax
es:EO'. e1,e2:E. n1,n2:
.
((
n,s:. e:E. (e1 
loc e 
(e <loc e2) n 
max_exch_Input()(e) s max_exch_Maximum()(e) (s < n)))
(e1 <loc e2)
n1 max_exch_Maximum()(e1)
n2 max_exch_Maximum()(e2)
(n1 < n2))
Proof not projected
Definitions occuring in Statement :
max_exch_Maximum: max_exch_Maximum(),
max_exch_Input: max_exch_Input(),
Message: Message,
classrel: v X(e),
event-ordering+: EO+(Info),
es-le: e loc e' ,
es-locl: (e <loc e'),
es-E: E,
all: x:A. B[x],
exists: x:A. B[x],
implies: P Q,
and: P Q,
less_than: a < b,
int:
Definitions :
all: x:A. B[x],
implies: P Q,
exists: x:A. B[x],
and: P Q,
max_exch_Input: max_exch_Input(),
imax: imax(a;b),
prop: 
,
trans: Trans(T;x,y.E[x; y]),
not: 
A,
member: t T,
so_lambda: 
x.t[x],
cand: A c B,
ifthenelse: if b then t else f fi ,
btrue: tt,
uiff: uiff(P;Q),
assert: 
b,
false: False,
bfalse: ff,
max_exch_int'base: max_exch_int'base(),
max_exch_exchange'base: max_exch_exchange'base(),
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,
max_exch_Maximum: max_exch_Maximum(),
uall: [x:A]. B[x],
so_apply: x[s1;s2],
bool: 
,
unit: Unit,
uimplies: b supposing a,
le: A B,
guard: {T},
so_apply: x[s],
it: 
,
subtype: S 
T
Lemmas :
Memory-class-progress,
Message_wf,
imax_wf,
single-bag_wf,
Id_wf,
max_exch_Input_wf,
decidable__lt,
less_than_wf,
sq_stable_from_decidable,
le_int_wf,
bool_wf,
uiff_transitivity,
equal_wf,
assert_wf,
le_wf,
eqtt_to_assert,
assert_of_le_int,
lt_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
not_wf,
classrel_wf,
Memory-class_wf,
es-locl_wf,
event-ordering+_inc,
es-le_wf,
parallel-class-single-val,
max_exch_int'base_wf,
simple-loc-comb-1_wf,
concat-lifting-loc-1_wf,
max_exch_exchange'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,
es-E_wf,
exists_wf,
max_exch_Maximum_wf,
event-ordering+_wf
\mforall{}es:EO'. \mforall{}e1,e2:E. \mforall{}n1,n2:\mBbbZ{}.
((\mexists{}n,s:\mBbbZ{}
\mexists{}e:E
(e1 \mleq{}loc e \mwedge{} (e <loc e2) \mwedge{} n \mmember{} max\_exch\_Input()(e) \mwedge{} s \mmember{} max\_exch\_Maximum()(e) \mwedge{} (s < n)))
{}\mRightarrow{} (e1 <loc e2)
{}\mRightarrow{} n1 \mmember{} max\_exch\_Maximum()(e1)
{}\mRightarrow{} n2 \mmember{} max\_exch\_Maximum()(e2)
{}\mRightarrow{} (n1 < n2))
Date html generated:
2012_02_20-PM-05_17_10
Last ObjectModification:
2012_02_17-PM-03_08_11
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