{ 
[L:Top List]. [ds,F:Top].
(data-stream(parallel-dataflow(
ds;
F);L) ~ map(
i.(F (k.data-stream(ds k;L)[i]));upto(||L||))) }
{ Proof }
Definitions occuring in Statement :
parallel-dataflow: parallel-dataflow,
data-stream: data-stream(P;L),
select: l[i],
map: map(f;as),
length: ||as||,
uall: [x:A]. B[x],
top: Top,
apply: f a,
lambda: x.A[x],
list: type List,
sqequal: s ~ t,
upto: upto(n)
Definitions :
uall: [x:A]. B[x],
top: Top,
parallel-dataflow: parallel-dataflow,
map: map(f;as),
select: l[i],
upto: upto(n),
length: ||as||,
member: t 
T,
ycomb: Y,
from-upto: [n, m),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
btrue: tt,
bfalse: ff,
pi2: snd(t),
dataflow-ap: df(a),
pi1: fst(t),
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
dataflow-out: dataflow-out(df;a),
le_int: i 
z j,
bnot: 
b,
compose: f o g,
all: x:A. B[x],
subtype: S 
T,
implies: P 
Q,
int_seg: {i..j
},
lelt: i j < k,
prop: 
,
and: P 
Q,
so_lambda: 
x.t[x],
sq_type: SQType(T),
uimplies: b supposing a,
guard: {T},
bool: 
,
unit: Unit,
le: A B,
iff: P 
Q,
not: A,
false: False,
so_apply: x[s],
it: 
Lemmas :
top_wf,
upto_decomp2,
length_wf1,
non_neg_length,
length_wf_nat,
data-stream-cons,
map-map,
upto_wf,
int_seg_wf,
subtype_base_sq,
int_subtype_base,
select-cons,
le_int_wf,
bool_wf,
iff_weakening_uiff,
le_wf,
uiff_transitivity,
assert_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,
set_subtype_base
\mforall{}[L:Top List]. \mforall{}[ds,F:Top].
(data-stream(parallel-dataflow(
ds;
F);L) \msim{} map(\mlambda{}i.(F (\mlambda{}k.data-stream(ds k;L)[i]));upto(||L||)))
Date html generated:
2011_08_10-AM-08_15_51
Last ObjectModification:
2011_06_18-AM-08_30_41
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