Nuprl Lemma : eval-parallel-dataflow-property
[A:Type]. [m:A]. [n:
]. [B:n 
Type]. [ds:k:n dataflow(A;B[k])].
(eval-parallel-dataflow(n;ds;m) = <
k.(fst(ds k(m))), k.dataflow-out(ds k;m)>)
Proof not projected
Definitions occuring in Statement :
eval-parallel-dataflow: eval-parallel-dataflow(n;s;m),
dataflow-out: dataflow-out(df;a),
dataflow-ap: df(a),
dataflow: dataflow(A;B),
int_seg: {i..j
},
nat: ,
uall: [x:A]. B[x],
so_apply: x[s],
pi1: fst(t),
apply: f a,
lambda: x.A[x],
function: x:A B[x],
pair: <a, b>,
product: x:A 
B[x],
natural_number: $n,
universe: Type,
equal: s = t
Definitions :
uall: [x:A]. B[x],
so_apply: x[s],
member: t 
T,
nat: ,
int_seg: {i..j},
all: x:A. B[x],
implies: P 
Q,
le: A 
B,
map: map(f;as),
upto: upto(n),
primrec: primrec(n;b;c),
ifthenelse: if b then t else f fi ,
eq_int: (i =
j),
ycomb: Y,
btrue: tt,
bfalse: ff,
and: P 
Q,
from-upto: [n, m),
lt_int: i <z j,
not: 
A,
guard: {T},
false: False,
lelt: i j < k,
null: null(as),
dataflow-ap: df(a),
subtype: S 
T,
squash: 
T,
true: True,
ge: i 
j ,
bool: 
,
unit: Unit,
uimplies: b supposing a,
uiff: uiff(P;Q),
prop: 
,
sq_type: SQType(T),
it: 
Lemmas :
int_seg_wf,
dataflow_wf,
nat_wf,
btrue_wf,
bool_wf,
uiff_transitivity,
equal_wf,
assert_wf,
eqtt_to_assert,
assert_of_eq_int,
it_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
not_functionality_wrt_uiff,
primrec_wf,
unit_wf2,
le_wf,
eq_int_wf,
subtype_base_sq,
int_subtype_base,
dataflow-ap_wf,
squash_wf,
true_wf,
lelt_wf,
tuple-type_wf,
map_wf,
nat_properties,
ge_wf
\mforall{}[A:Type]. \mforall{}[m:A]. \mforall{}[n:\mBbbN{}]. \mforall{}[B:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[ds:k:\mBbbN{}n {}\mrightarrow{} dataflow(A;B[k])].
(eval-parallel-dataflow(n;ds;m) = <\mlambda{}k.(fst(ds k(m))), \mlambda{}k.dataflow-out(ds k;m)>)
Date html generated:
2012_01_23-AM-11_57_00
Last ObjectModification:
2011_12_28-PM-12_07_41
Home
Index