{ 
[A,B,C:Type]. [P:dataflow(A;B)]. [f:B 
C]. [ms:A List].
(data-stream(map-dataflow(P;b.f[b]);ms) ~ map(
b.f[b];data-stream(P;ms))) }
{ Proof }
Definitions occuring in Statement :
map-dataflow: map-dataflow(P;b.f[b]),
data-stream: data-stream(P;L),
dataflow: dataflow(A;B),
map: map(f;as),
uall: [x:A]. B[x],
so_apply: x[s],
lambda: x.A[x],
function: x:A B[x],
list: type List,
universe: Type,
sqequal: s ~ t
Definitions :
less_than: a < b,
natural_number: $n,
length: ||as||,
lambda: x.A[x],
subtract: n - m,
add: n + m,
minus: -n,
not: 
A,
false: False,
ge: i 
j ,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
universe: Type,
dataflow: dataflow(A;B),
function: x:A B[x],
list: type List,
prop: 
,
sqequal: s ~ t,
so_lambda: 
x.t[x],
member: t 
T,
equal: s = t,
all: x:A. B[x],
implies: P 
Q,
guard: {T},
le: A 
B,
nat: 
,
int: 
,
subtype: S 
T,
grp_car: |g|,
real: 
,
set: {x:A| B[x]} ,
uimplies: b supposing a,
top: Top,
void: Void,
decidable: Dec(P),
l_disjoint: l_disjoint(T;l1;l2),
fset-closed: (s closed under fs),
f-subset: xs ys,
fset-member: a s,
p-outcome: Outcome,
i-closed: i-closed(I),
i-finite: i-finite(I),
exists: 
x:A. B[x],
product: x:A 
B[x],
q-rel: q-rel(r;x),
qless: r < s,
qle: r s,
fun-connected: y is f*(x),
infix_ap: x f y,
apply: f a,
l_all: (xL.P[x]),
l_exists: (xL. P[x]),
squash: 
T,
prime: prime(a),
reducible: reducible(a),
inject: Inj(A;B;f),
l_contains: A B,
l_member: (x l),
cand: A c
B,
grp_lt: a < b,
set_lt: a <p b,
set_leq: a b,
assoced: a ~ b,
divides: b | a,
assert: 
b,
or: P 
Q,
union: left + right,
append: as @ bs,
firstn: firstn(n;as),
cons: [car / cdr],
last: last(L),
nil: [],
data-stream: data-stream(P;L),
iterate-dataflow: P*(inputs),
so_apply: x[s],
map: map(f;as),
map-dataflow: map-dataflow(P;b.f[b]),
corec: corec(T.F[T]),
primrec: primrec(n;b;c),
subtype_rel: A r B,
sq_type: SQType(T),
uiff: uiff(P;Q),
and: P Q,
hd: hd(l),
tl: tl(l),
strong-subtype: strong-subtype(A;B),
qabs: |r|,
filter: filter(P;l),
pi2: snd(t),
dataflow-ap: df(a),
pi1: fst(t),
fpf: a:A fp-> B[a],
fpf-cap: f(x)?z,
pair: <a, b>,
fpf-dom: x dom(f),
ma-state: State(ds),
deq: EqDecider(T),
fpf-sub: f g,
true: True,
data_stream_nil: data_stream_nil{data_stream_nil_compseq_tag_def:o}(P),
int_iseg: {i...j},
rationals: 
,
select: l[i],
upto: upto(n),
int_seg: {i..j
},
base: Base,
lelt: i j < k,
iff: P 
Q,
rev_implies: P Q,
tactic: Error :tactic,
RepeatFor: Error :RepeatFor,
CollapseTHEN: Error :CollapseTHEN,
Try: Error :Try,
CollapseTHENA: Error :CollapseTHENA,
Auto: Error :Auto,
RepUR: Error :RepUR,
D: Error :D
Lemmas :
length_cons,
pos_length2,
assert_wf,
iterate-map-dataflow,
rev_implies_wf,
iff_wf,
int_subtype_base,
set_subtype_base,
map_wf,
int_seg_wf,
upto_wf,
select_wf,
pi2_wf,
false_wf,
not_wf,
length_firstn,
non_neg_length,
map_append_sq,
data-stream-cons,
subtype_rel_list,
subtype_rel_wf,
last_wf,
dataflow-ap_wf,
pi1_wf,
list_subtype_base,
subtype_base_sq,
append_wf,
data-stream_wf,
iterate-dataflow_wf,
map-dataflow_wf,
firstn_wf,
data-stream-append,
firstn_all,
firstn_decomp,
length_wf1,
decidable__lt,
top_wf,
member_wf,
length_wf_nat,
guard_wf,
le_wf,
comp_nat_ind_tp,
nat_wf,
uall_wf,
dataflow_wf,
nat_ind_tp,
nat_properties,
ge_wf
\mforall{}[A,B,C:Type]. \mforall{}[P:dataflow(A;B)]. \mforall{}[f:B {}\mrightarrow{} C]. \mforall{}[ms:A List].
(data-stream(map-dataflow(P;b.f[b]);ms) \msim{} map(\mlambda{}b.f[b];data-stream(P;ms)))
Date html generated:
2011_08_10-AM-08_17_27
Last ObjectModification:
2010_12_31-PM-12_51_55
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