{ 
[L:Top List]. [a,P:Top].
(data-stream(P;[a / L]) ~ [snd(P(a)) / data-stream(fst(P(a));L)]) }
{ Proof }
Definitions occuring in Statement :
data-stream: data-stream(P;L),
dataflow-ap: df(a),
uall: [x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
cons: [car / cdr],
list: type List,
sqequal: s ~ t
Definitions :
uall: [x:A]. B[x],
data-stream: data-stream(P;L),
member: t 
T,
nat_plus: 
,
length: ||as||,
ycomb: Y,
map: map(f;as),
select: l[i],
ifthenelse: if b then t else f fi ,
le_int: i 
z j,
bnot: 
b,
lt_int: i <z j,
bfalse: ff,
btrue: tt,
top: Top,
compose: f o g,
all: x:A. B[x],
subtype: S 
T,
implies: P 
Q,
prop: 
,
firstn: firstn(n;as),
sq_type: SQType(T),
uimplies: b supposing a,
guard: {T},
int_seg: {i..j
},
bool: 
,
lelt: i j < k,
unit: Unit,
le: A B,
iff: P 
Q,
and: P 
Q,
not: A,
false: False,
it: 
Lemmas :
top_wf,
upto_decomp2,
length_wf1,
non_neg_length,
length_wf_nat,
length_cons,
subtype_base_sq,
int_subtype_base,
first0,
map-map,
upto_wf,
int_seg_wf,
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,
bnot_of_lt_int,
int_seg_properties
\mforall{}[L:Top List]. \mforall{}[a,P:Top]. (data-stream(P;[a / L]) \msim{} [snd(P(a)) / data-stream(fst(P(a));L)])
Date html generated:
2011_08_10-AM-08_14_35
Last ObjectModification:
2011_06_18-AM-08_29_59
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