{ 
[L:Top List]. [P:Top]. [i:
].
(data-stream(P;L)[i] ~ if i <z ||L||
then snd(P*(firstn(i;L))(L[i]))
else []
fi ) }
{ Proof }
Definitions occuring in Statement :
data-stream: data-stream(P;L),
iterate-dataflow: P*(inputs),
dataflow-ap: df(a),
select: l[i],
firstn: firstn(n;as),
length: ||as||,
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
nat: ,
uall: [x:A]. B[x],
top: Top,
pi2: snd(t),
nil: [],
list: type List,
sqequal: s ~ t
Definitions :
uall: [x:A]. B[x],
ifthenelse: if b then t else f fi ,
member: t 
T,
all: x:A. B[x],
implies: P 
Q,
btrue: tt,
prop: 
,
bfalse: ff,
top: Top,
data-stream: data-stream(P;L),
int_seg: {i..j
},
subtype: S 
T,
lelt: i 
j < k,
le: A B,
and: P 
Q,
not: 
A,
false: False,
nat: ,
bool: 
,
unit: Unit,
iff: P 
Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
it: 
Lemmas :
lt_int_wf,
length_wf1,
bool_wf,
iff_weakening_uiff,
uiff_transitivity,
assert_wf,
eqtt_to_assert,
assert_of_lt_int,
le_wf,
le_int_wf,
bnot_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
nat_wf,
top_wf,
select-map,
upto_wf,
int_seg_wf,
length_upto,
length_wf_nat,
select_upto,
subtype_base_sq,
int_subtype_base,
select-is-nil,
map_wf,
length-data-stream
\mforall{}[L:Top List]. \mforall{}[P:Top]. \mforall{}[i:\mBbbN{}].
(data-stream(P;L)[i] \msim{} if i <z ||L|| then snd(P*(firstn(i;L))(L[i])) else [] fi )
Date html generated:
2011_08_10-AM-08_14_53
Last ObjectModification:
2011_06_18-AM-08_30_14
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