{ 
[A,B:Type]. [f,g:dataflow(A;B)].
(f 
g
as:A List
. (last(data-stream(f;as)) = last(data-stream(g;as)))) }
{ Proof }
Definitions occuring in Statement :
dataflow-equiv: d1 d2,
data-stream: data-stream(P;L),
dataflow: dataflow(A;B),
uall: [x:A]. B[x],
all: x:A. B[x],
iff: P Q,
universe: Type,
equal: s = t,
listp: A List,
last: last(L)
Definitions :
length: ||as||,
add: n + m,
sqequal: s ~ t,
guard: {T},
true: True,
subtype: S 
T,
top: Top,
null: null(as),
squash: 
T,
l_member: (x 
l),
void: Void,
false: False,
limited-type: LimitedType,
fpf: a:A fp-> B[a],
assert: 
b,
set: {x:A| B[x]} ,
corec: corec(T.F[T]),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
uiff: uiff(P;Q),
subtype_rel: A r B,
prop: 
,
list: type List,
axiom: Ax,
data-stream: data-stream(P;L),
last: last(L),
listp: A List,
rev_implies: P Q,
all: x:A. B[x],
equal: s = t,
universe: Type,
uall: [x:A]. B[x],
dataflow: dataflow(A;B),
isect: 
x:A. B[x],
iff: P Q,
and: P 
Q,
product: x:A 
B[x],
pair: <a, b>,
implies: P Q,
member: t T,
lambda: 
x.A[x],
dataflow-equiv: d1 d2,
function: x:A 
B[x],
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
Try: Error :Try,
tl: tl(l),
hd: hd(l),
cons: [car / cdr],
append: as @ bs,
nil: [],
data_stream_nil: data_stream_nil{data_stream_nil_compseq_tag_def:o}(P),
so_lambda: 
x.t[x],
CollapseTHENA: Error :CollapseTHENA,
tactic: Error :tactic,
iterate-dataflow: P*(inputs),
nat: 
,
label: ...$L... t,
rev_uimplies: rev_uimplies(P;Q),
le_int: i z j,
eq_int: (i =
j),
eq_atom: x =a y,
set_blt: a <
b,
grp_blt: a < b,
apply: f a,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (xL.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$n(x;y),
qeq: qeq(r;s),
q_less: q_less(r;s),
q_le: q_le(r;s),
deq-member: deq-member(eq;x;L),
deq-disjoint: deq-disjoint(eq;as;bs),
deq-all-disjoint: deq-all-disjoint(eq;ass;bs),
eq_id: a = b,
eq_lnk: a = b,
bnot: b,
bimplies: p q,
band: p q,
bor: p 
q,
int: 
,
natural_number: $n,
lt_int: i <z j,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
primrec: primrec(n;b;c),
bool: 
,
MaAuto: Error :MaAuto,
dataflow-ap: df(a),
pi2: snd(t),
fpf-sub: f g,
deq: EqDecider(T),
ma-state: State(ds),
fpf-dom: x dom(f),
rcv: rcv(l,tg),
locl: locl(a),
Knd: Knd,
fpf-cap: f(x)?z,
bag: Error :bag,
map: map(f;as),
sq_type: SQType(T),
select: l[i],
subtract: n - m,
RepUR: Error :RepUR
Lemmas :
subtype_rel_wf,
subtype_rel_list,
last_append,
data-stream-cons,
dataflow-ap_wf,
pi2_wf,
ifthenelse_wf,
lt_int_wf,
assert_of_lt_int,
length_wf1,
length_nil,
length_cons,
non_neg_length,
length_append,
length_wf_nat,
data-stream-append,
append_wf,
iterate-dataflow_wf,
last_induction,
assert_wf,
false_wf,
not_wf,
pos_length2,
data-stream_wf,
last_wf,
dataflow-equiv_wf,
listp_wf,
dataflow_wf,
squash_wf,
null_wf3,
top_wf,
member_wf,
listp_properties,
null-data-stream,
true_wf
\mforall{}[A,B:Type]. \mforall{}[f,g:dataflow(A;B)].
(f \mequiv{} g \mLeftarrow{}{}\mRightarrow{} \mforall{}as:A List\msupplus{}. (last(data-stream(f;as)) = last(data-stream(g;as))))
Date html generated:
2011_08_10-AM-08_22_17
Last ObjectModification:
2011_04_27-PM-03_39_03
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