{ 
[A,B:Type]. [f,g:dataflow(A;B)].
f = g supposing as:A List. (data-stream(f;as) = data-stream(g;as)) }
{ Proof }
Definitions occuring in Statement :
data-stream: data-stream(P;L),
dataflow: dataflow(A;B),
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
list: type List,
universe: Type,
equal: s = t
Definitions :
limited-type: LimitedType,
pair: <a, b>,
fpf: a:A fp-> B[a],
corec: corec(T.F[T]),
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
universe: Type,
uall: [x:A]. B[x],
uimplies: b supposing a,
prop: 
,
isect: 
x:A. B[x],
member: t 
T,
axiom: Ax,
product: x:A 
B[x],
function: x:A 
B[x],
lambda: 
x.A[x],
top: Top,
primrec: primrec(n;b;c),
equal: s = t,
data-stream: data-stream(P;L),
list: type List,
all: x:A. B[x],
implies: P 
Q,
dataflow: dataflow(A;B),
nat: 
,
CollapseTHEN: Error :CollapseTHEN,
void: Void,
subtract: n - m,
minus: -n,
false: False,
lt_int: i <z j,
le_int: i z j,
bfalse: ff,
btrue: tt,
eq_atom: x =a y,
null: null(as),
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,
bimplies: p q,
band: p q,
bor: p 
q,
eq_int: (i =
j),
assert: 
b,
bnot: b,
int: 
,
unit: Unit,
union: left + right,
ifthenelse: if b then t else f fi ,
bool: 
,
natural_number: $n,
set: {x:A| B[x]} ,
add: n + m,
Try: Error :Try,
Auto: Error :Auto,
so_lambda: 
x.t[x],
subtype: S T,
dataflow-ap: df(a),
pi1: fst(t),
tl: tl(l),
hd: hd(l),
cons: [car / cdr],
pi2: snd(t),
sqequal: s ~ t,
nil: [],
data_stream_nil: data_stream_nil{data_stream_nil_compseq_tag_def:o}(P),
IdLnk: IdLnk,
Id: Id,
rationals: 
,
so_apply: x[s],
or: P Q,
guard: {T},
Knd: Knd,
append: as @ bs,
l_member: (x l),
length: ||as||,
tactic: Error :tactic,
RepeatFor: Error :RepeatFor,
D: Error :D,
int_seg: {i..j
},
real: 
,
exists: x:A. B[x],
sq_type: SQType(T),
grp_car: |g|,
fpf-cap: f(x)?z,
SplitOn: Error :SplitOn,
ycomb: Y
Lemmas :
bool_subtype_base,
bool_cases,
subtype_base_sq,
isect_subtype_base,
int_seg_wf,
hd_wf,
le_wf,
false_wf,
pos_length3,
length_wf1,
tl_wf,
data-stream-cons,
pi1_wf_top,
pi1_wf,
dataflow-ap_wf,
member_wf,
subtype_rel_wf,
equal-top,
ge_wf,
nat_properties,
assert_wf,
assert_of_bnot,
uiff_transitivity,
not_wf,
eqff_to_assert,
bool_wf,
assert_of_eq_int,
eqtt_to_assert,
primrec_wf,
top_wf,
btrue_wf,
bnot_wf,
not_functionality_wrt_uiff,
nat_ind_tp,
nat_wf,
eq_int_wf,
data-stream_wf,
dataflow_wf
\mforall{}[A,B:Type]. \mforall{}[f,g:dataflow(A;B)].
f = g supposing \mforall{}as:A List. (data-stream(f;as) = data-stream(g;as))
Date html generated:
2011_08_10-AM-08_19_16
Last ObjectModification:
2011_04_28-AM-12_28_57
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