{ 
[A:
']. [dfps:DataflowProgram(A) List].
[B:Type]. [F,buf,P:Top].
(df-program-type(feedback-df-program(B;F;buf;P;dfps)) = B)
supposing 0 < ||dfps|| }
{ Proof }
Definitions occuring in Statement :
feedback-df-program: feedback-df-program(B;F;buf;P;dfps),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
length: ||as||,
uimplies: b supposing a,
uall: [x:A]. B[x],
top: Top,
less_than: a < b,
list: type List,
natural_number: $n,
universe: Type,
equal: s = t
Definitions :
lambda: 
x.A[x],
feedback-df-prog2: feedback-df-prog2(B;G;P;buf;dfp1;dfp2),
feedback-df-prog1: feedback-df-prog1(B;G;P;buf;dfp),
ifthenelse: if b then t else f fi ,
cons: [car / cdr],
tl: tl(l),
hd: hd(l),
bfalse: ff,
limited-type: LimitedType,
btrue: tt,
le_int: i 
z j,
eq_int: (i =
j),
eq_atom: x =a y,
null: null(as),
set_blt: a <
b,
grp_blt: a < b,
apply: f a,
infix_ap: x f y,
dcdr-to-bool: [d],
bl-all: (x
L.P[x])_b,
bl-exists: (
xL.P[x])_b,
b-exists: (i<n.P[i])_b,
eq_type: eq_type(T;T'),
eq_atom: eq_atom$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),
name_eq: name_eq(x;y),
eq_id: a = b,
eq_lnk: a = b,
bimplies: p 
q,
band: p 
q,
bor: p 
q,
lt_int: i <z j,
assert: 
b,
bnot: 
b,
unit: Unit,
union: left + right,
bool: 
,
pair: <a, b>,
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
product: x:A 
B[x],
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
false: False,
not: A,
void: Void,
set: {x:A| B[x]} ,
real: 
,
grp_car: |g|,
subtype: S T,
int: 
,
nat: 
,
le: A B,
guard: {T},
implies: P Q,
length: ||as||,
natural_number: $n,
function: x:A 
B[x],
all: x:A. B[x],
axiom: Ax,
feedback-df-program: feedback-df-program(B;F;buf;P;dfps),
df-program-type: df-program-type(dfp),
prop: 
,
member: t T,
so_lambda: 
x.t[x],
equal: s = t,
top: Top,
less_than: a < b,
list: type List,
dataflow-program: DataflowProgram(A),
universe: Type,
uimplies: b supposing a,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
minus: -n,
add: n + m,
subtract: n - m,
nil: [],
quotient: x,y:A//B[x; y],
valueall-type: valueall-type(T),
l_member: (x l),
bag-merge: bag-merge(as;bs),
bag: bag(T),
parallel-df-prog2: parallel-df-prog2(B;G;dfp1;dfp2),
atom: Atom$n,
atom: Atom,
rec: rec(x.A[x]),
tunion: 
x:A.B[x],
b-union: A B,
so_apply: x[s],
or: P Q
Lemmas :
non_neg_length,
union-valueall-type,
df-program-type-valueall-type,
false_wf,
bag_wf,
bag-merge_wf,
parallel-df-prog2_wf,
pos_length3,
valueall-type_wf,
pos_length2,
ge_wf,
nat_properties,
nat_ind_tp,
le_wf,
length_wf1,
dataflow-program_wf,
top_wf,
comp_nat_ind_tp,
nat_wf,
guard_wf,
uall_wf,
length_wf_nat,
member_wf,
feedback-df-program_wf,
df-program-type_wf,
bool_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
assert_wf,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
le_int_wf,
bnot_wf,
lt_int_wf,
tl_wf,
hd_wf,
feedback-df-prog1_wf,
ifthenelse_wf,
assert_of_eq_int,
not_wf,
assert_of_bnot,
not_functionality_wrt_uiff,
eq_int_wf,
feedback-df-prog2_wf
\mforall{}[A:\mBbbU{}']. \mforall{}[dfps:DataflowProgram(A) List].
\mforall{}[B:Type]. \mforall{}[F,buf,P:Top]. (df-program-type(feedback-df-program(B;F;buf;P;dfps)) = B)
supposing 0 < ||dfps||
Date html generated:
2011_08_16-AM-09_45_52
Last ObjectModification:
2011_06_18-AM-08_34_55
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