{ 
[A:
']. [dfp:DataflowProgram(A)]. [T:Type]. [G:bag(df-program-type(dfp))
bag(T)
bag(T)].
[P:bag(T) 
]. [buf:bag(T)].
better-feedback-dataflow(1;
k.[df-program-meaning(dfp)][k];
g,x.G[g 0;x];buf;s.P[s])
= df-program-meaning(feedback-df-prog1(T;G;P;buf;dfp))
supposing (buf:bag(T). ((G {} buf) = {})) 
valueall-type(T) }
{ Proof }
Definitions occuring in Statement :
feedback-df-prog1: feedback-df-prog1(B;G;P;buf;dfp),
df-program-meaning: df-program-meaning(dfp),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
better-feedback-dataflow: better-feedback-dataflow(n;ds;F;s;x.P[x]),
dataflow: dataflow(A;B),
select: l[i],
bool: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
all: x:A. B[x],
and: P Q,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
cons: [car / cdr],
nil: [],
natural_number: $n,
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
so_lambda: 
x y.t[x; y],
it: 
,
inr: inr x ,
evalall: evalall(t),
ifthenelse: if b then t else f fi ,
spread: spread def,
rec-dataflow: rec-dataflow(s0;s,m.next[s; m]),
limited-type: LimitedType,
prop: 
,
set: {x:A| B[x]} ,
so_lambda: x.t[x],
fpf: a:A fp-> B[a],
quotient: x,y:A//B[x; y],
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
axiom: Ax,
feedback-df-prog1: feedback-df-prog1(B;G;P;buf;dfp),
so_apply: x[s],
so_apply: x[s1;s2],
nil: [],
df-program-meaning: df-program-meaning(dfp),
cons: [car / cdr],
select: l[i],
natural_number: $n,
better-feedback-dataflow: better-feedback-dataflow(n;ds;F;s;x.P[x]),
dataflow: dataflow(A;B),
all: x:A. B[x],
valueall-type: valueall-type(T),
product: x:A 
B[x],
and: P Q,
uimplies: b supposing a,
equal: s = t,
dataflow-program: DataflowProgram(A),
universe: Type,
df-program-type: df-program-type(dfp),
bool: ,
function: x:A B[x],
member: t 
T,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
inl: inl x ,
empty-bag: {},
pair: <a, b>,
apply: f a,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
lambda: x.A[x],
unit: Unit,
union: left + right,
bag: bag(T),
parameter: parm{i},
atom: Atom$n,
int: 
,
atom: Atom,
rec: rec(x.A[x]),
tunion: 
x:A.B[x],
b-union: A B,
list: type List,
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
bag-member: bag-member(T;x;bs),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
fpf-sub: f g,
implies: P 
Q,
sq_stable: SqStable(P),
assert: 
b,
true: True,
squash: 
T,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
AssertBY: Error :AssertBY,
tactic: Error :tactic,
guard: {T},
l_member: (x l),
false: False,
subtype: S T,
pi2: snd(t),
void: Void,
top: Top,
cand: A c B,
pi1: fst(t),
isl: isl(x),
IdLnk: IdLnk,
Id: Id,
rationals: 
,
or: P 
Q,
append: as @ bs,
locl: locl(a),
Knd: Knd,
sq_type: SQType(T),
outl: outl(x),
sqequal: s ~ t,
ite: ite(b;x;y)
Lemmas :
ite_wf,
false_wf,
outl_wf,
subtype_base_sq,
union_subtype_base,
unit_subtype_base,
pi1_wf_top,
isl_wf,
pi1_wf,
assert_wf,
not_wf,
rec-dataflow-equal,
pi2_wf,
top_wf,
member_wf,
evalall-equal,
true_wf,
squash_wf,
rec-dataflow_wf,
ifthenelse_wf,
it_wf,
sq_stable__valueall-type,
product-valueall-type,
union-valueall-type,
bag-valueall-type,
equal-valueall-type,
bag_wf,
dataflow_wf,
unit_wf,
empty-bag_wf,
feedback-1-equiv,
dataflow-program_wf,
df-program-type_wf,
bool_wf,
valueall-type_wf
\mforall{}[A:\mBbbU{}']. \mforall{}[dfp:DataflowProgram(A)]. \mforall{}[T:Type]. \mforall{}[G:bag(df-program-type(dfp)) {}\mrightarrow{} bag(T) {}\mrightarrow{} bag(T)].
\mforall{}[P:bag(T) {}\mrightarrow{} \mBbbB{}]. \mforall{}[buf:bag(T)].
better-feedback-dataflow(1;\mlambda{}k.[df-program-meaning(dfp)][k];\mlambda{}g,x.G[g 0;x];buf;s.P[s])
= df-program-meaning(feedback-df-prog1(T;G;P;buf;dfp))
supposing (\mforall{}buf:bag(T). ((G \{\} buf) = \{\})) \mwedge{} valueall-type(T)
Date html generated:
2011_08_16-AM-09_43_19
Last ObjectModification:
2011_06_18-AM-08_33_38
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