{ 
[A:{A:
'| 
A} ]. [dfps:DataflowProgram(A) List]. [B:{B:Type|
valueall-type(B)} ].
[F:k:
||dfps|| 
bag(df-program-type(dfps[k])) bag(B) bag(B)].
[init:bag(B)].
better-feedback-dataflow(||dfps||;
k.map(dfp.df-program-meaning(dfp);dfps)[k];F;init;b.
null(b))
= df-program-meaning(feedback-df-program-case2(B;F;dfps;init))
supposing b:bag(B). f:k:||dfps|| bag(df-program-type(dfps[k])).
((
k:||dfps||. ((f k) = {})) 
((F f b) = {})) }
{ Proof }
Definitions occuring in Statement :
feedback-df-program-case2: feedback-df-program-case2(B;F;dfps;init),
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],
map: map(f;as),
length: ||as||,
null: null(as),
bnot: b,
int_seg: {i..j
},
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
squash: T,
implies: P Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
list: type List,
natural_number: $n,
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Lemmas :
tuple_wf,
select-tuple-tuple,
cons_member,
assert-bl-exists,
sq_stable__all,
decidable__l_all-better-extract,
decidable__assert,
true_wf,
assert_of_bnot,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
l_all_wf2,
sq_stable__and,
decidable__lt,
sq_stable__equal,
intensional-universe_wf,
intensional-universe_wf2,
df-program-type_wf,
select_wf,
dataflow-program_wf,
bag_wf,
length_wf1,
int_seg_wf,
valueall-type_wf,
squash_wf,
uall_wf,
dataflow_wf,
feedback-prog-meaning,
empty-bag_wf,
real-has-value,
int_inc_real,
rational-has-value,
upto_wf,
rationals_wf,
member_wf,
int_nzero_wf,
b-union_wf,
bool_wf,
ifthenelse_wf,
tunion_wf,
subtype_rel_wf,
int-rational,
btrue_wf,
bfalse_wf,
Id-has-valueall,
Id_wf,
list-valueall-type,
le_wf,
set-valueall-type,
int-valueall-type,
iff_wf,
rev_implies_wf,
better-feedback-dataflow_wf,
length_wf_nat,
top_wf,
map_wf,
df-program-meaning_wf,
bnot_wf,
null_wf3,
map_length,
non_neg_length,
nat_wf,
ge_wf,
not_wf,
false_wf,
permutation_wf,
int_seg_properties,
select-map,
null_wf,
bag-subtype-list,
tuple-type_wf,
select-tuple_wf,
length-map,
unit_wf,
bl-exists_wf,
l_member_wf,
isl_wf,
feedback-df-halt_wf,
assert_wf,
l_all_wf,
strict-bag-function_wf,
sq_stable_from_decidable
\mforall{}[A:\{A:\mBbbU{}'| \mdownarrow{}A\} ]. \mforall{}[dfps:DataflowProgram(A) List]. \mforall{}[B:\{B:Type| valueall-type(B)\} ].
\mforall{}[F:k:\mBbbN{}||dfps|| {}\mrightarrow{} bag(df-program-type(dfps[k])) {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(B)]. \mforall{}[init:bag(B)].
better-feedback-dataflow(||dfps||;\mlambda{}k.map(\mlambda{}dfp.df-program-meaning(dfp);dfps)[k];F;init;b.\mneg{}\msubb{}null(b))
= df-program-meaning(feedback-df-program-case2(B;F;dfps;init))
supposing \mforall{}b:bag(B). \mforall{}f:k:\mBbbN{}||dfps|| {}\mrightarrow{} bag(df-program-type(dfps[k])).
((\mexists{}k:\mBbbN{}||dfps||. ((f k) = \{\})) {}\mRightarrow{} ((F f b) = \{\}))
Date html generated:
2011_08_16-AM-09_41_49
Last ObjectModification:
2011_06_24-PM-08_56_35
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