{ 
[Info:{Info:Type| 
Info} ]
B:{B:Type| valueall-type(B)} . n:
.
[A:n 
Type]. [Xs:k:n EClass(A k)].
((k:n. NormalLProgrammable(A k;Xs k))
(init:Id bag(B). F:Id k:n bag(A k) bag(B) bag(B).
(((i:Id. b:bag(B). f:k:n bag(A k).
((
k:n. ((f k) = {})) ((F i f b) = {})))
(i:Id. b:bag(B). ((F i (
i.{}) b) = {})))
NormalLProgrammable(B;rec-comb(Xs;F;init))))) }
{ Proof }
Definitions occuring in Statement :
normal-locally-programmable: NormalLProgrammable(A;X),
rec-comb: rec-comb(X;f;init),
eclass: EClass(A[eo; e]),
Id: Id,
int_seg: {i..j
},
nat: ,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
squash: T,
implies: P Q,
or: P Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
natural_number: $n,
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Lemmas :
feedback-df-program-case1-meaning,
permutation_wf,
last_wf,
data-stream_wf,
df-program-meaning_wf,
iff_wf,
rev_implies_wf,
assert_wf,
null_wf3,
dataflow_wf,
feedback-df-program-case2-meaning,
rec-comb-locally-programmable,
es-interface-top,
es-le-before_wf,
es-info_wf,
sq_stable__subtype_rel,
es-base-E_wf,
pos_length2,
null-data-stream,
null-map,
es-le-before_wf2,
es-le_wf,
es-le-before-not-null,
subtype_base_sq,
bool_subtype_base,
int-rational,
b-union_wf,
int_nzero_wf,
tunion_wf,
bool_wf,
ifthenelse_wf,
rationals_wf,
rational-has-value,
int_inc_real,
real-has-value,
btrue_wf,
bfalse_wf,
Id-has-valueall,
list-valueall-type,
set-valueall-type,
int-valueall-type,
event-ordering+_inc,
es-E_wf,
event-ordering+_wf,
eclass_wf,
int_seg_wf,
normal-locally-programmable_wf,
bag_wf,
Id_wf,
empty-bag_wf,
squash_wf,
dataflow-program_wf,
local-program-at_wf,
rec-comb_wf,
nat_wf,
valueall-type_wf,
sq_stable__all,
sq_stable_from_decidable,
es-loc_wf,
upto_wf,
map_wf,
feedback-df-program-case2_wf,
select_wf,
df-program-type_wf,
member_wf,
le_wf,
not_wf,
false_wf,
subtype_rel_wf,
subtype_rel_function,
length_wf1,
subtype_rel_self,
subtype_rel_dep_function,
true_wf,
length_wf_nat,
int_seg_properties,
length-map,
nat_properties,
length-map-sq,
top_wf,
subtype_rel_set,
subtype_rel_sets,
length_upto,
select-map,
subtype_rel_bag,
unit_wf,
intensional-universe_wf,
select-upto,
subtype_rel-equal,
feedback-df-program-case1_wf
\mforall{}[Info:\{Info:Type| \mdownarrow{}Info\} ]
\mforall{}B:\{B:Type| valueall-type(B)\} . \mforall{}n:\mBbbN{}.
\mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[Xs:k:\mBbbN{}n {}\mrightarrow{} EClass(A k)].
((\mforall{}k:\mBbbN{}n. NormalLProgrammable(A k;Xs k))
{}\mRightarrow{} (\mforall{}init:Id {}\mrightarrow{} bag(B). \mforall{}F:Id {}\mrightarrow{} k:\mBbbN{}n {}\mrightarrow{} bag(A k) {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(B).
(((\mdownarrow{}\mforall{}i:Id. \mforall{}b:bag(B). \mforall{}f:k:\mBbbN{}n {}\mrightarrow{} bag(A k). ((\mexists{}k:\mBbbN{}n. ((f k) = \{\})) {}\mRightarrow{} ((F i f b) = \{\})))
\mvee{} (\mdownarrow{}\mforall{}i:Id. \mforall{}b:bag(B). ((F i (\mlambda{}i.\{\}) b) = \{\})))
{}\mRightarrow{} NormalLProgrammable(B;rec-comb(Xs;F;init)))))
Date html generated:
2011_08_16-PM-06_17_42
Last ObjectModification:
2011_07_25-PM-05_55_05
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