{ 
[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))
(F:k:n bag(A k) bag(B)
NormalLProgrammable(B;simple-comb(F;Xs))
supposing ((F (
i.{})) = {})
(f:k:n bag(A k)
((
k:n. ((f k) = {})) ((F f) = {}))))) }
{ Proof }
Definitions occuring in Statement :
normal-locally-programmable: NormalLProgrammable(A;X),
simple-comb: simple-comb(F;Xs),
eclass: EClass(A[eo; e]),
int_seg: {i..j
},
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
all: x:A. B[x],
exists: x:A. B[x],
squash: T,
implies: P Q,
and: 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)
Definitions :
set: {x:A| B[x]} ,
universe: Type,
dataflow-program: DataflowProgram(A),
upto: upto(n),
apply: f a,
map: map(f;as),
select: l[i],
df-program-type: df-program-type(dfp),
bag: bag(T),
function: x:A B[x],
int_seg: {i..j},
equal: s = t,
product: x:A 
B[x],
exists: x:A. B[x],
implies: P Q,
all: x:A. B[x],
natural_number: $n,
length: ||as||,
lambda: x.A[x],
es-E: E,
event-ordering+: EO+(Info),
Id: Id,
member: t 
T,
local-program-at: local-program-at{i:l}(Info;A;X;dfp;x),
empty-bag: {},
sq_exists: x:{A| B[x]},
eclass: EClass(A[eo; e]),
nat: ,
es-loc: loc(e),
suptype: suptype(S; T),
subtype: S 
T,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
rationals: 
,
real: 
,
int: 
,
lelt: i 
j < k,
and: P Q,
less_than: a < b,
le: A B,
not: 
A,
false: False,
prop: 
,
subtype_rel: A r B,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i 
j ,
strong-subtype: strong-subtype(A;B),
squash: T,
valueall-type: valueall-type(T),
atom: Atom$n,
record+: record+,
dep-isect: Error :dep-isect,
assert: 
b,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
eq_atom: eq_atom$n(x;y),
eq_atom: x =a y,
record-select: r.x,
void: Void,
list: type List,
fpf: a:A fp-> B[a],
combination: Combination(n;T),
listp: A List
,
grp_car: |g|
Lemmas :
bool_subtype_base,
subtype_base_sq,
es-le-before-not-null,
pos-length,
equal-nil-sq-nil,
non_null_iff_length,
es-le-before_wf2,
es-le_wf,
es-base-E_wf,
assert_wf,
int-valueall-type,
set-valueall-type,
list-valueall-type,
Id-has-valueall,
bfalse_wf,
btrue_wf,
real-has-value,
int_inc_real,
rational-has-value,
rationals_wf,
ifthenelse_wf,
bool_wf,
tunion_wf,
int_nzero_wf,
b-union_wf,
int-rational,
pos_length2,
es-info_wf,
es-le-before_wf,
last_wf,
data-stream_wf,
df-program-meaning_wf,
last-stream-parallel-df-program-case2-meaning,
parallel-df-program-case2_wf,
subtype_rel-equal,
select-upto,
intensional-universe_wf,
unit_wf,
subtype_rel_bag,
select-map,
length_upto,
subtype_rel_sets,
subtype_rel_set,
top_wf,
length-map-sq,
nat_properties,
length-map,
int_seg_properties,
length_wf_nat,
true_wf,
subtype_rel_dep_function,
subtype_rel_self,
length_wf1,
subtype_rel_function,
subtype_rel_wf,
false_wf,
not_wf,
le_wf,
member_wf,
df-program-type_wf,
select_wf,
map_wf,
upto_wf,
es-loc_wf,
sq_stable_from_decidable,
sq_stable__all,
simple-comb_wf,
dataflow-program_wf,
empty-bag_wf,
bag_wf,
normal-locally-programmable_wf,
eclass_wf,
es-E_wf,
event-ordering+_inc,
event-ordering+_wf,
nat_wf,
valueall-type_wf,
squash_wf,
local-program-at_wf,
Id_wf,
int_seg_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{}F:k:\mBbbN{}n {}\mrightarrow{} bag(A k) {}\mrightarrow{} bag(B)
NormalLProgrammable(B;simple-comb(F;Xs))
supposing ((F (\mlambda{}i.\{\})) = \{\})
\mwedge{} (\mforall{}f:k:\mBbbN{}n {}\mrightarrow{} bag(A k). ((\mexists{}k:\mBbbN{}n. ((f k) = \{\})) {}\mRightarrow{} ((F f) = \{\})))))
Date html generated:
2011_08_16-PM-06_16_39
Last ObjectModification:
2011_06_29-PM-09_24_16
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