{ 
[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:Id k:n bag(A k) bag(B)
NormalLProgrammable(B;F|Loc; Xs|)
supposing i:Id. ((F i (
i.{})) = {}))) }
{ Proof }
Definitions occuring in Statement :
normal-locally-programmable: NormalLProgrammable(A;X),
simple-loc-comb: F|Loc; Xs|,
eclass: EClass(A[eo; e]),
Id: Id,
int_seg: {i..j
},
nat: ,
uimplies: b supposing a,
uall: [x:A]. B[x],
all: 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],
natural_number: $n,
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
universe: Type,
prop: 
,
set: {x:A| B[x]} ,
squash: T,
implies: P Q,
false: False,
not: 
A,
le: A 
B,
int: 
,
nat: ,
function: x:A B[x],
all: x:A. B[x],
Id: Id,
true: True,
member: t 
T,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
subtype_rel: A 
r B,
uiff: uiff(P;Q),
and: P 
Q,
product: x:A 
B[x],
uimplies: b supposing a,
less_than: a < b,
ge: i 
j ,
strong-subtype: strong-subtype(A;B),
valueall-type: valueall-type(T),
atom: Atom$n,
sq_exists: 
x:{A| B[x]},
equal: s = t,
local-program-at: local-program-at{i:l}(Info;A;X;dfp;x),
int_seg: {i..j},
natural_number: $n,
apply: f a,
dataflow-program: DataflowProgram(A),
bool: 
,
bag: bag(T),
lambda: x.A[x],
empty-bag: {},
eclass: EClass(A[eo; e]),
es-loc: loc(e),
es-E: E,
event-ordering+: EO+(Info),
es-le-before: loc(e),
es-info: info(e),
map: map(f;as),
upto: upto(n),
parallel-df-program-case1: parallel-df-program-case1(B;F;dfps),
df-program-meaning: df-program-meaning(dfp),
data-stream: data-stream(P;L),
last: last(L),
simple-loc-comb: F|Loc; Xs|,
event_ordering: EO,
record+: record+,
dep-isect: Error :dep-isect,
assert: 
b,
ifthenelse: if b then t else f fi ,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
eq_atom: eq_atom$n(x;y),
eq_atom: x =a y,
record-select: r.x,
fpf: a:A fp-> B[a],
pair: <a, b>,
df-program-type: df-program-type(dfp),
limited-type: LimitedType,
subtype: S T
Lemmas :
bool_subtype_base,
subtype_base_sq,
non_null_iff_length,
es-le-before_wf2,
es-le_wf,
es-le-before-not-null,
assert_wf,
equal-nil-sq-nil,
pos-length,
es-base-E_wf,
pos_length2,
es-info_wf,
es-le-before_wf,
last-stream-parallel-df-program-case1-meaning,
df-program-meaning_wf,
data-stream_wf,
last_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,
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,
subtype_rel_function,
length_wf1,
subtype_rel_wf,
false_wf,
not_wf,
le_wf,
member_wf,
df-program-type_wf,
select_wf,
parallel-df-program-case1_wf,
map_wf,
upto_wf,
es-loc_wf,
sq_stable_from_decidable,
sq_stable__all,
simple-loc-comb_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,
dataflow-program_wf,
Id_wf,
int_seg_wf,
local-program-at_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:Id {}\mrightarrow{} k:\mBbbN{}n {}\mrightarrow{} bag(A k) {}\mrightarrow{} bag(B)
NormalLProgrammable(B;F|Loc; Xs|) supposing \mforall{}i:Id. ((F i (\mlambda{}i.\{\})) = \{\})))
Date html generated:
2011_08_16-PM-06_18_32
Last ObjectModification:
2011_06_29-PM-10_59_51
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