{ 
[Info:
']. [B:{B:Type| valueall-type(B)} ].
[Ps:eclass-program{i:l}(Info) List].
[F:k:
||Ps|| 
bag(eclass-program-type(Ps[k])) bag(B) bag(B)]
(rec-comb-program(F;B;Ps) 
eclass-program{i:l}(Info))
supposing 0 < ||Ps|| }
{ Proof }
Definitions occuring in Statement :
rec-comb-program: rec-comb-program(F;B;Ps),
eclass-program-type: eclass-program-type(prg),
eclass-program: eclass-program{i:l}(Info),
select: l[i],
length: ||as||,
int_seg: {i..j
},
uimplies: b supposing a,
uall: [x:A]. B[x],
member: t T,
less_than: a < b,
set: {x:A| B[x]} ,
function: x:A B[x],
list: type List,
natural_number: $n,
universe: Type,
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
atom: Atom$n,
exists: 
x:A. B[x],
df-program-type: df-program-type(dfp),
top: Top,
listp: A List
,
combination: Combination(n;T),
dataflow-program: DataflowProgram(A),
so_lambda: 
x.t[x],
eclass: EClass(A[eo; e]),
fpf-single: x : v,
fpf-join: f 
g,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
uiff: uiff(P;Q),
subtype_rel: A 
r B,
l_member: (x l),
product: x:A 
B[x],
Id: Id,
fpf-domain: fpf-domain(f),
union-list2: union-list2(eq;ll),
feedback-df-program: feedback-df-program(B;F;buf;P;dfps),
map: map(f;as),
fpf-cap: f(x)?z,
null-df-program: null-df-program(B),
id-deq: IdDeq,
fpf: a:A fp-> B[a],
eclass-program-flows: eclass-program-flows(p),
lt_int: i <z j,
bag-size: bag-size(bs),
empty-bag: {},
lambda: x.A[x],
mk_fpf: mk_fpf(L;f),
pair: <a, b>,
and: P 
Q,
lelt: i 
j < k,
void: Void,
implies: P 
Q,
false: False,
not: 
A,
le: A B,
real: 
,
rationals: 
,
subtype: S T,
int: 
,
all: x:A. B[x],
length: ||as||,
natural_number: $n,
axiom: Ax,
rec-comb-program: rec-comb-program(F;B;Ps),
int_seg: {i..j},
select: l[i],
eclass-program-type: eclass-program-type(prg),
equal: s = t,
valueall-type: valueall-type(T),
eclass-program: eclass-program{i:l}(Info),
list: type List,
uimplies: b supposing a,
prop: 
,
less_than: a < b,
uall: [x:A]. B[x],
isect: 
x:A. B[x],
member: t T,
function: x:A B[x],
bag: bag(T),
universe: Type,
set: {x:A| B[x]} ,
D: Error :D,
CollapseTHEN: Error :CollapseTHEN,
Auto: Error :Auto,
Complete: Error :Complete,
Try: Error :Try,
RepeatFor: Error :RepeatFor,
Unfold: Error :Unfold,
apply: f a,
grp_car: |g|,
nil: [],
sqequal: s ~ t,
nat: ,
suptype: suptype(S; T),
unit: Unit,
assert: 
b,
tag-by: zT,
rev_implies: P 
Q,
or: P 
Q,
iff: P Q,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
ifthenelse: if b then t else f fi ,
spread: spread def,
pi1: fst(t),
event_ordering: EO,
stream: stream(A),
dataflow: dataflow(A;B),
b-union: A 
B,
union: left + right,
fpf-sub: f g,
deq: EqDecider(T),
ma-state: State(ds),
fpf-dom: x dom(f),
guard: {T},
true: True,
squash: 
T,
class-program: ClassProgram(T),
es-E-interface: E(X),
MaAuto: Error :MaAuto,
ext-eq: A 
B,
bool: 
,
classrel: v X(e),
sq_stable: SqStable(P),
BHyp: Error :BHyp
Lemmas :
feedback-df-program-type,
sq_stable__subtype_rel,
ext-eq_inversion,
subtype_rel_weakening,
ext-eq_weakening,
true_wf,
squash_wf,
int_seg_properties,
subtype_rel_bag,
pi1_wf_top,
unit_wf,
null-df-program_wf,
fpf-cap_wf,
feedback-df-program_wf,
le_wf,
not_wf,
false_wf,
length-map,
length_wf_nat,
nat_wf,
empty-bag_wf,
lt_int_wf,
bag-size_wf,
select-map,
Id_wf,
map_wf,
eclass-program_wf,
union-list2_wf,
member_wf,
valueall-type_wf,
length_wf1,
bag_wf,
select_wf,
eclass-program-type_wf,
int_seg_wf,
dataflow-program_wf,
fpf_wf,
mk_fpf_wf,
id-deq_wf,
fpf-domain_wf,
eclass-program-flows_wf,
df-program-type_wf,
l_member_wf,
top_wf,
subtype_rel_wf,
fpf-trivial-subtype-top
\mforall{}[Info:\mBbbU{}']. \mforall{}[B:\{B:Type| valueall-type(B)\} ]. \mforall{}[Ps:eclass-program\{i:l\}(Info) List].
\mforall{}[F:k:\mBbbN{}||Ps|| {}\mrightarrow{} bag(eclass-program-type(Ps[k])) {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(B)]
(rec-comb-program(F;B;Ps) \mmember{} eclass-program\{i:l\}(Info))
supposing 0 < ||Ps||
Date html generated:
2011_08_16-PM-06_25_14
Last ObjectModification:
2011_06_20-AM-01_52_17
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