{ 
[Info:{Info:
'| 
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)]
(simple-comb-program(F;B;Ps) 
eclass-program{i:l}(Info))
supposing 0 < ||Ps|| }
{ Proof }
Definitions occuring in Statement :
simple-comb-program: simple-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],
squash: T,
member: t T,
less_than: a < b,
set: {x:A| B[x]} ,
function: x:A B[x],
list: type List,
natural_number: $n,
universe: Type,
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
true: True,
grp_car: |g|,
nil: [],
sqequal: s ~ t,
nat: ,
suptype: suptype(S; T),
atom: Atom$n,
fpf-single: x : v,
fpf-join: f 
g,
exists: 
x:A. B[x],
null-df-program: null-df-program(B),
fpf-cap: f(x)?z,
parallel-df-program-case1: parallel-df-program-case1(B;F;dfps),
l_member: (x l),
df-program-type: df-program-type(dfp),
top: Top,
fpf-domain: fpf-domain(f),
eclass-program-flows: eclass-program-flows(p),
lambda: 
x.A[x],
listp: A List
,
combination: Combination(n;T),
map: map(f;as),
id-deq: IdDeq,
union-list2: union-list2(eq;ll),
mk_fpf: mk_fpf(L;f),
Id: Id,
dataflow-program: DataflowProgram(A),
so_lambda: 
x.t[x],
pair: <a, b>,
lelt: i 
j < k,
void: Void,
implies: P 
Q,
false: False,
real: 
,
rationals: 
,
subtype: S 
T,
int: 
,
natural_number: $n,
eclass: EClass(A[eo; e]),
fpf: a:A fp-> B[a],
strong-subtype: strong-subtype(A;B),
le: A B,
ge: i 
j ,
not: 
A,
product: x:A 
B[x],
and: P 
Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
all: x:A. B[x],
length: ||as||,
axiom: Ax,
simple-comb-program: simple-comb-program(F;B;Ps),
int_seg: {i..j},
select: l[i],
eclass-program-type: eclass-program-type(prg),
bag: bag(T),
function: x:A B[x],
squash: T,
equal: s = t,
valueall-type: valueall-type(T),
uall: [x:A]. B[x],
eclass-program: eclass-program{i:l}(Info),
set: {x:A| B[x]} ,
universe: Type,
list: type List,
uimplies: b supposing a,
less_than: a < b,
prop: 
,
isect: 
x:A. B[x],
member: t T,
ext-eq: A 
B,
class-program: ClassProgram(T),
es-E-interface: E(X),
bool: 
,
fpf-sub: f g,
classrel: v X(e),
sq_stable: SqStable(P),
tag-by: zT,
record+: record+,
record: record(x.T[x]),
fset: FSet{T},
event_ordering: EO,
tuple-type: tuple-type(L),
stream: stream(A),
dataflow: dataflow(A;B),
isect2: T1 T2,
b-union: A 
B,
rev_implies: P 
Q,
union: left + right,
or: P 
Q,
iff: P Q,
MaAuto: Error :MaAuto,
CollapseTHEN: Error :CollapseTHEN,
D: Error :D,
Auto: Error :Auto,
THENM: Error :THENM,
Repeat: Error :Repeat,
CollapseTHENA: Error :CollapseTHENA,
Try: Error :Try,
Complete: Error :Complete,
tactic: Error :tactic,
atom: Atom,
rec: rec(x.A[x]),
qeq: qeq(r;s),
bfalse: ff,
btrue: tt,
tunion: x:A.B[x],
int_nzero: 
,
quotient: x,y:A//B[x; y],
has-valueall: has-valueall(a),
base: Base,
has-value: has-value(a),
pi2: snd(t),
map-tuple: map-tuple(len;f;t),
evalall: evalall(t),
ap2-tuple: ap2-tuple(len;f;x;t),
it: 
,
inr: inr x ,
select-tuple: x.n,
isl: isl(x),
bnot: 
b,
bl-all: (xL.P[x])_b,
ifthenelse: if b then t else f fi ,
empty-bag: {},
apply: f a,
decide: case b of inl(x) => s[x] | inr(y) => t[y],
spreadn: spread4,
df-program-state: df-program-state(dfp),
inl: inl x ,
tuple: tuple(n;i.F[i]),
parallel-df-prog: parallel-df-prog,
pi1: fst(t),
callbyvalue: callbyvalue,
callbyvalueall: callbyvalueall,
df-program-statetype: df-program-statetype(dfp),
unit: Unit,
upto: upto(n),
RepUR: Error :RepUR
Lemmas :
upto_wf,
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,
subtype_rel_function,
subtype_rel_dep_function,
subtype_rel_bag,
select-map,
sq_stable__subtype_rel,
subtype_rel_weakening,
ext-eq_weakening,
dataflow-program_wf,
Id_wf,
fpf_wf,
eclass-program-flows_wf,
fpf-domain_wf,
eclass-program_wf,
map_wf,
id-deq_wf,
union-list2_wf,
mk_fpf_wf,
squash_wf,
valueall-type_wf,
length_wf1,
bag_wf,
select_wf,
eclass-program-type_wf,
int_seg_wf,
member_wf,
df-program-type_wf,
l_member_wf,
top_wf,
subtype_rel_wf,
fpf-trivial-subtype-top,
parallel-df-program-case1_wf,
fpf-cap_wf,
null-df-program_wf,
le_wf,
not_wf,
false_wf,
length-map,
length_wf_nat,
nat_wf
\mforall{}[Info:\{Info:\mBbbU{}'| \mdownarrow{}Info\} ]. \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)]
(simple-comb-program(F;B;Ps) \mmember{} eclass-program\{i:l\}(Info))
supposing 0 < ||Ps||
Date html generated:
2011_08_16-PM-06_22_04
Last ObjectModification:
2011_06_20-AM-01_51_52
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