{ 
Info:Type. B:{B:Type| valueall-type(B)} . n:
. A:n 
Type.
Xs:k:n EClass(A k).
((k:n. Programmable(A k;Xs k))
(F:Id k:n bag(A k) bag(B)
Programmable(B;F|Loc; Xs|) supposing x:Id. ((F x (
k.{})) = {}))) }
{ Proof }
Definitions occuring in Statement :
programmable: Programmable(A;X),
simple-loc-comb: F|Loc; Xs|,
eclass: EClass(A[eo; e]),
Id: Id,
int_seg: {i..j
},
nat: ,
uimplies: b supposing a,
all: x:A. B[x],
implies: P Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: x.A[x],
function: x:A B[x],
natural_number: $n,
universe: Type,
equal: s = t,
empty-bag: {},
bag: bag(T),
valueall-type: valueall-type(T)
Definitions :
union: left + right,
or: P 
Q,
nat_plus: 
,
l_contains: A 
B,
cmp-le: cmp-le(cmp;x;y),
inject: Inj(A;B;f),
reducible: reducible(a),
prime: prime(a),
squash: 
T,
l_exists: (
x
L. P[x]),
l_all: (xL.P[x]),
fun-connected: y is f*(x),
rationals: 
,
qle: r 
s,
qless: r < s,
q-rel: q-rel(r;x),
sq_exists: x:{A| B[x]},
atom: Atom$n,
i-finite: i-finite(I),
i-closed: i-closed(I),
p-outcome: Outcome,
dstype: dstype(TypeNames; d; a),
fset-member: a s,
f-subset: xs ys,
fset: FSet{T},
fset-closed: (s closed under fs),
IdLnk: IdLnk,
Knd: Knd,
MaName: MaName,
l_disjoint: l_disjoint(T;l1;l2),
consensus-state3: consensus-state3(T),
cs-not-completed: in state s, a has not completed inning i,
cs-archived: by state s, a archived v in inning i,
cs-passed: by state s, a passed inning i without archiving a value,
cs-inning-committed: in state s, inning i has committed v,
cs-inning-committable: in state s, inning i could commit v ,
cs-archive-blocked: in state s, ws' blocks ws from archiving v in inning i,
cs-precondition: state s may consider v in inning i,
consensus-rcv: consensus-rcv(V;A),
infix_ap: x f y,
es-causl: (e < e'),
es-locl: (e <loc e'),
es-le: e loc e' ,
es-causle: e c e',
existse-before: e<e'.P[e],
existse-le: ee'.P[e],
alle-lt: e<e'.P[e],
alle-le: ee'.P[e],
alle-between1: e[e1,e2).P[e],
existse-between1: e[e1,e2).P[e],
alle-between2: e[e1,e2].P[e],
existse-between2: e[e1,e2].P[e],
existse-between3: e(e1,e2].P[e],
es-fset-loc: i locs(s),
es-r-immediate-pred: es-r-immediate-pred(es;R;e';e),
same-thread: same-thread(es;p;e;e'),
collect-event: collect-event(es;X;n;v.num[v];L.P[L];e),
cut-order: a (X;f) b,
path-goes-thru: x-f*-y thru i,
decidable: Dec(P),
void: Void,
sqequal: s ~ t,
rev_implies: P 
Q,
spread: spread def,
pi1: fst(t),
decide: case b of inl(x) => s[x] | inr(y) => t[y],
assert: 
b,
es-E-interface: E(X),
guard: {T},
sq_type: SQType(T),
lelt: i j < k,
eq_atom: eq_atom$n(x;y),
atom: Atom,
top: Top,
es-base-E: es-base-E(es),
token: "$token",
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
record-select: r.x,
dep-isect: Error :dep-isect,
record+: record+,
defined-class: defined-class(prg),
eclass-program-type: eclass-program-type(prg),
cand: A c
B,
pair: <a, b>,
bool: 
,
eclass-program: eclass-program{i:l}(Info),
iff: P Q,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
real: 
,
grp_car: |g|,
subtype: S T,
natural_number: $n,
limited-type: LimitedType,
fpf-single: x : v,
fpf-join: f 
g,
strong-subtype: strong-subtype(A;B),
ge: i 
j ,
less_than: a < b,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
uall: [x:A]. B[x],
dataflow: dataflow(A;B),
so_lambda: 
x.t[x],
false: False,
not: 
A,
le: A B,
simple-loc-comb: F|Loc; Xs|,
axiom: Ax,
empty-bag: {},
lambda: x.A[x],
member: t T,
list: type List,
fpf: a:A fp-> B[a],
product: x:A 
B[x],
exists: x:A. B[x],
valueall-type: valueall-type(T),
nat: ,
eclass: EClass(A[eo; e]),
so_lambda: x y.t[x; y],
implies: P Q,
programmable: Programmable(A;X),
prop: 
,
all: x:A. B[x],
set: {x:A| B[x]} ,
universe: Type,
function: x:A B[x],
bag: bag(T),
apply: f a,
int_seg: {i..j},
Id: Id,
uimplies: b supposing a,
isect: 
x:A. B[x],
upto: upto(n),
map: map(f;as),
length: ||as||,
int: 
,
equal: s = t,
dataflow-program: DataflowProgram(A),
df-program-type: df-program-type(dfp),
fpf-empty: 
,
bfalse: ff,
null: null(as),
es-loc: loc(e),
listp: A List,
combination: Combination(n;T),
compose: f o g,
es-le-before: loc(e),
es-info: info(e),
last: last(L),
data-stream: data-stream(P;L),
fpf_ap_pair: fpf_ap_pair{fpf_ap_pair_compseq_tag_def:o}(x; eq; f; d),
dataflow-set-class: dataflow-set-class(x.P[x]),
dataflow-history-val: dataflow-history-val(es;e;x.P[x]),
df-program-meaning: df-program-meaning(dfp),
null-df-program: null-df-program(B),
select: l[i],
base: Base,
rcv: rcv(l,tg),
locl: locl(a),
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
eqfun_p: IsEqFun(T;eq),
refl: Refl(T;x,y.E[x; y]),
urefl: UniformlyRefl(T;x,y.E[x; y]),
sym: Sym(T;x,y.E[x; y]),
usym: UniformlySym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
anti_sym: AntiSym(T;x,y.R[x; y]),
uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
uconnex: uconnex(T; x,y.R[x; y]),
coprime: CoPrime(a,b),
ident: Ident(T;op;id),
assoc: Assoc(T;op),
comm: Comm(T;op),
inverse: Inverse(T;op;id;inv),
bilinear: BiLinear(T;pl;tm),
bilinear_p: IsBilinear(A;B;C;+a;+b;+c;f),
action_p: IsAction(A;x;e;S;f),
dist_1op_2op_lr: Dist1op2opLR(A;1op;2op),
fun_thru_1op: fun_thru_1op(A;B;opa;opb;f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
cancel: Cancel(T;S;op),
monot: monot(T;x,y.R[x; y];f),
monoid_p: IsMonoid(T;op;id),
group_p: IsGroup(T;op;id;inv),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_leq: a b,
integ_dom_p: IsIntegDom(r),
prime_ideal_p: IsPrimeIdeal(R;P),
no_repeats: no_repeats(T;l),
value-type: value-type(T),
is_list_splitting: is_list_splitting(T;L;LL;L2;f),
is_accum_splitting: is_accum_splitting(T;A;L;LL;L2;f;g;x),
bag-member: bag-member(T;x;bs),
req: x = y,
rnonneg: rnonneg(r),
rleq: x y,
i-member: r I,
partitions: partitions(I;p),
modulus-of-ccontinuity: modulus-of-ccontinuity(omega;I;f),
tag-by: zT,
record: record(x.T[x]),
isect2: T1 T2,
stream: stream(A),
b-union: A 
B,
deq: EqDecider(T),
ma-state: State(ds),
fpf-dom: x dom(f),
class-program: ClassProgram(T),
fpf-sub: f g,
classrel: v X(e),
sq_stable: SqStable(P),
true: True,
fpf-cap: f(x)?z,
suptype: suptype(S; T),
simple-loc-comb-program: simple-loc-comb-program(F;B;Ps)
Lemmas :
select_wf,
simple-loc-comb-program_wf,
subtype_rel_function,
int_seg_properties,
sq_stable__subtype_rel,
subtype_rel_dep_function,
true_wf,
squash_wf,
subtype_rel_bag,
subtype_rel-equal,
sq_stable__and,
sq_stable__equal,
iff_wf,
rev_implies_wf,
defined-by-simple-loc-comb-program,
base_wf,
select-map,
le_wf,
length_wf1,
select_upto,
df-program-meaning_wf_null,
dataflow-history-val_wf,
es-info_wf,
es-le-before_wf,
map_wf,
data-stream-null-df-program,
map-map,
es-loc_wf,
es-le-before_wf2,
es-le_wf,
top_wf,
last-map,
es-le-before-not-null,
assert_wf,
not_wf,
false_wf,
bool_wf,
bool_subtype_base,
bfalse_wf,
length_wf_nat,
df-program-type_wf,
dataflow-program_wf,
fpf-empty_wf,
eclass_wf,
int_seg_wf,
nat_properties,
programmable_wf,
programmable-iff,
all_functionality_wrt_iff,
eclass-program_wf,
valueall-type_wf,
nat_wf,
event-ordering+_wf,
event-ordering+_inc,
es-E_wf,
bag_wf,
Id_wf,
empty-bag_wf,
fpf_wf,
dataflow_wf,
simple-loc-comb_wf,
eclass-program-type_wf,
es-base-E_wf,
subtype_rel_self,
defined-class_wf,
member_wf,
es-interface-top,
es-interface-subtype_rel2,
subtype_rel_wf,
upto_wf,
length-map,
length_upto,
decidable__equal_int,
subtype_base_sq,
int_subtype_base
\mforall{}Info:Type. \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. Programmable(A k;Xs k))
{}\mRightarrow{} (\mforall{}F:Id {}\mrightarrow{} k:\mBbbN{}n {}\mrightarrow{} bag(A k) {}\mrightarrow{} bag(B)
Programmable(B;F|Loc; Xs|) supposing \mforall{}x:Id. ((F x (\mlambda{}k.\{\})) = \{\})))
Date html generated:
2011_08_16-PM-06_29_50
Last ObjectModification:
2011_06_03-AM-11_43_31
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