{ 
Info,A:Type. B:{B:Type| valueall-type(B)} . X:EClass(A). Y:A 
EClass(B).
(Programmable(A;X)
(x:A. Programmable(B;Y[x]))
Programmable(B;X >x> Y[x])) }
{ Proof }
Definitions occuring in Statement :
programmable: Programmable(A;X),
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
so_apply: x[s],
all: x:A. B[x],
implies: P Q,
set: {x:A| B[x]} ,
function: x:A B[x],
universe: Type,
valueall-type: valueall-type(T)
Definitions :
pair: <a, b>,
rev_implies: P 
Q,
spread: spread def,
pi1: fst(t),
limited-type: LimitedType,
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),
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+,
cand: A c
B,
defined-class: defined-class(prg),
eclass-program-type: eclass-program-type(prg),
bool: 
,
eclass-program: eclass-program{i:l}(Info),
iff: P Q,
subtype: S 
T,
event_ordering: EO,
es-E: E,
event-ordering+: EO+(Info),
member: t 
T,
fpf-single: x : v,
fpf-join: f 
g,
strong-subtype: strong-subtype(A;B),
le: A 
B,
ge: i 
j ,
not: 
A,
less_than: a < b,
uimplies: b supposing a,
and: P Q,
uiff: uiff(P;Q),
subtype_rel: A r B,
isect: 
x:A. B[x],
uall: [x:A]. B[x],
Id: Id,
bag: bag(T),
dataflow: dataflow(A;B),
fpf: a:A fp-> B[a],
equal: s = t,
product: x:A 
B[x],
exists: 
x:A. B[x],
lambda: 
x.A[x],
so_lambda: 
x.t[x],
valueall-type: valueall-type(T),
so_lambda: x y.t[x; y],
implies: P Q,
prop: 
,
all: x:A. B[x],
bind-class: X >x> Y[x],
so_apply: x[s],
apply: f a,
function: x:A B[x],
eclass: EClass(A[eo; e]),
set: {x:A| B[x]} ,
programmable: Programmable(A;X),
universe: Type,
ext-eq: A 
B,
sqequal: s ~ t,
tag-by: zT,
or: P 
Q,
record: record(x.T[x]),
fset: FSet{T},
isect2: T1 T2,
stream: stream(A),
b-union: A 
B,
union: left + right,
deq: EqDecider(T),
ma-state: State(ds),
list: type List,
class-program: ClassProgram(T),
true: True,
uni_sat: a = !x:T. Q[x],
inv_funs: InvFuns(A;B;f;g),
inject: Inj(A;B;f),
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),
fpf-sub: f g,
classrel: v X(e),
squash: 
T,
sq_stable: SqStable(P),
df-program-type: df-program-type(dfp),
dataflow-program: DataflowProgram(A),
fpf-cap: f(x)?z,
suptype: suptype(S; T),
bind-comb-program: bind-comb-program(B;PX;PY),
Auto: Error :Auto,
CollapseTHEN: Error :CollapseTHEN,
tactic: Error :tactic
Lemmas :
true_wf,
iff_wf,
rev_implies_wf,
defined-by-bind-comb-program,
dataflow-program_wf,
bind-comb-program_wf,
sq_stable__all,
squash_wf,
sq_stable__subtype_rel,
ext-eq_inversion,
subtype_rel_weakening,
ext-eq_weakening,
es-interface-subtype_rel2,
defined-class_wf,
eclass_wf,
es-interface-top,
eclass-program-type_wf,
member_wf,
event-ordering+_wf,
event-ordering+_inc,
subtype_rel_self,
es-base-E_wf,
es-E_wf,
valueall-type_wf,
eclass-program_wf,
programmable_wf,
programmable-iff,
all_functionality_wrt_iff,
fpf_wf,
Id_wf,
dataflow_wf,
bag_wf,
subtype_rel_wf,
bind-class_wf
\mforall{}Info,A:Type. \mforall{}B:\{B:Type| valueall-type(B)\} . \mforall{}X:EClass(A). \mforall{}Y:A {}\mrightarrow{} EClass(B).
(Programmable(A;X) {}\mRightarrow{} (\mforall{}x:A. Programmable(B;Y[x])) {}\mRightarrow{} Programmable(B;X >x> Y[x]))
Date html generated:
2011_08_16-PM-06_32_43
Last ObjectModification:
2011_06_20-AM-01_54_14
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