{ 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 >xY[x])) }

{ Proof }



Definitions occuring in Statement :  programmable: Programmable(A;X) bind-class: X >xY[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 >xY[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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