(**)
intros. red. intro. replace 0%R with(0*c)%R. 2:ring. apply Rmult_ge_compat_r.
apply Rle_ge. intuition. auto. Qed.

(* Specifications: *)
Lemma simple_P13:
(forall(U:Type)(F:Ensemble(Ensemble U))(F':sigalg_0 _ F)(F'':sigalg_1 _ F)(F'''
:sigalg_2 _ F)(n:nat)(v:nat->R)(w:nat->Ensemble U)(S0:simple_0 _ n v w)(S1:
simple_1 _ n v w)(S2:simple_2 _ n v w)(S3:simple_3 _ n v w)(M:msurable _ _ F'
F'' F''' (fun x:U=>v(proj1_sig(simple_P0 _ n v w S0 S1 S2 S3 x)
))),
forall c:R,forall c':0<c,msurable _ _ F' F'' F''' (fun x:U=>(fun i:nat=>v i*c)(
proj1_sig(simple_P0 _ n (fun i:nat=>v i*c) w (simple_P9 _ n v w S0 S1 S2 S3 c
c')(simple_P10 _ n v w S0 S1 S2 S3 c c')(simple_P11 _ n v w S0 S1 S2 S3 c c')(
simple_P12 _ n v w S0 S1 S2 S3 c c') x))))%R.