intro; set (alpha_p := d2 alphas);
set (f := fun x : R => derive_pt alpha_p x (cond_D1 alphas x)).
change (derivable_pt (fun y : R => (Rs y * f y)%R) t) in |- *.
reg.
apply (cond_D2 alphas).
apply Rs_derivable.
Qed.

(* Specifications: *)
(**********)
Lemma D_Rs_alphas1 :
forall t : R,
derive_pt (fun y : R => (Rs y * derive_pt alphas y (cond_D1 alphas y))%R) t
(fct_der5 t) =
(derive_pt Rs t (Rs_derivable t) * derive_pt alphas t (cond_D1 alphas t) +
Rs t * derive_pt (derive alphas (cond_D1 alphas)) t (cond_D2 alphas t))%R.