apply F_derivable.
apply Rs_derivable.
Qed.

(**********)
Lemma D_G_alphas :
forall t : R,
(derive_pt G t (G_derivable t) *
(derive_pt Rs t (Rs_derivable t) + derive_pt F t (F_derivable t)))%R =
(- Rsqr (derive_pt alphas t (cond_D1 alphas t)) * G t * (Rs t + F t) +
Rsqr (F t) *
(Rsqr (rho (vi intr) / 2) - Rsqr (derive_pt alphas t (cond_D1 alphas t))))%R.