Qed.

(**********)
Lemma D_Rs_alphas2 :
forall t : R,
derive_pt (fun y : R => (Rs y * derive_pt alphas y (cond_D1 alphas y))%R) t
(fct_der5 t) =
(vi intr * cos (thetat t - alphas t) *
(derive_pt thetat t (thetat_derivable t) -
derive_pt alphas t (cond_D1 alphas t)))%R.