(* To prove the following axioms, you need more sophisticated analysis *)
Axiom
  D_Rs_pos :
    forall t : R,
    (0 <= t)%R ->
    (t < 2 / rho (vi intr))%R -> (0 < derive_pt Rs t (Rs_derivable t))%R.Axiom
  D_abs_alpha :
    forall t : R,
    (0 <= t)%R ->
    (t < 2 / rho (vi intr))%R ->
    (- rho (vi intr) / 2 <= derive_pt alphas t (cond_D1 alphas t))%R /\
    (derive_pt alphas t (cond_D1 alphas t) <= rho (vi intr) / 2)%R.Definition F (t : R) : R :=
  (2 * (vi intr / rho (vi intr)) * sin (rho (vi intr) * (t / 2)))%R.

(* Specifications: *)
Lemma F_derivable : derivable F.
Lemma D_F : forall t : R, derive_pt F t (F_derivable t) = (vi intr * cos (rho (vi intr) * (t / 2)))%R.
Lemma D_F_Rsqr_v : forall t : R, (Rsqr (derive_pt F t (F_derivable t)) + Rsqr (rho (vi intr) / 2) * Rsqr (F t))%R = Rsqr (vi intr).