intro; rewrite (D_F t); rewrite <- Rsqr_mult;
cut
((rho (vi intr) / 2 * F t)%R = (vi intr * sin (rho (vi intr) * (t / 2)))%R).
intro H; rewrite H; repeat rewrite Rsqr_mult;
replace
(Rsqr (vi intr) * Rsqr (cos (rho (vi intr) * (t / 2))) +
Rsqr (vi intr) * Rsqr (sin (rho (vi intr) * (t / 2))))%R with
(Rsqr (vi intr) *
(Rsqr (sin (rho (vi intr) * (t / 2))) +
Rsqr (cos (rho (vi intr) * (t / 2)))))%R.
rewrite sin2_cos2; rewrite Rmult_1_r; reflexivity.
ring.
unfold F in |- *; unfold Rdiv in |- *; rewrite <- Rmult_assoc;
replace (rho (vi intr) * / 2 * (2 * (vi intr * / rho (vi intr))))%R with
(2 * / 2 * (rho (vi intr) * / rho (vi intr)) * vi intr)%R.
repeat rewrite <- Rinv_r_sym.
repeat rewrite Rmult_1_l; reflexivity.
generalize (rho_pos (vi intr)); intro; red in |- *; intro; rewrite H0 in H;
elim (Rlt_irrefl 0 H).
discrR.
ring.
Qed.
Definition G (t : R) : R := (Rs t - F t)%R.

(* Specifications: *)
Lemma G_derivable : derivable G.
unfold G in |- *; reg.