intros; generalize (derive_increasing_interv 0 t Rs Rs_derivable H H0);
intros; cut (0 <= 0 <= t)%R;
[ cut (0 <= t <= t)%R;
[ intros; rewrite <- Rs_0; apply (H1 0%R t H3 H2 H)
| split; [ left; assumption | right; reflexivity ] ]
| split; [ right; reflexivity | left; assumption ] ].
Qed.
(* 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.

Lemma F_derivable : derivable F.
unfold F in |- *; reg.