intros; unfold RR in |- *; apply sqrt_positivity; apply Rplus_le_le_0_compat;
apply Rle_0_sqr.
Qed.

(**********)
Lemma derivative_eq_zero_tmin :
forall (intruder evader : State) (t : R),
(RR intruder evader (tmin intruder evader) <= RR intruder evader t)%R.