intros; unfold RR in |- *; unfold div_tau in H;
generalize
(Rplus_eq_R0 (Rsqr (dxdt intruder)) (Rsqr (dydt intruder))
(Rle_0_sqr (dxdt intruder)) (Rle_0_sqr (dydt intruder)) H);
intro; elim H0; intros; generalize (Rsqr_eq_0 (dxdt intruder) H1);
intro; generalize (Rsqr_eq_0 (dydt intruder) H2);
intro; rewrite <- (dx_dxdt intruder evader t1);
rewrite <- (dx_dxdt intruder evader t2);
rewrite <- (dy_dydt intruder evader t1);
rewrite <- (dy_dydt intruder evader t2); rewrite H3;
rewrite H4; repeat rewrite Rmult_0_r; repeat rewrite Rplus_0_r;
reflexivity.
Qed.

(**********)
Lemma RR_pos :
forall (intruder evader : State) (t : R), (0 <= RR intruder evader t)%R.