Proof with trivial.
intros; unfold RR, distance in |- *; unfold dx, dy in |- *;
repeat rewrite Rmult_0_l; repeat rewrite Rplus_0_r;
rewrite (Rsqr_neg (xt intruder - xt evader));
rewrite (Rsqr_neg (yt intruder - yt evader));
repeat rewrite Ropp_minus_distr...
Qed.
(*********************************************)
(************** MAIN THEOREM *****************)
(*********************************************)

Lemma step1 :
forall evader intruder : State,
alerting_distance evader intruder -> chktrack intruder evader 0.