Proof with trivial.
intros; unfold alerting_distance in H; unfold chktrack in |- *;
case (Rle_dec (tau intruder evader 0) 0); intro...
unfold chkrange in |- *; split...
rewrite R_distance; rewrite distance_sym...
unfold AlertTime in |- *; left; prove_sup...
case (Rlt_dec AlertTime (0 + tau intruder evader 0)); intro...
rewrite Rplus_0_l in r; cut (0 <= AlertTime)%R...
intro;
assert
(H1 :=
asymptotic_decrease_tau intruder evader 0 0 AlertTime
(Rlt_le AlertTime (tau intruder evader 0) r) H0);
repeat rewrite Rplus_0_l in H1; rewrite R_distance in H1;
rewrite distance_sym in H1; apply Rle_trans with (distance evader intruder)...
unfold AlertTime in |- *; left; prove_sup...
assert (H0 := derivative_eq_zero_min intruder evader 0 0);
repeat rewrite Rplus_0_l in H0; rewrite R_distance in H0;
rewrite distance_sym in H0; apply Rle_trans with (distance evader intruder)...
Qed.

Lemma step2 :
forall (evader intruder : State) (x : nat),
(distance evader intruder <= AlertRange)%R ->
trkrate (bank intruder) <> 0%R ->
arc_loop intruder evader (Rsqr intruderSpeed / (g * tand (bank intruder)))
(trkrate (bank intruder)) x 0.