intros; case (Req_EM_var (div_tau intruder evader) 0); intro;
[ elim H; exact e | repeat rewrite tau_tmin; [ ring | exact H | exact H ] ].
Qed.

(**********)
Lemma tau_gt_time :
forall (intruder evader : State) (t1 t2 t : R),
(t < tau intruder evader t2)%R ->
(t1 <= t2)%R -> (t < tau intruder evader t1)%R.