intros; unfold tau in |- *; case (Req_EM_var (div_tau intruder evader) 0);
intro; [ reflexivity | elim n; exact H ].
Qed.

Lemma asymptotic_tau_gt :
forall (intruder evader : State) (t dt : R),
(0 <= dt)%R ->
(RR intruder evader (t + dt) < RR intruder evader t)%R ->
(0 < tau intruder evader t)%R.