intros; case (Req_EM_var (div_tau intruder evader) 0); intro;
[ right; apply R_equal_when_zero; assumption
| rewrite (tau_tmin intruder evader t n) in H;
apply asymptotic_increase_tmin;
[ apply Rplus_le_reg_l with (- t)%R; repeat rewrite <- Rplus_assoc;
rewrite Rplus_opp_l; rewrite Rplus_0_l; rewrite Rplus_comm;
assumption
| apply (Rplus_le_compat_l t t1 t2 H0) ] ].
Qed.

(**********)
Lemma tau_equal_when_zero :
forall (intruder evader : State) (t : R),
div_tau intruder evader = 0%R -> tau intruder evader t = 0%R.