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_decrease_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 asymptotic_increase_tmin :
forall (intruder evader : State) (t1 t2 : R),
(tmin intruder evader <= t1)%R ->
(t1 <= t2)%R -> (RR intruder evader t1 <= RR intruder evader t2)%R.