intros; case (Req_EM_var (div_tau intruder evader) 0); intro;
[ right; apply R_equal_when_zero; assumption
| rewrite (tau_tmin intruder evader t1 n);
replace (t1 + (tmin intruder evader - t1))%R with (tmin intruder evader);
[ apply derivative_eq_zero_tmin | ring ] ].
Qed.

(**********)
Lemma asymptotic_decrease_tmin :
forall (intruder evader : State) (t1 t2 : R),
(t2 <= tmin intruder evader)%R ->
(t1 <= t2)%R -> (RR intruder evader t2 <= RR intruder evader t1)%R.