intros; case (Rtotal_order 0 (tau intruder evader t)); intro;
[ assumption
| cut (tau intruder evader t <= 0)%R;
[ intro; elim H1; intro;
generalize (asymptotic_increase_tau intruder evader t 0 dt H2 H);
rewrite Rplus_0_r; intro;
elim
(Rlt_irrefl (RR intruder evader t)
(Rle_lt_trans (RR intruder evader t) (RR intruder evader (t + dt))
(RR intruder evader t) H4 H0))
| elim H1; intro;
[ right; symmetry  in |- *; assumption | left; assumption ] ] ].
Qed.

(**********)
Lemma tau_is_uniform :
forall (intruder evader : State) (t1 t2 : R),
div_tau intruder evader <> 0%R ->
tau intruder evader (t1 + t2) = (tau intruder evader t1 - t2)%R.