intros.
case (Req_EM_var (div_tau intruder evader) 0); intro.
rewrite (tau_equal_when_zero intruder evader t1 e).
rewrite (tau_equal_when_zero intruder evader t2 e) in H.
assumption.
cut (t1 = (t2 + (t1 - t2))%R).
intro.
rewrite H1.
rewrite (tau_is_uniform intruder evader t2 (t1 - t2) n).
unfold Rminus in |- *.
cut (0 <= - (t1 - t2))%R.
intro.
generalize
(Rplus_lt_le_compat t (tau intruder evader t2) 0 (- (t1 - t2)) H H2).
rewrite Rplus_0_r.
intro; assumption.
rewrite <- Ropp_0.
apply Ropp_ge_le_contravar.
apply Rle_ge.
apply Rplus_le_reg_l with t2.
rewrite <- H1; rewrite Rplus_0_r; assumption.
ring.
Qed.

Lemma tau_ge_time :
forall (intruder evader : State) (t1 t2 t : R),
(t <= tau intruder evader t2)%R ->
(t1 <= t2)%R -> (t <= tau intruder evader t1)%R.