intros; case (Req_EM_var (div_tau intruder evader) 0); intro.
right; apply (R_equal_when_zero intruder evader (tmin intruder evader) t e).
apply Rsqr_incr_0.
repeat rewrite R_Rmin.
apply Rplus_le_compat_r; apply Rmult_le_compat_l.
apply Ax2_R_pos.
unfold Rminus in |- *; rewrite Rplus_opp_r; rewrite Rsqr_0; apply Rle_0_sqr.
assumption.
assumption.
apply RR_pos.
apply RR_pos.
Qed.

(* Specifications: *)
(**********)
Lemma derivative_eq_zero_min :
forall (intruder evader : State) (t1 t2 : R),
(RR intruder evader (t1 + tau intruder evader t1) <=
RR intruder evader (t1 + t2))%R.