Proof with trivial.
intros intr evad T hyp_intr hyp_evad; intros;
apply
Rle_trans with (RR (measure2state intr 0) (measure2state (tr evad) 0) T)...
rewrite <- (Rplus_0_l AlertTime); rewrite <- (Rplus_0_l T);
apply asymptotic_decrease_tau...
left...
unfold AlertTime in |- *; apply Rle_trans with MaxT...
apply (cond_2 T)...
unfold MaxT in |- *; left; prove_sup...
apply (alarm_NOT_Omega_T _ _ _ hyp_intr hyp_evad H H0 H1 H2)...
Qed.

(* Specifications: *)
Lemma chktrack_NOT_Omega_trkrate_eq_0 :
forall (intr : Trajectory) (evad : EvaderTrajectory) (T : TimeT),
h intr = V ->
h (tr evad) = V ->
(MinDistance T <= l intr evad T)%R ->
(l intr evad T <= MaxDistance T)%R ->
Omega (beta intr evad T + thetat intr 0) = false ->
conflict intr evad T = true ->
(0 < tau (measure2state intr 0) (measure2state (tr evad) 0) 0)%R ->
chktrack (measure2state intr 0) (measure2state (tr evad) 0) 0.