intros; case (Rle_dec 1 t); intro.
apply Rsqr_incrst_0.
unfold e in |- *; rewrite Rsqr_sqrt.
apply (no_conflict_scenario_1_Omega t r H1 H2).
apply Rsqr_evader_distance_pos.
left; unfold ConflictRange in |- *; prove_sup.
unfold e in |- *; apply sqrt_positivity; apply Rsqr_evader_distance_pos.
cut (t < 1)%R.
intro; apply (no_conflict_scenario_0_1s t H0 H3 H).
auto with real.
Qed.
(**********************************************************)
(************************** THEOREMS **********************)
(**********************************************************)

(* Specifications: *)
Theorem no_conflict_gt_max :
let MaxDistance := (vi intr * T + ConflictRange)%R in
(MaxDistance < l)%R -> conflict T = false.