Proof with trivial.
intros; apply Rlt_le_trans with (l - vi intr * t)%R...
unfold MaxDistance in H0; rewrite Rplus_comm in H0;
generalize
(Rplus_lt_compat_r (- (vi intr * t)) (ConflictRange + vi intr * t) l H0);
repeat rewrite Rplus_assoc; rewrite Rplus_opp_r; rewrite Rplus_0_r...
apply (YCNGFTYS_evader t H)...
Qed.

(* Specifications: *)
Lemma no_conflict_lt_min_t :
forall t : R,
let MinDistance := (2 * r_vi * sin (rho_vi * (t / 2)) - ConflictRange)%R in
(0 <= t)%R ->
(0 <= rho_vi * t)%R ->
(rho_vi * t < 2)%R -> (l < MinDistance)%R -> (ConflictRange < e t)%R.