Proof with trivial.
intros; apply Rlt_le_trans with (l - vi intr * t)%R...
apply Rplus_lt_reg_l with (v (vi intr));
rewrite <- (Rplus_comm ConflictRange); apply Rlt_trans with l...
apply Rplus_lt_reg_l with (- l)%R; rewrite Rplus_opp_l;
replace (- l + (vi intr + (l - vi intr * t)))%R with (vi intr * (1 - t))%R...
apply Rmult_lt_0_compat...
apply TypeSpeed_pos...
generalize (Rplus_lt_compat_r (- t) t 1 H0); rewrite Rplus_opp_r...
unfold Rminus in |- *; rewrite Rmult_plus_distr_l; ring...
apply (YCNGFTYS_evader t H)...
Qed.

(* Specifications: *)
Lemma no_conflict_gt_max_t :
forall t : R,
let MaxDistance := (vi intr * t + ConflictRange)%R in
(0 <= t)%R -> (MaxDistance < l)%R -> (ConflictRange < e t)%R.