Proof with trivial.
intros; apply Rlt_le_trans with (2 * r_vi * sin (rho_vi * (t / 2)) - l)%R...
unfold MinDistance in H2; apply Rplus_lt_reg_l with (- ConflictRange + l)%R;
replace (- ConflictRange + l + ConflictRange)%R with l...
replace (- ConflictRange + l + (2 * r_vi * sin (rho_vi * (t / 2)) - l))%R
with (2 * r_vi * sin (rho_vi * (t / 2)) - ConflictRange)%R;
try ring...
ring...
apply (YCNGSTYS_evader t H H1)...
Qed.

(* Specifications: *)
Lemma no_conflict_Omega_t :
forall t : R,
(ConflictRange + vi intr < l)%R ->
(0 <= t)%R ->
(rho_vi * t <= PI - rho_vi)%R ->
Omega (beta + thetat intr 0) = true -> (ConflictRange < e t)%R.