intros; apply Rle_trans with (r_vi * sin (rho_vi * t))%R;
[ apply Rmult_le_pos;
[ unfold r_vi in |- *; unfold r in |- *; left; unfold Rdiv in |- *;
apply Rmult_lt_0_compat;
[ apply TypeSpeed_pos | apply Rinv_0_lt_compat; apply rho_pos ]
| apply sin_ge_0;
[ apply Rmult_le_pos;
[ unfold rho_vi in |- *; left; apply rho_pos | assumption ]
| assumption ] ]
| apply (xpt_Omega t H H0 H1) ].
Qed.

(* Specifications: *)
Lemma no_conflict_xp_1_Omega :
forall t : R,
(1 <= t)%R ->
(rho_vi * t <= PI - rho_vi)%R ->
Omega (beta + thetat intr 0) = true -> (ConflictRange < xp t)%R.