intros; cut (2 * r_vi * sin (rho_vi * (t / 2)) <= i t)%R;
[ intro; intros; unfold Rminus in |- *; rewrite Rplus_comm;
apply Rplus_le_reg_l with l; repeat rewrite <- Rplus_assoc;
rewrite Rplus_opp_r; rewrite Rplus_0_l; apply Rle_trans with (i t);
[ assumption | apply L_i ]
| unfold i in |- *; unfold Rsqr_intruder_distance in |- *;
apply (YCNGSTYS intr t H H0) ].
Qed.

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