intros; generalize (xpt t H H0); unfold hx in |- *; intro;
apply Rle_trans with (r_vi * sin (rho_vi * t))%R;
[ apply (r_sin_pos t H H0) | assumption ].
Qed.

Lemma xpt_PI :
forall t : R,
(0 <= t)%R ->
(rho_vi * t <= PI)%R ->
(r_vi * sin (rho_vi * t) - l * cos (beta + thetat intr 0) <= xp t)%R.