intros; apply Rmult_le_pos;
[ left; unfold r_vi in |- *; unfold r in |- *; unfold Rdiv in |- *;
apply Rmult_lt_0_compat;
[ apply (TypeSpeed_pos (vi intr))
| apply Rinv_0_lt_compat; apply (rho_pos (vi intr)) ]
| apply sin_ge_0; [ apply (rho_t_pos t H) | assumption ] ].
Qed.

(* Specifications: *)
Lemma xpt_pos :
forall t : R, (0 <= t)%R -> (rho_vi * t <= PI)%R -> (0 <= xp t - xp 0)%R.