Proof with trivial.
intro; unfold hy in |- *; reg...
replace (vi intr:R) with (r_vi * rho_vi)%R.
ring.
unfold rho_vi, r_vi in |- *; unfold r in |- *.
field.
assert (H := rho_pos (vi intr)); red in |- *; intro; rewrite H0 in H;
elim (Rlt_irrefl _ H)...
Qed.

(* Specifications: *)
Lemma ypt :
forall t : R,
(0 <= t)%R ->
(rho_vi * t <= PI / 2)%R -> (hy t - hy 0 <= yp t - yp 0 <= hy 0 - hy t)%R.