Definition hx (t : R) : R := (r_vi * sin (rho_vi * t))%R.

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