Definition hy (t : R) : R := (r_vi * cos (rho_vi * t))%R.

(* Specifications: *)
Lemma hy_derivable : derivable hy.
Lemma Dhy : forall t : R, derive_pt hy t (hy_derivable t) = (- vi intr * sin (rho_vi * t))%R.
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.
Lemma ypt_PI2 : forall t : R, (0 <= t)%R -> (rho_vi * t <= PI / 2)%R -> (l * sin (beta + thetat intr 0) + r_vi * (cos (rho_vi * t) - 1) <= yp t)%R /\ (yp t <= l * sin (beta + thetat intr 0) - r_vi * (cos (rho_vi * t) - 1))%R.
Lemma Dxp : forall t : R, derive_pt xp t (xp_derivable t) = (vi intr * cos (thetat intr t - thetat intr 0))%R.
Lemma Dx0_PI : forall t : R, (0 <= t)%R -> (rho_vi * t <= PI)%R -> (vi intr * cos (rho_vi * t) <= derive_pt xp t (xp_derivable t))%R.
Lemma xp0 : xp 0 = (- l * cos (thetat intr 0 + beta))%R.