intro; reg.
Qed.

(* Specifications: *)
(**********)
Lemma u_epsilon_le_vt :
forall (eps : posreal) (t : R), (0 <= t)%R -> (u eps t - eps <= vi * t)%R.
Lemma init_tr_derivable_y :
forall h : TypeSpeed, derivable (fun t : R => 0%R).
Lemma init_tr_cond_x :
forall (h : TypeSpeed) (t : R),
derive_pt (fun t : R => (h * t)%R) t (init_tr_derivable_x h t) =
(h * cos ((fun t : R => 0) t))%R.