(** * Some limits on real functions *)
Definition Rbar_loc_seq (x : Rbar) (n : nat) := match x with
| Finite x => x + / (INR n + 1)
| p_infty => INR n
| m_infty => - INR n
end.

Lemma locally_pt_comp (P : R -> Prop) (f : R -> R) (x : R) :
locally (f x) P -> continuity_pt f x ->
locally x (fun x => P (f x)).