(** * 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 continuity_pt_filterlim :
forall (f : R -> R) (x : R),
continuity_pt f x <->
filterlim f (locally x) (locally (f x)).