(** * 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 filterlim_Rbar_loc_seq :
forall x, filterlim (Rbar_loc_seq x) eventually (Rbar_locally' x).