(** Notations *)

Definition Sup_seq (u : nat -> Rbar) := proj1_sig (ex_sup_seq u).Definition Inf_seq (u : nat -> Rbar) := proj1_sig (ex_inf_seq u).

Lemma Inf_eq_glb (u : nat -> Rbar) : Inf_seq u = Rbar_glb (fun x => exists n, x = u n).