(** 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 Sup_seq_le (u v : nat -> Rbar) : (forall n, Rbar_le (u n) (v n)) -> Rbar_le (Sup_seq u) (Sup_seq v).