(** 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 is_inf_seq_le (u v : nat -> Rbar) {l1 l2 : Rbar} : (forall n, Rbar_le (u n) (v n)) -> (is_inf_seq u l1) -> (is_inf_seq v l2) -> Rbar_le l1 l2.