(** 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_scal_l (a : R) (u : nat -> Rbar) : 0 <= a -> Sup_seq (fun n => Rbar_mult a (u n)) = Rbar_mult a (Sup_seq u).