(** 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_opp_inf (u : nat -> Rbar) : Sup_seq u = Rbar_opp (Inf_seq (fun n => Rbar_opp (u n))).