(** 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_seq_ext (u v : nat -> Rbar) : (forall n, (u n) = (v n)) -> Inf_seq u = Inf_seq v.