(** 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_unique (u : nat -> Rbar) (l : Rbar) : is_inf_seq u l -> Inf_seq u = l.