(** 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_minor_lt (u : nat -> Rbar) (M : R) : Rbar_lt M (Sup_seq u) <-> exists n, Rbar_lt M (u n).