(** Functions *)

Definition LimSup_seq (u : nat -> R) :=
  proj1_sig (ex_LimSup_seq u).Definition LimInf_seq (u : nat -> R) :=
  proj1_sig (ex_LimInf_seq u).

Lemma LimSup_le (u v : nat -> R) : eventually (fun n => u n <= v n) -> Rbar_le (LimSup_seq u) (LimSup_seq v).