(** 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_LimInf_seq_le (u : nat -> R) : Rbar_le (LimInf_seq u) (LimSup_seq u).