(** 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 is_LimSup_LimInf_seq_le (u : nat -> R) (ls li : Rbar) : is_LimSup_seq u ls -> is_LimInf_seq u li -> Rbar_le li ls.