(** 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_seq_scal_pos (a : R) (u : nat -> R) (l : Rbar) : (0 < a) -> is_LimSup_seq u l -> is_LimSup_seq (fun n => a * u n) (Rbar_mult a l).