(** 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_ind_1 (u : nat -> R) (l : Rbar) : is_LimSup_seq u l <-> is_LimSup_seq (fun n => u (S n)) l.