(** 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_seq_opp (u : nat -> R) : LimSup_seq (fun n => - u n) = Rbar_opp (LimInf_seq u).