(** 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).
(** Uniqueness *)

Lemma LimSup_InfSup_seq (u : nat -> R) :
LimSup_seq u = Inf_seq (fun m => Sup_seq (fun n => u (n + m)%nat)).