(** *** Additional limits *)

Lemma ex_lim_seq_adj (u v : nat -> R) :
(forall n, u n <= u (S n)) -> (forall n, v (S n) <= v n)
-> is_lim_seq (fun n => v n - u n) 0
-> ex_finite_lim_seq u /\ ex_finite_lim_seq v /\ Lim_seq u = Lim_seq v.