(** * Limits *)

Definition C_lim (f : C -> C) (z : C) : C :=
  (real (Lim (fun x => fst (f (x, snd z))) (fst z)),
  real (Lim (fun x => snd (f (x, snd z))) (fst z))).

Lemma is_C_lim_unique (f : C -> C) (z l : C) : filterlim f (locally' z) (locally l) -> C_lim f z = l.