(** * 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))).

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