intros f g x l fg df e ep; destruct (df e ep) as [d pd]; exists d; intros h;
rewrite <- !fg; apply pd.
Qed.
(* extensionally equal functions have the same derivative, locally. *)

Lemma derivable_pt_lim_locally_ext : forall f g x a b l,
a < x < b ->
(forall z, a < z < b -> f z = g z) ->
derivable_pt_lim f x l -> derivable_pt_lim g x l.