(** *** Extensionality *)

(* Specifications: *)
Lemma continuity_pt_ext_loc :
forall f g x,
locally x (fun x => f x = g x) ->
continuity_pt f x -> continuity_pt g x.
Lemma continuity_pt_ext :
forall f g x,
(forall x, f x = g x) ->
continuity_pt f x -> continuity_pt g x.
Lemma continuity_2d_pt_ext_loc :
forall f g x y,
locally_2d (fun u v => f u v = g u v) x y ->
continuity_2d_pt f x y -> continuity_2d_pt g x y.
Lemma continuity_2d_pt_ext :
forall f g x y,
(forall x y, f x y = g x y) ->
continuity_2d_pt f x y -> continuity_2d_pt g x y.