(** *** Additive operators *)

(* Specifications: *)
Lemma continuity_2d_pt_opp (f : R -> R -> R) (x y : R) :
continuity_2d_pt f x y ->
continuity_2d_pt (fun u v => - f u v) x y.
Lemma continuity_2d_pt_plus (f g : R -> R -> R) (x y : R) :
continuity_2d_pt f x y ->
continuity_2d_pt g x y ->
continuity_2d_pt (fun u v => f u v + g u v) x y.
Lemma continuity_2d_pt_minus (f g : R -> R -> R) (x y : R) :
continuity_2d_pt f x y ->
continuity_2d_pt g x y ->
continuity_2d_pt (fun u v => f u v - g u v) x y.