(** * 2D Taylor-Lagrange inequality *)

Definition DL_regular_n f m x y :=
  exists D, locally_2d (fun u v =>
    Rabs (f u v - DL_pol m f x y (u-x) (v-y)) <= D * (Rmax (Rabs (u-x)) (Rabs (v-y))) ^ (S m)) x y.

Theorem Taylor_Lagrange_2d : forall f n x y, locally_2d (fun u v => ex_diff_n f (S n) u v) x y -> DL_regular_n f n x y.