theorem
  f1 is_hpartial_differentiable`22_in z0 & f2
  is_hpartial_differentiable`22_in z0 implies pdiff1(f1,2)(#)pdiff1(f2,2)
  is_partial_differentiable_in z0,2
proof
  assume f1 is_hpartial_differentiable`22_in z0 & f2
  is_hpartial_differentiable`22_in z0;
  then pdiff1(f1,2) is_partial_differentiable_in z0,2 & pdiff1(f2,2)
  is_partial_differentiable_in z0,2 by Th12;
  hence thesis by PDIFF_2:20;
end;
