theorem
  f1 is_hpartial_differentiable`12_in z0 & f2
  is_hpartial_differentiable`12_in z0 implies pdiff1(f1,1)(#)pdiff1(f2,1)
  is_partial_differentiable_in z0,2
proof
  assume f1 is_hpartial_differentiable`12_in z0 & f2
  is_hpartial_differentiable`12_in z0;
  then pdiff1(f1,1) is_partial_differentiable_in z0,2 & pdiff1(f2,1)
  is_partial_differentiable_in z0,2 by Th10;
  hence thesis by PDIFF_2:20;
end;
