theorem
  f1 is_hpartial_differentiable`33_in u0 &
  f2 is_hpartial_differentiable`33_in u0 implies
  pdiff1(f1,3)(#)pdiff1(f2,3) is_partial_differentiable_in u0,3
proof
  assume f1 is_hpartial_differentiable`33_in u0 &
  f2 is_hpartial_differentiable`33_in u0;
  then pdiff1(f1,3) is_partial_differentiable_in u0,3 &
  pdiff1(f2,3) is_partial_differentiable_in u0,3
  by Th27;
  hence thesis by PDIFF_4:30;
end;
