theorem
  f1 is_hpartial_differentiable`31_in u0 &
  f2 is_hpartial_differentiable`31_in u0 implies
  pdiff1(f1,3)(#)pdiff1(f2,3) is_partial_differentiable_in u0,1
proof
  assume f1 is_hpartial_differentiable`31_in u0 &
  f2 is_hpartial_differentiable`31_in u0;
  then pdiff1(f1,3) is_partial_differentiable_in u0,1 &
  pdiff1(f2,3) is_partial_differentiable_in u0,1
  by Th25;
  hence thesis by PDIFF_4:28;
end;
