reserve x,x0,x1,y,y0,y1,r,r1,s,p,p1 for Real;
reserve z,z0 for Element of REAL 2;
reserve n for Element of NAT;
reserve s1 for Real_Sequence;
reserve f,f1,f2 for PartFunc of REAL 2,REAL;
reserve R,R1 for RestFunc;
reserve L,L1 for LinearFunc;

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;
