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`11_in z0 & f2
  is_hpartial_differentiable`11_in z0 implies pdiff1(f1,1)(#)pdiff1(f2,1)
  is_partial_differentiable_in z0,1
proof
  assume f1 is_hpartial_differentiable`11_in z0 & f2
  is_hpartial_differentiable`11_in z0;
  then pdiff1(f1,1) is_partial_differentiable_in z0,1 & pdiff1(f2,1)
  is_partial_differentiable_in z0,1 by Th9;
  hence thesis by PDIFF_2:19;
end;
