reserve h,r,r1,r2,x0,x1,x2,x3,x4,x5,x,a,b,c,k for Real,
  f,f1,f2 for Function of REAL,REAL;

theorem
  (for x holds f.x = k/x & x+h/2<>0 & x-h/2<>0) implies for x holds cD(f
  ,h).x = (-k*h)/((x-h/2)*(x+h/2))
proof
  assume
A1: for x holds f.x = k/x & x+h/2<>0 & x-h/2<>0;
  let x;
A2: x+h/2<>0 by A1;
A3: x-h/2<>0 by A1;
  cD(f,h).x = f.(x+h/2) - f.(x-h/2) by DIFF_1:5
    .= k/(x+h/2)- f.(x-h/2) by A1
    .= k/(x+h/2)-k/(x-h/2) by A1
    .= k*(x-h/2)/((x-h/2)*(x+h/2))-k/(x-h/2) by A3,XCMPLX_1:91
    .= k*(x-h/2)/((x-h/2)*(x+h/2))-k*(x+h/2) /((x-h/2)*(x+h/2)) by A2,
XCMPLX_1:91
    .= (k*x-k*(h/2)-k*(x+h/2))/((x-h/2)*(x+h/2)) by XCMPLX_1:120;
  hence thesis;
end;
