 reserve n,m,i,p for Nat,
         h,k,r,r1,r2,x,x0,x1,x2,x3 for Real;
 reserve f,f1,f2,g for Function of REAL,REAL;

theorem
  cD(fD(f,h),h).x = fD(f,h).(x+h/2)-cD(f,h).x
proof
  cD(fD(f,h),h).x = fD(f,h).(x+h/2)-fD(f,h).(x-h/2) by DIFF_1:5
    .= fD(f,h).(x+h/2)-(f.((x-h/2)+h)-f.(x-h/2)) by DIFF_1:3
    .= fD(f,h).(x+h/2)-cD(f,h).x by DIFF_1:5;
  hence thesis;
end;
