 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
  bD(cD(f,h),h).x = cD(f,h).x-bD(f,h).(x-h/2)
proof
  bD(cD(f,h),h).x = cD(f,h).x-cD(f,h).(x-h) by DIFF_1:4
    .= cD(f,h).x-(f.((x-h)+h/2)-f.((x-h)-h/2)) by DIFF_1:5
    .= cD(f,h).x-(f.(x-h/2)-f.((x-h/2)-h))
    .= cD(f,h).x-bD(f,h).(x-h/2) by DIFF_1:4;
  hence thesis;
end;
