reserve n,m for Element of NAT;
reserve h,k,r,r1,r2,x,x0,x1,x2,x3 for Real;
reserve f,f1,f2 for Function of REAL,REAL;

theorem
  cD(f,h).x = bD(f,h/2).x - bD(f,-h/2).x
proof
 fD(f,h/2).x = -bD(f,-h/2).x
  proof
    fD(f,h/2).x = f.(x+h/2) - f.x by DIFF_1:3
      .= -(f.x-f.(x-(-h/2)))
      .= -bD(f,-h/2).x by DIFF_1:4;
    hence thesis;
  end;
  then cD(f,h).x = -bD(f,-h/2).x - fD(f,-h/2).x by Th1
    .= -bD(f,-h/2).x - (-bD(f,h/2).x) by Th2
    .= bD(f,h/2).x - bD(f,-h/2).x;
  hence thesis;
end;
