
theorem for a,b be positive Real, n be positive Real holds
  2*((a+b) to_power n) > (a+b) to_power n + (a to_power n) > 2*(a to_power n)
  proof
    let a,b be positive Real, n be positive Real;
    a + b > a + 0 by XREAL_1:6; then
    (a + b) to_power n > a to_power n by POWER:37; then
    (a+b) to_power n + (a+b) to_power n > (a+b) to_power n + a to_power n >
      a to_power n + a to_power n by XREAL_1:6;
    hence thesis;
  end;
