
theorem
  for a,b,c be positive Real, n be positive Real holds
  (a+b+c) to_power n / (a+b) to_power n < (a+c) to_power n / a to_power n
  proof
    let a,b,c be positive Real, n be positive Real;
    (a+b+c) to_power n / (a+b) to_power n = ((a+b+c)/(a+b)) to_power n &
    (a+c) to_power n / a to_power n = ((a+c)/a) to_power n by POWER:31;
    hence thesis by FRAC,POWER:37;
  end;
