
theorem
  for a,b be positive Real, n be Real holds
  (a + b) to_power n < a to_power n + b to_power n iff n < 1
  proof
    let a,b be positive Real, n be Real;
    n is heavy positive iff n > 1 by TA1; then
    (a+b) to_power n <= (a to_power n) + (b to_power n) iff n <= 1 by LME;
    hence thesis by NE1,XXREAL_0:1;
  end;
