
theorem APB:
  for a,b be positive Real, n be heavy positive Real holds
  a to_power n + b to_power n < (a + b) to_power n
  proof
    let a,b be positive Real, n be heavy positive Real;
    reconsider m = n - 1 as positive Real;
    a to_power 1 + b to_power 1 = (a + b) to_power 1; then
    a to_power (1+m) + b to_power (1+m) < (a + b) to_power (1+m) by NEW;
    hence thesis;
  end;
