
theorem for a,b be positive Real, n be Real holds
  a to_power (n+1) + b to_power (n+1) =
    ((a to_power n + b to_power n)*(a + b) + (a - b) *
      (a to_power n - b to_power n))/2
  proof
    let a,b be positive Real, n be Real;
    a to_power 1 = a & b to_power 1 = b;
    hence thesis by N158;
  end;
