reserve n, k, r, m, i, j for Nat;

theorem Th6:
  for k being non zero Real, m being odd Integer holds k
  to_power m to_power n = k to_power (m * n)
proof
  let k be non zero Real, m be odd Integer;
    k to_power (m * n) = k #Z (m * n) by POWER:def 2
      .= k #Z m #Z n by PREPOWER:45
      .= k to_power m #Z n by POWER:def 2
      .= k to_power m to_power n by POWER:def 2;
    hence thesis;
end;
