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

theorem Th35:
  (-tau) to_power ((-1) * n) = (-tau) to_power (-1) to_power n
proof
  (- tau) to_power ((-1) * n) = (- tau) #Z ((-1) * n) by POWER:def 2
    .= ((- tau) #Z (-1)) #Z n by PREPOWER:45
    .= (1 / (- tau) #Z 1) #Z n by PREPOWER:41
    .= (1 / (- tau)) #Z n by PREPOWER:35
    .= (1 / (- tau)) to_power n by POWER:def 2
    .= ((1 / (- tau)) to_power 1) to_power n by POWER:25
    .= ((1 / (- tau)) #Z 1) to_power n by POWER:def 2
    .= (1 / (- tau) #Z 1) to_power n by PREPOWER:42
    .= ((- tau) #Z (-1)) to_power n by PREPOWER:41;
  hence thesis by POWER:def 2;
end;
