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

theorem Th9:
  (-1) to_power (-2 * n) = 1
proof
  (-1) to_power (-2 * n) = (-1) #Z ((-1) * (2 * n)) by POWER:def 2
    .= ((-1) #Z (-1)) #Z (2 * n) by PREPOWER:45
    .= (1 / (-1) #Z 1) #Z (2 * n) by PREPOWER:41
    .= (1 / (-1)) #Z (2 * n) by PREPOWER:35
    .= (-1) |^ (2 * n) by PREPOWER:36
    .= 1 |^ (2 * n) by WSIERP_1:2
    .= (1 |^2) |^ n
    .= 1 |^ n
    .= 1;
  hence thesis;
end;
