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

theorem Th8:
  for a being non zero Real holds (a to_power (-k)) * (a
  to_power (-m)) = a to_power (-k-m)
proof
  set K = -k;
  set M = -m;
  let a be non zero Real;
  (a to_power (-k)) *(a to_power (-m)) = (a #Z (-k)) * (a to_power (- m))
  by POWER:def 2
    .= (a #Z K) * (a #Z M) by POWER:def 2
    .= a #Z (K+M) by PREPOWER:44
    .= a to_power (-k-m) by POWER:def 2;
  hence thesis;
end;
