theorem Th39:
  for f, g being Element of Permutations n holds f * g in Permutations n
proof
  let f, g be Element of Permutations n;
  reconsider F = f, G = g as Permutation of Seg n by MATRIX_1:def 12;
  F * G is Permutation of Seg n;
  hence thesis by MATRIX_1:def 12;
end;
