reserve x,O for set,
  o for Element of O,
  G,H,I for GroupWithOperators of O,
  A, B for Subset of G,
  N for normal StableSubgroup of G,
  H1,H2,H3 for StableSubgroup of G,
  g1,g2 for Element of G,
  h1,h2 for Element of H1,
  h for Homomorphism of G,H;

theorem Th31:
  for N1,N2 being strict normal StableSubgroup of G holds the
  carrier of N1 "\/" N2 = N1 * N2
proof
  let N1,N2 be strict normal StableSubgroup of G;
  N1 * N2 = N2 * N1 by Th28;
  hence thesis by Th30;
end;
