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 Th32:
  for N1,N2 being strict normal StableSubgroup of G holds N1 "\/"
  N2 is normal StableSubgroup of G
proof
  let N1,N2 be strict normal StableSubgroup of G;
  (ex N be strict normal StableSubgroup of G st the carrier of N = carr N1
  * carr N2 )& the carrier of N1 "\/" N2 = N1 * N2 by Th23,Th31;
  hence thesis by Lm4;
end;
