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 Th34:
  (Omega).G "\/" H1 = (Omega).G & H1 "\/" (Omega).G = (Omega).G
proof
  (the carrier of (Omega).G) \/ carr H1 = [#] the carrier of G by SUBSET_1:11;
  hence thesis by Th25;
end;
