 reserve G, A for Group;
 reserve phi for Homomorphism of A,AutGroup(G);

theorem Th62:
  for G being Group
  for H1,H2 being Subgroup of G
  holds H1 * H2 c= the carrier of H1 "\/" H2
  & H2 * H1 c= the carrier of H1 "\/" H2
proof
  let G be Group;
  let H1,H2 be Subgroup of G;
  thus H1 * H2 c= the carrier of H1 "\/" H2 by Th61;
  H2 * H1 c= the carrier of H2 "\/" H1 by Th61;
  hence H2 * H1 c= the carrier of H1 "\/" H2 by GROUP_4:56;
end;
