theorem Th6:
  H1 is Subgroup of H2 implies a * H1 c= a * H2 & H1 * a c= H2 * a
proof
  assume H1 is Subgroup of H2;
  then the carrier of H1 c= the carrier of H2 by GROUP_2:def 5;
  hence thesis by Th4;
end;
