reserve X for set;
reserve G for Group;
reserve H for Subgroup of G;

theorem Th10:
  H is proper iff the carrier of H <> the carrier of G
proof
  (the carrier of H c= the carrier of G) & (the multF of H =
  (the multF of G)||(the carrier of H)) by GROUP_2:def 5;
  hence thesis;
end;
