theorem Th36:
  for H2 being strict StableSubgroup of G holds H1 is
  StableSubgroup of H2 iff H1 "\/" H2 = H2
proof
  let H2 be strict StableSubgroup of G;
  thus H1 is StableSubgroup of H2 implies H1 "\/" H2 = H2
  proof
    assume H1 is StableSubgroup of H2;
    then H1 is Subgroup of H2 by Def7;
    then the carrier of H1 c= the carrier of H2 by GROUP_2:def 5;
    hence H1 "\/" H2 = the_stable_subgroup_of carr H2 by XBOOLE_1:12
      .= H2 by Th25;
  end;
  thus thesis by Th35;
end;
