theorem Th42:
  for G being strict GroupWithOperators of O holds G is trivial
  implies (1).G = G
proof
  let G be strict GroupWithOperators of O;
  reconsider H=G as StableSubgroup of G by Lm3;
  assume G is trivial;
  then ex x be object st the carrier of G = {x};
  then the carrier of H = {1_G} by TARSKI:def 1;
  hence thesis by Def8;
end;
