
theorem Th2:
  for X being set holds the carrier of BoolePoset X = bool X
proof
  let X be set;
  set L = BoolePoset X;
  L = InclPoset bool X by YELLOW_1:4;
  then L = RelStr(#bool X, RelIncl bool X#) by YELLOW_1:def 1;
  hence thesis;
end;
