reserve X for set,
  x,y,z for Element of BooleLatt X,
  s for set;
reserve y for Element of BooleLatt X;

theorem Th4:
  BooleLatt X is upper-bounded & Top BooleLatt X = X
proof
A1: bool X = carr(BooleLatt X) by Def1;
  then reconsider x = X as Element of BooleLatt X by ZFMISC_1:def 1;
A2: x"\/"y = x by A1,XBOOLE_1:12;
A3: y"\/"x = x by A1,XBOOLE_1:12;
  thus BooleLatt X is upper-bounded
  proof
    take x;
    thus thesis by A1,XBOOLE_1:12;
  end;
  hence thesis by A2,A3,LATTICES:def 17;
end;
