reserve X for set;

theorem
  Bottom BoolePoset X = {}
proof
  thus Bottom BoolePoset X = "\/"({},LattPOSet BooleLatt X) by YELLOW_0:def 11
    .= "\/"({},BooleLatt X) by YELLOW_0:29
    .= Bottom BooleLatt X by LATTICE3:49
    .= {} by LATTICE3:3;
end;
