reserve x, y for object, I for set,
  A, B, X, Y for ManySortedSet of I;

theorem :: ZFMISC_1:1
  bool EmptyMS I = I --> {{}}
proof
  now
    let i be object;
    assume
A1: i in I;
    then (bool EmptyMS I).i = bool (EmptyMS I.i) by Def1
      .= bool{} by PBOOLE:5
      .= {{}} by ZFMISC_1:1;
    hence (bool EmptyMS I).i = (I --> {{}}).i by A1,FUNCOP_1:7;
  end;
  hence thesis;
end;
