reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: ZFMISC_1:116, 135
  X c= [|X,Y|] or X c= [|Y,X|] implies X = EmptyMS I
proof
  assume
A1: X c= [|X,Y|] or X c= [|Y,X|];
  per cases by A1;
  suppose
A2: X c= [|X,Y|];
    now
      let i be object;
      assume
A3:   i in I;
      then X.i c= [|X,Y|].i by A2;
      then X.i c= [:X.i,Y.i:] by A3,PBOOLE:def 16;
      hence X.i = {} by ZFMISC_1:111
        .= EmptyMS I.i by PBOOLE:5;
    end;
    hence thesis;
  end;
  suppose
A4: X c= [|Y,X|];
    now
      let i be object;
      assume
A5:   i in I;
      then X.i c= [|Y,X|].i by A4;
      then X.i c= [:Y.i,X.i:] by A5,PBOOLE:def 16;
      hence X.i = {} by ZFMISC_1:111
        .= EmptyMS I.i by PBOOLE:5;
    end;
    hence thesis;
  end;
end;
