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_1:113
  X = EmptyMS I or Y = EmptyMS I implies [|X,Y|] = EmptyMS I
proof
  assume
A1: X = EmptyMS I or Y = EmptyMS I;
  per cases by A1;
  suppose
A2: X = EmptyMS I;
    now
      let i be object;
      assume
A3:   i in I;
A4:   X.i = {} by A2,PBOOLE:5;
      thus [|X,Y|].i = [:X.i,Y.i:] by A3,PBOOLE:def 16
        .= {} by A4,ZFMISC_1:90
        .= EmptyMS I.i by PBOOLE:5;
    end;
    hence thesis;
  end;
  suppose
A5: Y = EmptyMS I;
    now
      let i be object;
      assume
A6:   i in I;
A7:   Y.i = {} by A5,PBOOLE:5;
      thus [|X,Y|].i = [:X.i,Y.i:] by A6,PBOOLE:def 16
        .= {} by A7,ZFMISC_1:90
        .= EmptyMS I.i by PBOOLE:5;
    end;
    hence thesis;
  end;
end;
