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

theorem :: ZFMISC_1:99
  union bool A = A
proof
  now
    let i be object;
    assume
A1: i in I;
    hence (union bool A).i = union ((bool A).i) by Def2
      .= union bool (A.i) by A1,Def1
      .= A.i by ZFMISC_1:81;
  end;
  hence thesis;
end;
