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

theorem :: ZFMISC_1:100
  A c= bool union A
proof
  let i be object;
  assume
A1: i in I;
  then (bool union A).i = bool ((union A).i) by Def1
    .= bool union (A.i) by A1,Def2;
  hence thesis by ZFMISC_1:82;
end;
