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

theorem :: ZFMISC_1:79
  A c= B implies bool A c= bool B
proof
  assume
A1: A c= B;
  let i be object;
  assume
A2: i in I;
  then
A3: A.i c= B.i by A1;
  (bool A).i = bool (A.i) & (bool B).i = bool (B.i) by A2,Def1;
  hence thesis by A3,ZFMISC_1:67;
end;
