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

theorem :: ZFMISC_1:95
  A c= B implies union A c= union B
proof
  assume
A1: A c= B;
  let i be object;
  assume
A2: i in I;
  then A.i c= B.i by A1;
  then union (A.i) c= union (B.i) by ZFMISC_1:77;
  then (union A).i c= union (B.i) by A2,Def2;
  hence thesis by A2,Def2;
end;
