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

theorem :: ZFMISC_1:96
  union (A (\/) B) = union A (\/) union B
proof
  now
    let i be object;
    assume
A1: i in I;
    hence (union (A (\/) B)).i = union (A.i \/ B.i) by Lm6
      .= union (A.i) \/ union (B.i) by ZFMISC_1:78
      .= (union A).i \/ union (B.i) by A1,Def2
      .= (union A).i \/ (union B).i by A1,Def2
      .= (union A (\/) union B).i by A1,PBOOLE:def 4;
  end;
  hence thesis;
end;
