reserve i for object, I for set,
  f for Function,
  x, x1, x2, y, A, B, X, Y, Z for ManySortedSet of I;

theorem     :: ZFMISC_1:46
  x in X implies {x} (\/) X = X
proof
  assume
A1: x in X;
  now
    let i be object;
    assume
A2: i in I;
    then
A3: x.i in X.i by A1;
    thus ({x} (\/) X).i = {x}.i \/ X.i by A2,PBOOLE:def 4
      .= {x.i} \/ X.i by A2,Def1
      .= X.i by A3,ZFMISC_1:40;
  end;
  hence thesis;
end;
