reserve x, y for set;

theorem Th10:
  for s being non empty finite set
  holds card(derangements s) = round ((card s)! / number_e)
  proof
    let s be non empty finite set;
    |. card(derangements s) - (((card s)!) / number_e) .| < 1/2 by Th9;
    hence card(derangements s) = round ((card s)! / number_e) by Th4;
  end;
