
theorem Th18:
  for X being set,
      f being Function of bool X, bool X st
    f.{} = {} holds
  (Flip f).X = X
  proof
    let X be set,
        f be Function of bool X, bool X;
    assume
A1: f.{} = {};
    X c= X; then
    reconsider y = X as Subset of X;
    (Flip f).y = (f.y`)` by Def14
              .= ({}X)` by A1
              .= y;
    hence thesis;
  end;
