
theorem Th23:
  for X being set,
      f being Function of bool X, bool X holds
    Flip Flip f = f
  proof
    let X be set,
        f be Function of bool X, bool X;
    set g = Flip Flip f;
    for x being Subset of X holds g.x = f.x
    proof
      let x be Subset of X;
      g.x = ((Flip f).x`)` by Def14
         .= (f.x``)`` by Def14
         .= f.x;
      hence thesis;
    end;
    hence thesis;
  end;
