
theorem Th19:
  for X being set,
      f being Function of bool X, bool X st
    f.X = X holds
  (Flip f).{} = {}
  proof
    let X be set,
        f be Function of bool X, bool X;
    assume
A1: f.X = X;
    set y = {}X;
    (Flip f).y = (f.y`)` by Def14
              .= {}X by A1;
    hence thesis;
  end;
