
theorem
  for X being set,
      f being Function of bool X, bool X st
    f = id bool X holds
  Flip f = f
  proof
    let X be set,
        f be Function of bool X, bool X;
    assume
A1: f = id bool X;
    for x being Subset of X holds (Flip f).x = f.x
    proof
      let x be Subset of X;
      thus (Flip f).x = (f.x`)` by Def14
                     .= x`` by A1
                     .= f.x by A1;
    end;
    hence thesis;
  end;
