
theorem
  for a be Integer holds  parity (Parity a) = parity a
  proof
    let a be Integer;
    per cases;
    suppose
      A1: a is even; then
      Parity a is even;
      hence thesis by A1;
    end;
    suppose
      A1: a is odd; then
      Parity a is odd;
      hence thesis by A1;
    end;
  end;
