
theorem PPM: for a,b be Integer holds parity (a+b) = parity (a-b)
  proof
    let a,b be Integer;
    parity (a+b) = parity (parity(a)+parity(b)) by NAT_D:66
    .= parity (parity(a) + parity(-b)) by P1
    .= parity (a + -b) by NAT_D:66;
    hence thesis;
  end;
