
theorem PM:
  for a be Integer holds Parity a = Parity (-a)
  proof
    let a be Integer;
    per cases;
    suppose a <> 0; then
      reconsider a as non zero Integer;
      B1: 2 is non trivial Nat by NAT_2:def 1;
      Parity (-a) = 2|^(2|-count (a*(-1))) by Def1
      .= 2|^((2|-count a)+(2|-count (-1))) by NEWTON03:57,INT_2:28
      .= 2|^((2|-count a)+0) by B1;
      hence thesis by Def1;
    end;
    suppose a = 0;
      hence thesis;
    end;
  end;
