
theorem P1: for a be Integer holds parity a = parity (-a)
  proof
    let a be Integer;
    per cases;
    suppose
      A1: a is even;
      0 is even; then
      0 - a is even by A1;
      hence thesis by A1;
    end;
    suppose
      A1: a is odd; then
      -a is odd;
      hence thesis by A1;
    end;
  end;
