
theorem Th3:
  for a be Integer holds Parity a divides a
  proof
    let a be Integer;
    per cases;
    suppose a = 0;
      hence thesis by Def1;
    end;
    suppose
      A1: a <> 0;
      |.2.| > 1; then
      2|^(2|-count a) divides a by A1,NEWTON03:def 7;
      hence thesis by A1,Def1;
    end;
  end;
