
theorem
  for a be Integer holds Parity a <= |.a.|
  proof
    let a be Integer;
    per cases;
    suppose a = 0;
      hence thesis by Def1;
    end;
    suppose
      a  <> 0; then
      Parity |.a.| <= |.a.| by Th3,NAT_D:7;
      hence thesis by PMP;
    end;
  end;
