
theorem Th4:
  for a,b be Integer holds
    Parity a divides Parity b or Parity b divides Parity a
  proof
    let a,b be Integer;
    per cases;
    suppose
      a = 0 or b = 0; then
      Parity a = 0 or Parity b = 0 by Def1;
      hence thesis by INT_2:12;
    end;
    suppose
      B1: a <> 0 & b <> 0; then
      reconsider a as non zero Integer;
      reconsider b as non zero Integer by B1;
      B2: Parity a = 2|^(2|-count a) & Parity b = 2|^(2|-count b) by Def1;
      per cases;
      suppose 2|-count a >= 2|-count b;
        hence thesis by B2,NEWTON:89;
      end;
      suppose 2|-count b >= 2|-count a;
        hence thesis by B2,NEWTON:89;
      end;
    end;
  end;
