
theorem P2P:
  for a,b be non zero Integer st Parity a > Parity b holds
  2*(Parity b) divides Parity a
  proof
    let a,b be non zero Integer such that
    A1: Parity a > Parity b;
    A2: Parity a = 2|^(2|-count a) & Parity b = 2|^(2|-count b) by Def1; then
    2|-count a > 2|-count b by A1,PREPOWER:93; then
    2|-count a >= (2|-count b) + 1 by NAT_1:13; then
    2|^((2|-count b) + 1) divides 2|^(2|-count a) by NEWTON:89;
    hence thesis by A2,NEWTON:6;
  end;
