
theorem PEPIN31: for a,b be non zero Integer holds
  Parity a divides Parity b iff Parity b >= Parity a
  proof
    let a,b be non zero Integer;
    A1: Parity a = 2|^(2|-count a) & Parity b = 2|^(2|-count b) by Def1;
    Parity b >= Parity a implies Parity a divides Parity b
    proof
      assume Parity b >= Parity a; then
      2|-count b  >= 2|-count a by A1,PEPIN:66;
      hence thesis by A1,NEWTON:89;
    end;
    hence thesis by NAT_D:7;
  end;
