
theorem
  for a be Nat holds Parity (a + Parity a) >= 2*Parity a
  proof
    let a be Nat;
    per cases;
    suppose
      a = 0; then
      Parity a = 0 by Def1;
      hence thesis;
    end;
    suppose a <> 0;
      hence thesis by ADA,NAT_D:7;
    end;
  end;
