
theorem A4I:
  for a be even Integer st not 4 divides a holds a is non square
  proof
    let a be even Integer such that
    A1: not 4 divides a;
    not 2 divides a/2
    proof
      assume not thesis; then
      2*2 divides (a/2)*2 by NEWTON02:2;
      hence contradiction by A1;
    end; then
    reconsider b = a/2 as odd Integer by ABIAN:def 1;
    2*b is non square;
    hence thesis;
  end;
