theorem
  for V being finite-rank free Z_Module, I being Basis of V holds
  ex J being OrdBasis of V st rng J = I
  proof
    let V be finite-rank free Z_Module, I be Basis of V;
    consider p be FinSequence such that
    A2: rng p = I and
    A3: p is one-to-one by FINSEQ_4:58;
    reconsider p as FinSequence of V by A2,FINSEQ_1:def 4;
    take f = p;
    thus f is one-to-one by A3;
    thus thesis by A2;
  end;
