 reserve V for Z_Module;
 reserve W for Subspace of V;
 reserve v, u for Vector of V;
 reserve i for Element of INT.Ring;

theorem ThLIV1:
  for V being Z_Module, A being Subset of V, v being Vector of V
  st A is linearly-independent & v in A holds
  v is non torsion
  proof
    let V be Z_Module, A be Subset of V, v be Vector of V such that
    A1: A is linearly-independent & v in A;
    {v} is linearly-independent by A1,ZMODUL02:56,ZFMISC_1:31;
    hence v is non torsion by ThnTV3;
  end;
