 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
  v is non torsion & i <> 0 implies i * v is non torsion
  proof
    assume A1: not v is torsion & i <> 0;
    assume i * v is torsion;
    then consider i1 be Element of INT.Ring such that
    A3: i1 <> 0 & i1 * (i * v) = 0.V;
    (i1 * i) * v = 0.V by A3,VECTSP_1:def 16;
    hence contradiction by A1,A3;
  end;
