 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 implies -v is non torsion
  proof
    assume A1: not v is torsion;
    assume -v is torsion;
    then consider i be Element of INT.Ring such that
    A3: i <> 0 & i*(-v) = 0.V;
    (-i)*v = 0.V by A3,ZMODUL01:5;
    hence contradiction by A1,A3;
  end;
