 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 torsion implies -v is torsion
  proof
    assume v is torsion;
    then consider i be Element of INT.Ring such that
    A1: i <> 0 & i * v = 0.V;
    i*(-v) = - (i*v) by ZMODUL01:6
    .= 0.V by A1;
    hence thesis by A1;
  end;
