
theorem LmFGND41:
  for V being non trivial finitely-generated torsion Z_Module,
  i being Element of INT.Ring st i <> 0 & for v being Vector of V
  holds i * v = 0.V
  holds V is non divisible
  proof
    let V be non trivial finitely-generated torsion Z_Module,
    i be Element of INT.Ring such that
    A1: i <> 0 & for v being Vector of V holds i * v = 0.V;
    assume AS: V is divisible;
    set v = the non zero Vector of V;
    v is divisible by AS;
    then consider u be Vector of V such that
    A2: i * u = v by A1;
    thus contradiction by A1,A2;
  end;
