
theorem ThFGND:
  for V being non trivial finitely-generated Z_Module holds V is non divisible
  proof
    let V be non trivial finitely-generated Z_Module;
    per cases;
    suppose V is torsion;
      hence thesis by LmFGND4;
    end;
    suppose B2: V is non torsion;
      assume V is divisible;
      then VectQuot(V, torsion_part(V)) is divisible by LMLT2;
      hence contradiction by B2,LmFGND3;
    end;
  end;
