 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
  for V being Z_Module holds rank((0).V) = 0
  proof
    let V be Z_Module;
    reconsider 0Vs = (Omega).((0).V) as strict finite-rank free Z_Module;
    (Omega).0Vs = (0).((0).V) by ZMODUL01:51;
    hence thesis by ZMODUL05:1;
  end;
