reserve V,W for Z_Module;
reserve T for linear-transformation of V,W;

theorem
  for V being finite-rank free Z_Module holds rank ((0).V) = 0
  proof
    let V be finite-rank free Z_Module;
    (Omega).((0).V) = (0).((0).V) by ZMODUL01:51;
    hence thesis by RL5Th33;
  end;
