 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 torsion-free Z_Module,
  W1, W2 being finite-rank free Subspace of V,
  I being Basis of W1
  st rank(W1 /\ W2) < rank(W1) holds
  ex v being Vector of V st v in I & (W1 /\ W2) /\ Lin{v} = (0).V
  by ThISRank2;
