 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 ThISRank1:
  for V being torsion-free Z_Module,
  W1, W2 being finite-rank free Subspace of V holds
  rank(W1 /\ W2) <= rank(W1)
  proof
    let V be torsion-free Z_Module,
    W1, W2 be finite-rank free Subspace of V;
    W1 /\ W2 is Subspace of W1 by ZMODUL01:105;
    hence thesis by ZMODUL05:2;
  end;
