reserve x, y, y1, y2 for object;
reserve V for Z_Module;
reserve W, W1, W2 for Submodule of V;
reserve u, v for VECTOR of V;
reserve i, j, k, n for Element of NAT;

theorem LmTF1D:
  for V being finite-rank free Z_Module,
  I being linearly-independent Subset of V
  holds I is finite
  proof
    let V be finite-rank free Z_Module, I be linearly-independent Subset of V;
    set IV = the Basis of V;
    card(I) c= card(IV) by ZMODUL04:20;
    hence thesis;
  end;
