reserve V for Z_Module;
reserve W, W1, W2 for Submodule of V;

theorem RL5Th25:
  for V be finite-rank free Z_Module holds for A being Subset of V
  st A is linearly-independent holds A is finite
  proof
    let V be finite-rank free Z_Module;
    let A be Subset of V;
    consider I be finite Subset of V such that
    A1: I is Basis of V by ZMODUL03:def 3;
    assume A is linearly-independent;
    then card A c= card I by A1,XXTh3,XBOOLE_0:def 8;
    hence thesis;
  end;
