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

theorem ThLin7:
  for V being LeftMod of INT.Ring,
      A being linearly-independent Subset of V
  holds A is Basis of Lin(A)
  proof
    let V be LeftMod of INT.Ring,
        A be linearly-independent Subset of V;
    reconsider AA = A as Subset of Lin(A) by ThLin4;
    (Omega).Lin(A) = Lin(AA) by ZMODUL03:20;
    hence thesis by ZMODUL03:16,VECTSP_7:def 3;
  end;
