reserve x for set,
  K for Ring,
  r for Scalar of K,
  V, M, M1, M2, N for LeftMod of K,
  a for Vector of V,
  m, m1, m2 for Vector of M,
  n, n1, n2 for Vector of N,
  A for Subset of V,
  l for Linear_Combination of A,
  W, W1, W2, W3 for Subspace of V;

theorem Th8:
  for A being Subset of W holds A is Subset of V
proof
  let A be Subset of W;
  the carrier of W c= the carrier of V by VECTSP_4:def 2;
  hence thesis by XBOOLE_1:1;
end;
