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 Th14:
 for x being object holds
  M c= N implies (x in M implies x in N) & (x is Vector of M
  implies x is Vector of N)
by VECTSP_4:9,VECTSP_4:10;
