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
  M1 c= N & M2 c= N implies 0.M1 = 0.M2 & 0.M1 in M2 & (the carrier of
  M1 c= the carrier of M2 implies M1 c= M2) & ((for n st n in M1 holds n in M2)
implies M1 c= M2) & (the carrier of M1 = the carrier of M2 & M1 is strict & M2
  is strict implies M1 = M2) & (0).M1 c= M2
by VECTSP_4:12,VECTSP_4:18,VECTSP_4:27,VECTSP_4:28,VECTSP_4:29,VECTSP_4:40;
