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
  M c= N implies M c= (Omega).N
proof
  assume M c= N;
  then
A1: M is Subspace of N;
  N is Subspace of (Omega).N by Th4;
  then M is Subspace of (Omega).N by A1,VECTSP_4:26;
  hence thesis;
end;
