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 Th11:
  A c= [#]Lin(A)
proof
  let x be object;
  assume x in A;
  then x in Lin(A) by MOD_3:5;
  hence thesis;
end;
