reserve GF for Field,
  V for VectSp of GF,
  W for Subspace of V,
  x, y, y1, y2 for set,
  i, n, m for Nat;

theorem Th13:
  for A being Basis of W ex B being Basis of V st A c= B
proof
  let A be Basis of W;
  A is linearly-independent by VECTSP_7:def 3;
  then reconsider B = A as linearly-independent Subset of V by Th11;
  consider I being Basis of V such that
A1: B c= I by VECTSP_7:19;
  take I;
  thus thesis by A1;
end;
