reserve V for RealLinearSpace,
  W for Subspace of V,
  x, y, y1, y2 for set,
  i, n for Element of NAT,
  v for VECTOR of V,
  KL1, KL2 for Linear_Combination of V,
  X for Subset of V;

theorem Th16:
  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 RLVECT_3:def 3;
  then A is linearly-independent Subset of V by Th14;
  then consider I being Basis of V such that
A1: A c= I by Th2;
  take I;
  thus thesis by A1;
end;
