However, if some of the eigenvalues of a n are degenerate (such as having degenerate energy levels), then the above result no longer holds. In such a case, we need to distinguish between the eigenfunctions corresponding to the same eigenvalue. To do this, a second observable is introduced (let us call that B ), which is compatible with A . The compatibility theorem tells us that a common basis of eigenfunctions of A ^ ^ and B ^ ^ can be found. Now if each pair of the eigenvalues ( a n , b n ) uniquely specifies a state vector of this basis, we claim to have formed a CSCO: the set { A , B } . The degeneracy in A ^ ^ is completely removed.