Zeros of the Wronskian and renormalized oscillation theory

For general Sturm-Liouville operators with separated boundary conditions, we prove the following: If E_1,2 ∈ R and if u_1,2 solve the differential equation Hu_j = E_ju_j, j = 1, 2 and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection P_(E1,E2)(H) of H equals the number of zeros of the Wronskian of u₁ and u₂.