  We study the density of states (DoS) $\nu(E)$ in a normal-metallic (N) film
contacted by a bulk superconductor (S). We assume that the system is diffusive
and the SN interface is transparent. In the limit of thin N layer (compared to
the coherence length), we analytically find three different types of the DoS
peculiarity at energy equal to the bulk superconducting order parameter
$\Delta_0$. (i) In the absence of the inverse proximity effect, the peculiarity
has the check-mark form with $\nu(\Delta_0)=0$ as long as the thickness of the
N layer is smaller than a critical value. (ii) When the inverse proximity
effect comes into play, the check-mark is immediately elevated so that
$\nu(\Delta_0)>0$. (iii) Upon further increasing of the inverse proximity
effect, $\nu(E)$ gradually evolves to the vertical peculiarity (with an
infinite-derivative inflection point at $E=\Delta_0$). This crossover is
controlled by a materials-matching parameter which depends on the relative
degree of disorder in the S and N materials.
