  The differential cross-section of inelastic coherent diffractive dissociation
off nuclei $p~+~^4$He $\rightarrow X ~+ ~^4$He is expressed in terms of the
relative cumulants of the cross-section distribution $P_N(\sigma)$. The
theoretical result for the ratio
$r=\Bigg(\frac{d\sigma_{diff}}{dt}\Bigg)^{pHe}_{t=0} \Bigg/
\Bigg(\frac{d\sigma_{diff}}{dt}\Bigg)^{pp}_{t=0}=6.8 \div 7.6$ is close to the
value $r=7.1 \pm 0.75$ which we extracted from the FNAL data. These are the
only $A>2$ data of this kind. The comparison provides the first confirmation of
the cross-section fluctuation approach to the description of the absolute value
of the inelastic diffraction cross-section off nuclei. It provides also a new
constraint on the first 4 cumulants of the cross-section distribution.
