It is shown that the Glauber theory for the scattering of a high-energy hadron on a nucleus becomes unitary when all the possible inelastic intermediate states are included between successive scatterings. This result is used to prove that the nth-order multiple inelastic contributions satisfy the Abramovskii, Gribov and Kancheli cancellation (1973), which is therefore a consequence of the multiple scattering structure of the theory.
