Information flow security in a multilevel system aims at guaranteeing that no high level information is revealed to low level users, even in the presence of any possible malicious process. Persistent_BNDC (P_BNDC, for short) is an information-flow security property which is suitable to deal with processes in dynamic contexts. In this work we show that P_BNDC is compositional with respect to the replication operator. Then, by exploiting the compositionality properties of the class of P_BNDC processes, we define a proof system which provides a very efficient technique for the stepwise development and the verification of recursively defined P_BNDC processes.