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This paper proposes an approach to prove reachability properties of the form AG(@j@?EF@f) using substitution refinement in classical B. Such properties denote that there exists an execution path for each state satisfying @j to a state satisfying @f. These properties frequently occur in security policies and information systems. We show how to use Morgan@?s specification statement to represent a property and refinement laws to prove it. The idea is to construct by stepwise refinement a program whose elementary statements are operation calls. Thus, the execution of such a program provides an execution satisfying AG(@j@?EF@f). Proof obligations are represented using assertions (ASSERTIONS clause of B) and can be discharged using Atelier B.