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A compositional method is presented for the verification of multi-agent systems. The advantages of the method are the well-structuredness of the proofs and the reusability of parts of these proofs in relation to reuse of components. The method is illustrated for an example multi-agent system, consisting of co-operative information gathering agents. This application of the verification method results in a formal analysis of pro-activeness and reactiveness of agents, and shows which combinations of pro-activeness and reactiveness in a specific type of information agents lead to a successful cooperation.