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Verification of Simple Recursive Programs in Theorema: Completeness of the Method

We report work concerning the theoretical basis and the implementation in the Theorema system of a methodology for the generation of verification conditions for recursive procedures, with the aim of practical verification of recursive programs. We develop a method for proving total correctness properties of programs which have simple functional recursive definitions, and we discuss its different aspects. We also define a class of programs for which the method is complete and we give a detailed proof of the completeness statement.