Mixing list recursion and arithmetic

A procedure that constructs mechanically the appropriate lemmas for proving assertions about programs with arrays is described. A certain subclass of formulas for which the procedure is guaranteed to terminate and thus constitutes a decision procedure is exhibited. This subclass allows for ordering over integers but not for incrementation. A more general subclass that allows for incrementation, but without the termination property, is considered. It is also indicated how to apply the method to a still more general subclass that allows for full arithmetic. These results are extended to the case in which predicates have more than one list argument