Efficient Rewriting of Operations on Finite Structures in ACL2

We give a useful set of unconditional rewrite rules for reasoning about record structures, which are essentially nite functions. The problem, then, is to deene functions for which these rules are true and then prove the rules. We begin with a series of deenitions that attempt to satisfy these rules but fall short for various reasons. Then we give two solutions, one of which generalizes to other nite structures. The deenitions of our access and update functions are somewhat subtle, complex, and ineeecient, but they return the expected values and the theorems exported are elegant and eecient for automatic, unconditional rewriting.