  We report on the automation of a technique to prove the correctness of
program transformations in higher-order program calculi which may permit
recursive let-bindings as they occur in functional programming languages. A
program transformation is correct if it preserves the observational semantics
of programs. In our LRSX Tool the so-called diagram method is automated by
combining unification, matching, and reasoning on alpha-renamings on the
higher-order meta-language, and automating induction proofs via an encoding
into termination problems of term rewrite systems. We explain the techniques,
we illustrate the usage of the tool, and we report on experiments.
