Layer Systems for Confluence - Formalized.

Toyama’s theorem states that the union of two confluent term rewrite systems with disjoint signatures is again confluent. This is a fundamental result in term rewriting, and several proofs appear in the literature. The underlying proof technique has been adapted to prove further results like persistence of confluence (if a many-sorted term rewrite system is confluent, then the underlying unsorted system is confluent) or the preservation of confluence by currying.