Z is a formal specification language combining typed set theory, predicate calculus, and a schema calculus. This paper describes an extension of Z that allows transformation and reasoning rules to be written in a Z-like notation. This gives a high-level, declarative, way of specifying transformations of Z terms, which makes it easier to build new Z manipulation tools. We describe the syntax and semantics of these rules, plus some example reasoning engines that use sets of rules to manipulate Z terms. The utility of these rules is demonstrated by discussing two sets of rules. One set defines expansion of Z schema expressions. The other set is used by the ZLive animator to preprocess Z expressions into a form more suitable for animation.