Rewriting Logic is a simply, flexible, and powerful framework for specifying and analysing concurrent systems. Reachability Logic is a recently introduced formalism, which is currently used for defining the operational semantics of programming languages and for stating properties about program executions. Reachability Logic has its roots in a wider-spectrum framework, namely, in Rewriting Logic Semantics. In this paper we show how Reachability Logic can be adapted for stating properties of transition systems described by Rewriting-Logic specifications. We propose a procedure for verifying Rewriting-Logic specifications against Reachability-Logic properties. We prove the soundness of the procedure and illustrate it by verifying a communication protocol specified in Maude.