This paper reports a formal methodology for verifying a broad class of synthesized register-transfer-level (RTL) designs by accommodating various register allocation/optimization schemes commonly found in high-level synthesis tools. Performing register optimization as part of synthesis process implies that the mapping between the specification variables and RTL registers is not bijective. We propose a formalization of dynamic variable-register mapping, and techniques based on symbolic analysis and higher-order logic theorem proving for verifying synthesized RTL designs. The proposed verification methodology has been successfully implemented using the PVS theorem prover.