A methodology for mechanically verifying a family of parameterized multiplier circuits, including many well-known multiplier circuits such as the linear array, the Wallace tree and the 7-3 multiplier is proposed. A top level specification for these multipliers is obtained by abstracting the commonality in their behavior. The behavioral correctness of any multiplier in the family can be mechanically verified by a uniform proof strategy. Proofs of properties axe done by rewriting and induction using an automated theorem prover RRL (Rewrite Rule Laboratory). The behavioral correctness of the circuits is established with respect to addition and multiplication on numbers. The automated proofs involve minimal user intervention in terms of intermediate lemmas required. Generic hardware components are used to segregate the specification and the implementation aspects, enabling verification of circuits in terms of behavioral constraints that can be realized in different ways. The use of generic components aids reuse of proofs and helps modularize the correctness proofs, allowing verification to go hand in hand with the hardware design process in a hierarchical fashion.