We propose a new method for verifying synchronous circuits using the Boyer-Moore Theorem Prover (BMTP) based on an efficient use of induction. The method contains two techniques. The one is the representation method of signals. Each signal is represented not as a waveform, but as a time parameterized function. The other is the mechanical transformation of the circuit description. A simple description of the logical connection of the components of a circuit is transformed into such a form that is not only acceptable as a definition of BMTP but also adequate for applying induction. We formalize the method and show that it realizes an efficient proof.