In previous work, we explored the interaction between different formal hardware development techniques in the implementation of a fault-tolerant clock synchronization circuit. This case study presents a clever optimization of the earlier design and illustrates how we have extended our framework to support its incremental design refinement. The primary design tool represents circuits as systems of stream equations, where each stream corresponds to a signal within the circuit. These signals are annotated with invariants which can be established using proof by co-induction. These invariants are exploited to verify localized design refinements. This study lays groundwork for a more formal integration of disparate reasoning tools.