We exhibit a methodology to develop mechanically-checkable parameterized proofs of the correctness of fault-tolerant round-based distributed algorithms in an asynchronous message-passing setting. Motivated by a number of case studies, we sketch how to replace often-used informal and incomplete pseudo code by mostly syntax-free formal and complete definitions of a global-state transition system. Special emphasis is put on the required deepening of the level of proof detail to be able to check them within an interactive theorem proving environment.