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This paper aims at verifying properties of generic fault-tolerance algorithms. Our goal is to enhance the testing process with information extracted from the proof of the algorithm, whether this proof is formal or informal: ideally, testing is intended to focus on the weak parts of the proof (e.g., unproved lemmas or doubtful informal evidence). We use the Fault-Tolerant Rate Monotonic Scheduling algorithm as a case study. This algorithm was proven by informal demonstration, but two faults were revealed afterwards. In this paper, we focus on the analysis of the informal proof, which we restructure in a semiformal proof tree based on natural deduction. From this proof tree, we extract several functional cases and use them for testing a prototype of the algorithm. Experimental results show that a flawed informal proof does not necessarily provide relevant information for testing. It remains to investigate whether formal (partial) proofs allow better connection with potential faults.