We propose a general framework to build certified proofs of distributed self-stabilizing algorithms with the proof assistant Coq. We first define in Coq the locally shared memory model with composite atomicity, the most commonly used model in the self-stabilizing area. We then validate our framework by certifying a non trivial part of an existing silent self-stabilizing algorithm which builds a -clustering of the network. We also certify a quantitative property related to the output of this algorithm. Precisely, we show that the computed -clustering contains at most clusterheads, where is the number of nodes in the network. To obtain these results, we also developed a library which contains general tools related to potential functions and cardinality of sets.