We propose a framework to build certified proofs of self-stabilizing algorithms using 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 self-stabilizing algorithm which builds a k-hop dominating set of the network. We also certify a quantitative property related to its output: we show that the size of the computed k-hop dominating set is at most $$\lfloor \frac{n-1}{k+1} \rfloor + 1$$⌊n-1k+1⌋+1, where n is the number of nodes. To obtain these results, we developed a library which contains general tools related to potential functions and cardinality of sets.