Petri nets constitute a well-studied model to verify and study concurrent systems, among others, and computing the coverability set is one of the most fundamental problems about Petri nets. Using the proof assistant Coq , we certified the correctness and termination of the MinCov algorithm by Finkel, Haddad, and Khmelnitsky (FOSSACS 2020). This algorithm is the most recent algorithm in the literature that computes the minimal basis of the coverability set, a problem known to be prone to subtle bugs. Apart from the intrinsic interest of a computer-checked proof, our certification provides new insights on the MinCov algorithm. In particular, we introduce as an intermediate algorithm a small-step variant of MinCov of independent interest.