Proving programs correct is hard. During the last decades computer scientists developed various logics dedicated to program verification. One such effort is Reachability Logic (RL): a language-parametric generalisation of Hoare Logic. Recently, based on RL, an automatic verification procedure was given and proved sound. In this paper we generalise this procedure and prove its soundness formally in the Coq proof assistant. For the formalisation we had to deal with all the minutiae that were neglected in the paper proof (i.e., an insufficient assumption, implicit hypotheses, and a missing case in the paper proof). The Coq formalisation provides us with a certified program-verification procedure.