Frequent itemset mining is one pillar of machine learning and is very important for many data mining applications. There are many different algorithms for frequent itemset mining, but to our knowledge no implementation has been proven correct using computer aided verification. Hu et al. derived on paper an efficient algorithm for this problem, starting from an inefficient functional program and by using program calculation derived an efficient version. Based on their work, we propose a formally verified functional implementation for frequent itemset mining developed with the Coq proof assistant. All the proposed programs are evaluated on classical datasets and are compared to a non verified Java implementation of the Apriori algorithm.