Regular expressions can be extended with lookarounds for contextual matching. This paper discusses a Coq formalization of the theory of regular expressions with lookarounds. We provide an efficient and purely functional algorithm for matching expressions with lookarounds and verify its correctness. The algorithm runs in time linear in both the size of the regular expression as well as the input string. Our experimental results provide empirical support to our complexity analysis. To the best of our knowledge, this is the first formalization of a linear-time matching algorithm for regular expressions with lookarounds.