Payment channel networks are an approach to improve the scalability of blockchain-based cryptocurrencies. Because payment channel networks are used for transfer of financial value, their security in the presence of adversarial participants should be verified formally. We formalize the protocol of the Lightning Network, a payment channel network built for Bitcoin, and show that the protocol fulfills the expected security properties. As the state space of a specification consisting of multiple participants is too large for model checking, we formalize intermediate specifications and use a chain of refinements to validate the security properties where each refinement is justified either by model checking or by a pen-and-paper proof.