Handling concurrency using a shared memory and locks is tedious and error-prone. One solution is to use message passing instead. We study here a particular, contract-based flavor that makes the ownership transfer of messages explicit. In this case, ownership of the heap region representing the content of a message is lost upon sending, which can lead to efficient implementations. In this paper, we define a proof system for a concurrent imperative programming language implementing this idea and inspired by the Singularity OS. The proof system, for which we prove soundness, is an extension of separation logic, which has already been used successfully to study various ownership-oriented paradigms.