This paper addresses the open technical problems of evolving executable, event-based process models by refinement, that is, by iteratively expanding a model until it has the required level of detail. Such iterative development is helpful because of the expectation that the next-step model is semantically compatible with the previous one, only with more detail. We provide in this paper a formal notion of refinement of single atomic actions (events) into entire subprocesses, and a theoretical framework for providing guarantees that such a next-step model is formally a refinement of the previous one. Our work is set within the declarative, event-based process modelling language of timed Dynamic Condition Response (DCR) graphs, which can express timed constraints (conditions with delay and obligations with deadlines) between events, liveness, safety, and concurrency. Concretely, we extend DCR graph syntax and semantics with a notion of subprocess, provide examples of its use, and give sound approximations of situations where replacing an event with a subprocess formally is a refinement of the original process.