In Cyber-Physical Systems (CPS), concurrently executing software components interact with each other and the physical environment to deliver functionality that is often safety-critical and time-sensitive. Verifying the correctness of the joint behavior of concurrent software components, however, is challenging. It is helpful to eliminate nondeterminism in the software, at the level of the programming model, and provide first-class programming constructs for expressing timed behavior. The Lingua Franca (LF) coordination language achieves this through the use of the Reactor model as its underlying model of computation. In this paper, we present the first formal operational semantics for the Reactor model, and prove its key properties of progress and determinism. The Reactor model and its associated proofs are fully mechanized in the Lean theorem prover. As an operational model, our semantics are close to the intuition for implementation and a helpful reference. The computational objects of the Reactor model are formalized in a modular fashion, which provides insights into the different structural properties of the model, and their effect on execution behavior.