Modern processors integrate heterogeneous devices to expose unified shared memory. Yet, the de-facto design pattern used to compose their disparate coherence protocols lacks a formal foundation. This leaves the door open for subtle consistency bugs, in a critical gap between practice and correctness. This paper provides the first formal, machine-checked proof that a de-facto design pattern, which we call the Principle of Synchronous Propagation, is correct. Leveraging a new unifying abstraction for coherence protocols, our central theorem (machine checked in Lean) proves that Synchronous Propagation is sufficient to guarantee the Compound Memory Consistency Model for a wide class of protocols. Our work provides long-needed assurance for current designs and delivers a reusable, compositional framework for verifying future heterogeneous systems.