Many of the current software systems rely on garbage collectors for automatic memory management. This is also the case for various software systems in real-time appli-cations. However, a real-time application often requires an incremental working style of the underlying garbage collection, which renders the garbage collector more complex and less trustworthy. We present a formal veriˉcation of the Yuasa incremental garbage collector in Hoare-style logic. The speciˉcation and proof of the collector are built on a concrete machine model and cover detailed behaviors of the collector which may lead to safety prob- lems but are often ignored in high-level veriˉcations. The work is fully implemented with the Coq proof assistant and can be packed as foundational proof-carrying-code packages.Our work makes an important step toward providing high-assurance garbage collection for mission-critical real-time systems.