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The Unified Modeling Language (UML) is an industry standard for modeling analysis and design. However, the semantics of UML is not precisely defined and the correctness of refinement relations cannot be verified. In this study, we use the theorem proof assistant Coq to formalize and mechanize the semantics of UML-Statecharts and the refinement relations between models. Based on the mechanized semantics, the desired properties of both the semantics and the refinement relations can be described and proven as predicates and lemmas. This approach provides a promising way to obtain certified fault-free modeling and refinement.