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We provide support for polymorphism in static typestate analysis for object-oriented languages with upcasts and downcasts. Recent work has shown how typestate analysis can be embedded in the development of Java programs to obtain safer behaviour at runtime, e.g., absence of null pointer errors and protocol completion. In that approach, inheritance is supported at the price of limiting casts in source code, thus only allowing those at the beginning of the protocol, i.e., immediately after objects creation, or at the end, and in turn seriously affecting the applicability of the analysis. In this paper, we provide a solution to this open problem in typestate analysis by introducing a theory based on a richer data structure, named typestate tree, which supports upcast and downcast operations at any point of the protocol by leveraging union and intersection types. The soundness of the typestate tree-based approach has been mechanised in Coq. The theory can be applied to most object-oriented languages statically analysable through typestates, thus opening new scenarios for acceptance of programs exploiting inheritance and casting. To defend this thesis, we show an application of the theory, by embedding the typestate tree mechanism in a Java-like object-oriented language, and proving its soundness.