Abstract. Isar is an extension of the theorem prover Isabelle with a language for writing human-readable structured proofs. This paper is an introduction to the basic constructs of this language. 1

We present a complete formalization of the Hahn-Banach theorem in the simply-typed set-theory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for high-level reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.

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A safety-critical system needs fault-tolerant communication between its components. This is especially important for automotive domain, as it consists of distributed real-time systems that are based on the results of the communication. To realize distributed systems with predictable time behavior the time-triggered paradigm is used. According to this paradigm, a time-triggered communication protocol, FlexRay, and an operating system OSEKtime with corresponding communication layer FTCom for the fault-tolerant communication are introduced. In this paper we present the formal specifications of FlexRay and FTCom that allow us to argue about their properties in a precise, formal manner and also infer the collaboration between their properties. 1.

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