Tarski's Geometry and the Euclidean Plane in Mizar
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چکیده
We discuss the formal approach to Tarski geometry axioms modelled with the help of the Mizar computerized proof assistant system. We try however to go much further from the use of simple predicates in the direction of the use of structures with their inheritance, attributes as a tool of more human-friendly namespaces for axioms, and registrations of clusters to obtain more automation (with the possible use of external equational theorem provers like Otter/Prover9). The formal proof that Euclidean plane satisfies all eleven axioms proposed by Tarski is an essential development, allowing to show the independence of the parallel postulate, one of the items from “Top 100 mathematical theorems”.
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تاریخ انتشار 2016