Mechanical theorem proving in Tarski's geometry

Authors:
Julien Narboux
Affiliations:
Équipe LogiCal, LIX, École Polytechnique, Palaiseau Cedex, France
Venue:
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Year:
2006

Citing 6
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Abstract

This paper describes the mechanization of the proofs of the first height chapters of Schwabäuser, Szmielew and Tarski's book: Meta-mathematische Methoden in der Geometrie. The proofs are checked formally using the Coq proof assistant. The goal of this development is to provide foundations for other formalizations of geometry and implementations of decision procedures. We compare the mechanized proofs with the informal proofs. We also compare this piece of formalization with the previous work done about Hilbert's Grundlagen der Geometrie. We analyze the differences between the two axiom systems from the formalization point of view.