From Tarski to Hilbert

Abstract. In this paper, we report on the formal proof that Hilbert’s axiom system can be derived from Tarski’s system. For this purpose we mechanized the proofs of the first twelve chapters of Schwabäuser, Szmielew and Tarski’s book: Metamathematische Methoden in der Ge-ometrie. The proofs are checked formally within classical logic using the Coq proof assistant. The goal of this development is to provide clear foundations for other formalizations of geometry and implementations of decision procedures.