Automated methods for formal proofs in simple arithmetics and algebra (Automatische Methoden für formale Beweise in einfachen Arithmetiken und Algebren)

In an LCF-like theorem prover, any proof must be produced from a small set of inference rules. The development of automated proof methods in such systems is extremely important. In this thesis we study the following question: How should we integrate a proof procedure in an LCF-like theorem prover, both in general and in the special case of arithmetics? We investigate three integration paradigms and present several proof procedures. These include universal and weak existential problems over rings, universal polynomial problems over the reals, quantifier elimination for parametric linear problems over ordered fields, Presburger arithmetic, mixed real-integer linear arithmetic, algebraically and real closed fields. Our work has been carried out in the Isabelle framework.

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