Computer-assisted human-oriented inductive theorem proving by descente infinie - a manifesto

Progress in Computer-Assisted Inductive Theorem Proving by Human-Orientedness and Descente Infinie?

In this position paper we briefly review the development history of automated inductive theorem proving and computer-assisted mathematical induction. We think that the current low expectations on progress in this field result from a faulty narrow-scope historical projection. Our main motivation is to explain—on an abstract but hopefully sufficiently descriptive level—why we believe that future ...

Descente Infinie + Deduction

Although induction is omnipresent, inductive theorem proving in the form of descente infinie has not yet been integrated into full first-order deductive calculi. We present such an integration that even works for higher-order logic. This integration is based on lemma and induction hypothesis application for free variable sequent and tableau calculi. We discuss the appropriateness of these types...

History and Future of Implicit and Inductionless Induction: Beware the Old Jade and the Zombie!

In this survey on implicit induction I recollect some memories on the history of implicit induction as it is relevant for future research on computer-assisted theorem proving, esp. memories that significantly differ from the presentation in a recent handbook article on “inductionless induction”. Moreover, the important references excluded there are provided here. In order to clear the fog a lit...

A Self-Contained and Easily Accessible Discussion of the Method of Descente Infinie and Fermat's Only Explicitly Known Proof by Descente Infinie

We present the only proof of PIERRE FERMAT by descente infinie that is known to exist today. As the text of its Latin original requires active mathematical interpretation, it is more a proof sketch than a proper mathematical proof. We discuss descente infinie from the mathematical, logical, historical, linguistic, and refined logic-historical points of view. We provide the required preliminarie...

Mathematical Induction by Descente Infinie