Descente Infinie + Deduction

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

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 ...

Automatic 'Descente Infinie' Induction Reasoning

We present a framework and a methodology to build and analyse automatic provers using the ’Descente Infinie’ induction principle. A stronger connection between different proof techniques like those based on implicit induction and saturation is established by uniformly and explicitly representing them as applications of this principle. The framework offers a clear separation between logic and co...

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

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 fut...