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

@article{Wirth2009ProgressIC, title={Progress in Computer-Assisted Inductive Theorem Proving by Human-Orientedness and Descente Infinie?}, author={Claus-Peter Wirth}, journal={ArXiv}, year={2009}, volume={abs/0902.3294} }

In this position paper we briefly review the development hist ory of automated inductive theorem provingandcomputer-assisted mathematical induction . We think that the current low expectations on progress in this field result from a faulty na rrow-scope historical projection. Our main motivation is to explain — on an abstract but hopeful ly sufficiently descriptive level — why we believe that future progress in the field is to re sult from human-orientedness anddescente infinie .

## 4 Citations

Sequent calculus proof systems for inductive definitions

- Mathematics, Computer Science
- 2006

These systems are formulated as sequent calculi for classical first-order logic extended with a framework for (mutual) inductive definitions, and it is shown how the formulation of both systems can be generalised to obtain soundness conditions for a general class of infinite proof systems and their corresponding cyclic restrictions.

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

- Computer ScienceArXiv
- 2009

This paper presents the only proof of Pierre Fermat by descente infinie that is known to exist today and develops a self-contained proof in a modern form, which nevertheless is intended to follow Fermat's ideas closely.

Automation of Mathematical Induction as part of the History of Logic

- MathematicsFLAP
- 2017

The history of the automation of mathematical induction is reviewed and the role of computer programming in this work is reviewed.

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