# A machine-checked direct proof of the Steiner-lehmus theorem

@article{Kellison2021AMD, title={A machine-checked direct proof of the Steiner-lehmus theorem}, author={Ariel E. Kellison}, journal={Proceedings of the 11th ACM SIGPLAN International Conference on Certified Programs and Proofs}, year={2021} }

A direct proof of the Steiner-Lehmus theorem has eluded geometers for over 170 years. The challenge has been that a proof is only considered direct if it does not rely on reductio ad absurdum. Thus, any proof that claims to be direct must show, going back to the axioms, that all of the auxiliary theorems used are also proved directly. In this paper, we give a proof of the Steiner-Lehmus theorem that is guaranteed to be direct. The evidence for this claim is derived from our methodology: we haveβ¦Β

## References

SHOWING 1-10 OF 15 REFERENCES

### The Steiner-Lehmus angle-bisector theorem

- MathematicsThe Mathematical Gazette
- 2014

In 1840 C. L. Lehmus sent the following problem to Charles Sturm: βIf two angle bisectors of a triangle have equal length, is the triangle necessarily isosceles?β The answer is βyesβ, and indeed weβ¦

### A Common Axiom Set for Classical and Intuitionistic Plane Geometry

- PhilosophyAnn. Pure Appl. Log.
- 1998

### βOutsideβ as a primitive notion in constructive projective geometry

- Mathematics
- 1996

In intuitionistic (or constructive) geometry there are positive counterparts, βapartβ and βoutsideβ, of the relations β=β and βincidentβ. In this paper it is shown that the relation βoutsideββ¦

### Implementing mathematics with the Nuprl proof development system

- Mathematics
- 1986

This ebook presents full variant of this ebook in DjVu, PDF, ePub, doc, txt forms, and on the website you may read guides and different art eBooks online, either downloading or downloading.

### Implementing Euclidβs straightedge and compass constructions in type theory

- MathematicsAnnals of Mathematics and Artificial Intelligence
- 2018

Constructions are central to the methodology of geometry presented in the Elements. This theory therefore poses a unique challenge to those concerned with the practice of constructive mathematics:β¦

### Parallel Postulates and Continuity Axioms: A Mechanized Study in Intuitionistic Logic Using Coq

- MathematicsJournal of Automated Reasoning
- 2017

In this paper we focus on the formalization of the proofs of equivalence between different versions of Euclidβs 5th postulate. Our study is performed in the context of Tarskiβs neutral geometry, orβ¦