# Towards Intuitive Reasoning in Axiomatic Geometry

## TL;DR

This paper discusses an approach to make reasoning in axiomatic geometry more intuitive by integrating automated theorem proving with an interactive system that accepts natural language, facilitating teaching and learning.

## Contribution

It introduces the Elfe system, which combines natural language input with ATP to simplify formalization and proof development in axiomatic geometry for educational purposes.

## Key findings

- Automated theorem provers can now efficiently prove many intermediate lemmas.
- Elfe enables formalized geometric proofs using natural language, easing learning.
- The approach supports teaching axiomatic geometry without prior formalization experience.

## Abstract

Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean they can prove many of these intermediate lemmas. The interactive theorem prover Elfe accepts mathematical texts written in fair English and verifies them with the help of ATP. Geometrical texts can thereby easily be formalized in Elfe, leaving only the cornerstones of a proof to be derived by the user. This allows for teaching axiomatic geometry to students without prior experience in formalized mathematics.