Mechanization of Incidence Projective Geometry in Higher Dimensions, a Combinatorial Approach

Abstract

Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present a few examples of incidence geometry theorems in dimensions 3, 4, and 5. We then prove them with the help of a combinatorial prover based on matroid theory applied to geometry.

Towards Automatic Transformations of Coq Proof Scripts

“…Even though our framework can be used to implement other proof script transformations, this one is of special interest to us. Indeed, we recently designed a prover for projective incidence geometry [3,12] which relies on the concept of rank to carry out proofs of geometric theorems such as Desargues or Dandelin-Gallucci automatically. This prover produces a trace (a large Coq proof script containing several statements and their proofs).…”

“…We recently developed a new way [3,12], based on ranks, to automatically prove statements in projective incidence geometry. Our approach works well but produces proof scripts which are very large and often feature several auxiliary lemmas.…”