Theorem proving by analogy — A compelling example

Abstract

This paper shows how a new approach to theorem proving by analogy is applicable to real maths problems. This approach works at the level of proof-plans and employs reformulation that goes beyond symbol mapping. The Heine-Borel theorem is a widely known result in mathematics. It is usually stated in R1 and similar versions are also true in R2, in topology, and metric spaces. Its analogical transfer was proposed as a challenge example and could not be solved by previous approaches to theorem proving by analogy. We use a proof-plan of the Heine-Borel theorem in R1 as a guide in automatically producing a proof-plan of the Heine-Borel theorem in R2 by analogy-driven proof-plan construction.