The Heine–Borel Challenge Problem. In Honor of Woody Bledsoe

Woody Bledsoe’s last challenge problem is the analogical transfer of the Heine–Borel theorem for real intervals to the two-dimensional case. This could not be solved by the up-to-then-known techniques of analogical theorem proving. The Heine–Borel theorem is a widely known result in mathematics. It is usually stated in the field of real numbers R1, and similar versions are also true in R2, in topology, and in metric spaces. This article shows how analogy-driven proof plan construction is applicable to this genuinely mathematical problem. Our goal here was to use a source proof plan of HB1 (the Heine–Borel theorem in R1) as a guide to automatically produce a proof plan of HB2 (the Heine–Borel theorem in R2). We were able to accomplish our goal by generating the target proof plan of HB2 by reformulation and analogical replay.