Certified Kruskal's Tree Theorem

Abstract

This article presents the first formalization of Kurskal's tree theorem in aproof assistant. The Isabelle/HOL development is along the lines of Nash-Williams' original minimal bad sequence argument for proving the treetheorem. Along the way, proofs of Dickson's lemma and Higman's lemma, as well as some technical details of the formalization are discussed.

Keywords

• almost-full relations
• well-quasi-orders
• Dickson's lemma
• HIgman's lemma
• Kruskal's tree theorem
• minimal bad sequences