Aristotle API Aids Lean 4 Formalisation of IMO 2009 Grasshopper Problem

A recent preprint on arXiv (2605.20120) presents a case study utilizing the Aristotle API to aid in theorem proving within Lean 4, specifically addressing the Grasshopper problem from IMO 2009 Problem 6. The artifact generated by AI articulates a generalized version of the theorem in Lean and features four verified lemmas that address local aspects of a maximality and adjacent-swap exchange strategy. These lemmas demonstrate that the final partial sum matches the total sum, that an adjacent transposition influences only the relevant intermediate partial sum, that the altered partial sum takes the anticipated form, and that maximality at a position allowing an adjacent successor swap enforces a corresponding forbidden condition. Nevertheless, the principal theorem remains unproven, marked by an unresolved 'sorry'. This study underscores both the strengths and weaknesses of AI-assisted theorem proving in olympiad-level mathematics.