The Theorem Prover Follows the Library's Dependency Trails

A useful lemma may be several proof dependencies away from anything that looks lexically similar to the theorem at hand. LeanGraphSearch builds a graph from Mathlib's forward dependencies, spreads relevance from semantically matched declarations and reranks the expanded candidates. Across two retrieval benchmarks, the authors report recall gains of up to 12 percent over LeanSearch v2 and coverage of additional complete proof routes. In iterative Lean-guided proving, pass rates improved by as much as 40 percent over the vanilla prover and at most 10 percent over LeanSearch v2 at matched reflection-turn budgets. The gains are benchmark-bound, but they connect better retrieval to machine-checked downstream proofs.