Reflections on Trusting Lean
arXiv:2610.30433
Abstract
It is known, by works of Werner and Carneiro, that the type theory of Lean (and indeed of CIC plus a version of choice) is equiconsistent with ZFC plus "there are infinitely many strongly inaccessible cardinals". We prove a finer connection between these two formal systems; namely, given any formula in the language of second order arithmetic, that formula is provable in the aforementioned extension of ZFC if and only if the same formula, when viewed as a type in Lean, is inhabited.
arXiv commentThis work has been presented at ICMS 2026 on 23 July 2026