Simple Type Theory is not too Simple: Grothendieck’s Schemes Without Dependent Types

Automated mathematics and the reconfiguration of proof and labor

“…It is also worth noting that the difficulty of encoding theorems in a given system may vary depending on its axiomatic foundations. In 2021, Anthony Bordg, Lawrence Paulson, and Wenda Li formalized Grothendieck's schemes in Isabelle, despite the difficulty of doing so with Isabelle's higher-order logic, which is weaker than Lean's dependent type theory [15].…”