In a practical sense, hasn't type theory already replaced ZFC in the foundations of math? Lean is what working mathematicians currently use to formally prove theorems, and Lean is based on type theory rather than ZFC.

But HoTT is removed from lean core?

From https://news.ycombinator.com/item?id=42440016#42444882 :

> /? Hott in lean4 https://www.google.com/search?q=hott+in+lean4

https://github.com/forked-from-1kasper/ground_zero :

> Lean 4 HoTT Library

Still, both should be taught.

"Should Type Theory Replace Set Theory as the Foundation of Mathematics?" (2023) https://link.springer.com/article/10.1007/s10516-023-09676-0