lean2

Homotopy type theory (HoTT) https://en.wikipedia.org/wiki/Homotopy_type_theory /? From a set like {0,1} to a wave function of reals in Hilbert space [to Constructor Theory and Quantum Counterfactuals] https://www.google.com/search?q=From+a+set+like+%7B0%2C1%7D+... , https://www.google.com/search?q=From+a+set+like+%7B0%2C1%7D+... From "What do we mean by "the foundations of mathematics"?" (2023) https://news.ycombinator.com/item?id=38102096#38103520 : > HoTT in CoQ: Coq-HoTT: https://github.com/HoTT/Coq-HoTT >>> The HoTT library is a development of homotopy-theoretic ideas in the Coq proof assistant. It draws many ideas from Vladimir Voevodsky's Foundations library (which has since been incorporated into the UniMath library) and also cross-pollinates with the HoTT-Agda library. See also: HoTT in Lean2, Spectral Sequences in Lean2, and Cu

Homotopy type theory is a mathematical foundation, like set theory, or Martin Lof's type theory. This is different from a proof assistant like Coq or Lean. In fact, Lean has a library which implements part of HoTT (see https://github.com/leanprover/lean2/blob/master/hott/hott.md). In short, there is no comparison between Lean and HoTT.