For all my skepticism towards using LLM in programming (I think that the current trajectory leads to slow degradation of the IT industry and massive loss of expertise in the following decades), LLM-based advanced proof assistants is the only bright spot for which I have high hopes.

Generation of proofs requires a lot of complex pattern matching, so it's a very good fit for LLMs (assuming sufficiently big datasets are available). And we can automatically verify LLM output, so hallucinations are not the problem. You still need proper engineers to construct and understand specifications (with or without LLM help), but it can significantly reduce development cost of high assurance software. LLMs also could help with explaining why a proof can not be generated.

But I think it would require a Rust-like breakthrough, not in the sense of developing the fundamental technology (after all, Rust is fairly conservative from the PLT point of view), but in the sense of making it accessible for a wider audience of programmers.

I also hope that we will get LLM-guided compilers which generate equivalency proofs as part of the compilation process. Personally, I find it surprising that the industry is able to function as well as it does on top of software like LLVM which feels like a giant with feet of clay with its numerous miscompilation bugs and human-written optimization heuristics which are applied to a somewhat vague abstract machine model. Just look how long it took to fix the god damn noalias atrtibute! If not for Rust, it probably would've still been a bug ridden mess.