For me the barrier to proving the "hard bits" was never that I couldn't reason about it—I quite enjoyed formal methods in school, and when introduced to them by coworker's who'd done similar—but it was that I didn't have the time to dedicate to learning enough about how to model my problem in a particular new language or system when none of my coworkers were spending such time and my boss wasn't already convinced.

The AI tools are great at lowering the learning curve by changing "how would I possibly express this" to "ah, let's see if this expression of it is actually right?" and "hm, is there a simpler way to express the same thing?"

Like StackOverflow for javascript questions, but for an area that was far to obscure to have a good library of example answers.

I'm not looking to prove the entirety of every system. Usually just some core bits. And often not connected automatically to the code (which may not be gonna change much).