Yeah, if you have a formal proof of something but you don't know exactly what then you might as well vibe code the system itself. I've been wondering if it would be possible to formally define a property (like deadlock freedom or linearizability) and then vibe-code the spec (and associated implementation).

I don't know if that's possible but it seems like that's where the value would be.

It is but we're not there yet. You can use a refinement style system like Verus in which your spec is a very high level statement of system behavior, like "this system provides the properties that paxos is supposed to guarantee"(1), and then be guaranteed that the things that implement it are preserving that spec.

But this is still double black diamond expert territory - it remains a challenging thing to identify ways to state and refine those properties to enable the proof. But it's getting easier by the year and the LLMs are getting more useful as part of it.

https://github.com/verus-lang/verus

(1) You would have to state the consistency and conditional liveness properties directly, of course, as Verus doesn't understand "what paxos does". That would look like TLA+-style statements, "at some time in the future, a command submitted now will be executed, etc."