I like that. That's a powerful argument! For it to work, it requires that every number be returned as part of the result, and that all calculations are monoton

I like that. That's a powerful argument! For it to work, it requires that every number be returned as part of the result, and that all calculations are monotonically increasing, as you said. Most algorithms won't have those invariants, but perhaps you can tweak them until they do. Once you have, you can extend an infinite-width proof to a finite-width proof.