> He says that once you have a hierarchical proof, you can use pieces of it in new proofs very easily. For example, if you want to change one assumption slightly or focus on solutions that have different properties, you will be able to tell very easily which parts of the proof can stay the same and which parts will need to change.
If only that were true of a piece of LaTeX moved from one place to another, haha!
If you move a piece of LaTeX from your prose to another proof, there's nothing at all there to help you ensure you get it right. I think the point here is this hierarchical system allows you to very easily discover what parts of the proof depend on what other parts, so if you make a change to one part, you can "invalidate" everything that depended on it easily. With prose, you have no assistance in figuring out what pieces of the proof need to be updated for any given change.
If only that were true of a piece of LaTeX moved from one place to another, haha!