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

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.