Our goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and automated reasoning perspective and give an in-depth analysis for a sample textbook proof. We propose a framework for natural language proof understanding that extends and integrates state-of-the-art technologies from Natural Language Processing (Discourse Representation Theory) and Automated Reasoning (Proof Planning) in a novel and promising way, having the potential to initiate progress in both of these disciplines.