Help understanding a theorem Kleinberg proves related to sequence alignment


This is from Kleinberg’s Algorithm Design text (Theorem 6.14)

Let $ M$ be an alignment of $ X$ and $ Y$ . If $ (m, n) \notin M$ , then either the $ m^{\text{th}}$ position of $ X$ or the $ n^{\text{th}}$ position of $ Y$ is not matched in $ Y$ .

The theorem does not state that $ m, n$ must be the last elements of $ X$ and $ Y$ respectively, but earlier, when introducing the topic, he uses $ m, n$ to denote the last entries of the two strings. Which of these is correct?