# 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?