Suppose I am writing a paper in which an important lemma has a proof which is either long and unenlightening or requires additional background of the reader (or both). Thus, to avoid disrupting the narrative flow, I want to postpone the proof of the lemma to a later section. So I have a lemma in section 3 (say) whose proof is postponed to section 7 (say). And in section 7, I restate the lemma before proving it.
Now I can think of three ways to assign numbers to the lemma:
- The statement in section 3 and the restatement in section 7 each get their own number. Thus we have Lemma 3.4 and Lemma 7.2 which are identical.
- The restatement in section 7 gets the same number as the original statement in section 3. Thus we have only Lemma 3.4, which is stated in section 3 and then restated with the same number and proven in section 7.
- The statement in section 3 gets the same number as the restatement in section 7. Thus we have only Lemma 7.2, which is stated and proven in section 7, and also stated with a forward reference in section 3.
(Some questions on tex.stackexchange here and here explain how to accomplish the latter two options technically.)
Which of these options is preferable?
Edit: Note that the first statement of the lemma is in section 3. This is not the introduction (at least, I've never read a paper where section 3 was the introduction). The situation of stating one or more of the paper's main theorems in the introduction is similar, but not quite the same.
Best Answer
It depends on what you want for your reader, who will be referred to it a number of times, I suppose. I would rather choose the second option, because I assume you explain why it is so important when it first appears, so the reader should be constantly referred to that occurrence, and not to the cumbersome demonstration.