There could be two ways:
- The creatures 'theorem', 'lemma', ... remain separate. So, Theorem 2 can come after Lemma 5, because they are separately numbered. OR
- A consolidated numbering scheme, e.g., Theorem 1, Lemma 2, Lemma 3, Theorem 4, ... But in this case, a reader does not know at the end of the paper how many theorems (or lemmata) the paper has just by looking at the last theorem number, while in the previous scheme, she does.
My question is not to debate about which one is better than other. Rather, I want to know under what circumstances which one of these schemes are more meaningful. Naturally, I used one scheme and my coauthor wanted the other scheme -- while we can converge to any, I want to be sure which one applies where.