I'm writing a mathematical paper. In it, I use a lemma. The lemma is not hard to prove and I have verified it myself. The proof is too tedious to include in the paper, so I want to just include a citation. I found a paper that includes the result. However, that paper does not actually include a proof. I cannot find any other place where this lemma appears.
I see three options:
State the lemma without proof or citation.
State the lemma without proof, but cite the paper (that states the lemma without proof or citation).
Provide a proof of the lemma.
Which is most appropriate? Option 1 is easiest, but might annoy some readers who don't believe me. Option 2 seems like a cop out. Option 3 is safest, but I don't think it's necessary, as the proof is really just a long and boring calculation.
ADDED: To be clear, the lemma is basically an integral. The proof consists of splitting up the domain of integration to remove absolute values, evaluating each of the parts (easy enough for symbolic integration packages like mathematica), and then joining them back up. This is "obvious", but messy because the expressions are quite long. My writeup is two pages.
Maybe a better way to phrase my question: The result is trivial -- I think so, the authors of the other paper think so, and the journal they published in thinks so. Should I still provide a citation? Is it misleading to cite the other paper without clarifying that it doesn't provide a proof?