# Lemma or proposition?

Let statement 1 be an obvious consequence of the statement 2. Let the statement 1 go before the statement 2 in the text. The statement 1 is actually used to prove statement 2.

I label the statement 2 as a theorem.

Should statement 1 be labeled as a proposition or a lemma?

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How can statement 1 be an obvious consequence and be used to prove statement 2? Sounds like there might be a circularity in your argument. –  Emilio Ferrucci Apr 28 '12 at 16:58
@Emilio: Statement 1 is an obvious consequence of statement 2 but in the actual text statement 2 goes after the statement 1 and the statement 2 is not used in the actual proof of statement 1. –  porton Apr 28 '12 at 16:59
There's lots of debate and gray area on what's a lemma and what's a proposition and what's a corollary, but in this case I would call Statement 1 a lemma and make a remark after statement 2 to the effect that statement 1 is an obvious corollary of statement 2 but is used in the proof of statement 2. –  user29743 Apr 28 '12 at 17:02
Yes I agree with this, all that really counts is that statement 1 is used in the proof of statement 2, and if you think 2 is more important call 1 a lemma and 2 a theorem. –  Emilio Ferrucci Apr 28 '12 at 17:09
@porton : I think you have your "1" and "2" interchanged. –  Michael Hardy Apr 28 '12 at 17:49