“We prove a theorem that …” or “We prove the theorem that …”?

One of my papers proves a theorem. And in the abstract I want to introduce what I do in this paper, so I began with "We prove A theorem that ...". But then I was aware of this: Could it be "We prove THE theorem that ..."?

Which one is the correct one?

• If it is an introduction, wouldn't you write "We will prove..."? – user3169 Sep 12 '14 at 3:01

I think it depends on whether the rest of your sentence fully or only partly describes the theorem. Compare:

We prove the theorem that all cats enjoy Grieg

with

We prove a theorem that shows the relationship between pet species and appreciation of Norwegian classical composers

In the first case it wouldn't make sense to say a theorem because there isn't more than one to choose from: you've exactly stated what the theorem is, so it's the theorem. In the second case there could be many theorems fitting that description, so it's a.

• I agree with that. From wikipedia: "a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms." If you say "we prove a theorem about the relation between A and B" then "a" is correct, whereas if you say "we prove the theorem that B always follows from A" then "the" seems better. – painfulenglish Sep 12 '14 at 7:46
• I see what you meant. And the clause describing "theorem" is indeed partly describes the theorem that I proved, so right, using "a" is more legitimate than using "the". Thanks so much! – Megadeth Sep 12 '14 at 7:53

Since you're introducing the theorem to the reader, I believe you should use the indefinite article.

We prove a theorem that...

Looking for examples at Google Books, I found dosens of instances using the indefinite article in similar contexts, such as:

We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. (COLING-92: proceedings of the 15th International Conference on Computational Linguistics)

or:

In his 1857 paper, Kummer proved a theorem which assured that FLT holds for a certain class of irregular primes (see Lecture VII). (13 Lectures on Fermat's Last Theorem, page 200)

• Ah, appreciated. :) I see, I see. – Megadeth Sep 12 '14 at 3:18