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)
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)