I was working(in maths) for some months on a paper. After I got the results, I found out that some of those were already obtained in another paper that was not very related to my topic. In fact, in that paper, the result is stated as of ‘minor’ importance because the main purpose of the paper was quite different. It is the technique that he used to prove this, the one that I rediscovered and used in my paper to prove this result and others in the same domain. Due to this, I didn’t have a reason to search there in the first place. Although I have other results in my paper, this one was one of the main ones. Of course, I want to cite the old paper. Hence my questions:

- Is it worth publishing this with a proof?
- Assume now that I do publish it with proof. Is a phrase like: “Although we arrive at this result independently, it turns out that this was already obtained in [Ref]” acceptable in the paper?
- Is there a more correct way than the phrase above to cite the old paper?