Some time ago, me together with a coauthor submitted a mathematical article to a journal. It was rejected because the anonymous referee found a simpler proof of our main result. He wrote his simpler proof (schematically) in his review. It is indeed simpler, but it is not obvious or trivial by no means.
Also, the simpler proof is only for the main result, which is the main, but not the only result in the article. Other, smaller results are not affected by the simpler proof at all.
Now I am thinking about what to do with this article. I still think that there is some value in our article as it is, even knowing that there is a simpler proof of the main result.
So, I am thinking about the possible options:
Throw away the article completely. Do nothing.
Submit the article to another journal. Include a disclaimer at the beginning or at the end of the article with the full explanation of the situation.
Publish the article on ArXiv without submitting it to any journals. Include a disclaimer at the beginning of the article with the full explanation of the situation.
In the case of options 2 and 3, there is also a question of whether to include in the article the simpler proof itself (not just to indicate its existence, but to give the full proof) attributing it to the anonymous referee. I am thinking not to include it.
Any suggestions about what to do with the article?