A weaker version of a published theorem with a simpler method; what should be done? A paper contains three theorems. After submitting the paper, the author finds out that one of their theorems was already published by someone else with stronger result. Although their result is not as strong, the author’s method is much simpler.

They have two choices:


Keep the theorem and mention the result already done, and state that the method in current paper is simpler.
Just drop the theorem from the paper, and keep 2 theorems instead. 


Given that they have already submitted the paper, the author just has to wait for referee's report. So their choice will come after the decision of the referee. 

What would be the best choice?
Choice 1 seems pretty clear. It is honest about prior work (existing theorem) and the contribution (new proof).

You could also inform the editor that you have found a theorem that someone else has done, but that you believe your proof to be novel. This will allow the editor to better judge your work.