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Instead of simply referring to a Lemma from another paper I want to

  • copy it to my paper (using my Lemma numbering),
  • cite it's original source and
  • provide a proof of my own which might differ from the original proof in notation (it is adapted to my notation) and might slightly differ from the original proof in substance.

Is this good practice? Or should I simply cite the Lemma from the other paper?

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    Sounds good to me. I hate papers where to follow the train of thought you have to have 20 expensive PDFs at hand just to see what on Earth were they referring to. A double whammy when the author does this reference-only approach with obscure lemmas. A triple whammy is when their reasoning is subtly wrong or incomplete because the lemma isn't visually integrated into the narrative, and even reviewers miss that because nobody has time to hunt down dozens of papers just to review some often inconsequential paper. – Kuba hasn't forgotten Monica Jun 11 at 1:07
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You can use other paper's Lemma as long as you give the proper credit to it. This is what science is all about.

All your options are valid, and might fit in different situations. However, even if you give your own proof, you should give credit to the original proof (stating that your proof is different / better/ clearer).

Maybe to be clear, I usually do this:

  • If the lemma is secondary, I just refer to the other paper.
  • If the Lemma is important, but the details are not, I cite it and refer to the other paper for details.
  • If the Lemma is crucial, I state it formally with all the parameters and details. If the statement I use is exactly the same as the lemma in the other paper, I refer to the proof there. If it is slightly different, I acknowledge the other Lemma and state that "my" lemma is a simple variant of it. I add a proof when needed.

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