Can I change a Lemma to a Proposition?

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I am getting confused about one thing:

I am reading a paper say X. Paper X has a Lemma in it. I am also writing a paper for my dissertation. I want to use the Lemma from Paper X in proving a theorem in my paper.

While quoting Lemma from paper X, do I need to state the Lemma as Lemma in my dissertation, or I can write it as a Proposition.

My question is simple: While citing a Lemma from a paper, is it required to call it as Lemma in my dissertation too? Or I can cite the Lemma but name it as Proposition in my paper?

If someone could tell me what is the standard procedure here, I shall be grateful.

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You can cite Lemma 2.3 from paper X, and, when quoting it, write it as Proposition 8.7.

For example:

 “...<in-text citation of Lemma 2.3> (which we reproduce here as Proposition 8.7).”