Recently I am writing something up for possible publication. I am struggling with this question:
What is the most appropriate way to cite others' results as a Lemma?
For example, this is a theorem of Arhangelskii's:
Theorem 3.7 Suppose that $X$ is a regular space with a strong rank 1-digonal. Then any bounded subset $Y$ of $X$ is a Moore space.
I want to cite his theorem, however I don't need so much. (Note that if $X$ is a pseudocompact, then it is bounded.) I think if I cite the original theorem, it seems wordy, since I will need to explain not only pseudocompactness but also bounded set. Indeed, I want to write a Lemma as follows:
Lemma [I will note where it is from]: Suppose that $X$ is a regular pseudocompact space with a strong rank 1-diagonal. Then $X$ is a Moore space.
Could I directly do this?
Thanks for your help.