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How can I use one stylesheet for multiple sub-sites on my multi-site network?

I have a multi-site WordPress setup. Each sub-site uses it’s own child theme, but there is one stylesheet that has CSS rules that should be used on several of these sub-sites. I do not want to have multiple identical stylesheet files for each sub-site, because when I make changes to it, I would have to make these changes in every instance of the stylesheet, or have to copy-paste it to each sub-site.

How can I tell each sub-site to use just one instance of that stylesheet? Perhaps I can create a style.css file for every sub-site, and inside it, write some kind of redirect to the main style.css (one that actually contains the rules)?