Summary

Yosef Karo Shulchan Aruch — Yoreh Deah 115Laws of Milk…

But if a non-Jew takes a break, the Jew needs to be there, because it is like the case of the non-Jew's house. And even a Jewish child will suffice, because the non-Jew appears before him. In any case, if a Jew is not present until after he has finished milking, this milk is considered the milk of non-Jews that is forbidden, even thought no non-kosher animal exists in his herd. Milk of a non-Jew makes vessels non-kosher when they are cooked in them, just as any prohibited food, even though this is only an uncertainty whether he has mixed in something non-kosher.
Source: Wikisource

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