Hartshorne Lemma(II 6.1) Hi I am wondering what Hartshorne means by "an open affine subset on which $f$ is regular". This is part of the first sentence in the proof of lemma 6.1 in chapter two of the book "Algebraic Geometry by Hartshorne".  I Tried looking up regular in the index, but this just refers me to regular functions on varieties which as far as I know has absolutely nothing to do with the lemma. Could someone please tell me what he means by this. 
Thanks

"$f$ is regular on $U$" just means $f\in\mathcal{O}(U)$.
