E with one endpoint in each side, and by assumption, this E, this edge E, participates in some cycle that we're calling capital C. And if you look at the picture, you realize that the claim in this lemma is obvious, t hat, because the cycle has to loop back on itself, if it has an edge with one endpoint on either side, there has to be a path connecting the two dots, connecting those two endpoints back to each other and that path has to cross back for, over this cut A, B. 