I met with a problem in the proof of Theorem 1.3 in page 14 of "Combinatorics and Graph Theory", 2nd Edition, John Harris, Jeffry L. Hirst, Michael Mossinghoff. The proof is excerpted as follows:
My problem comes from the claim $v'=v_i=w_i$ underlined with a red line. Why $v_i$ and $w_i$ must have the same subscript $i$? Thank you.