Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 4I / iii / Solution

In every derivation beginning at $wA$, the terminal prefix $w$ remains unchanged because no production has a terminal on its left-hand side. By the sentential-form result, each step rewrites the sole variable at the right and appends terminals immediately before its successor variable. Henceforces $v=wu$ for some $u\in {\Sigma }^{\ast }$. Removing the inert prefix $w$ from every sentential form in the derivation gives