For k ≥ 2, assume that (i), (ii) and (iii) holds for any derivation of length less than k. [Proof of (i)] If A G k ⇒ α, then the rule used at the first step must be of the form A → B(C).
a Here, we have to think of the two cases: (1) yield(γ) = λ and (2) yield(γ) = λ.