By induction on the depth of the subtrees we first define for each nonterminal n a function ρ n from all nonterminal nodes dominated by n into R such that (a) ρ n licenses the subtree of c with root n, Suppose n with dts(n) = n 1 ..n m is expanded by ρ n = A:t:IR → X 1 :t 1 :IR 1 ..X m :t m :IR m in c , then there is a rule r ∈ R satisfying the conditions of Definition 16(ii).
r ex- IR j , and (r, (n, dts(n))[ψ]) = (r, (t, t 1 ..t m )) by definition of ψ.