“…In this case, consider ζ = f −qm (ζ) and ζ = f −qm+2 (ζ ) and the corresponding interval J = f −qm−qm+2 (J −i ), and apply Lemma 3.7. Then either ζ ∈ D m+1 , in which case the induction step is complete, or else dist (ζ , I m+1 ) ≤ C|I m | and angle (ζ , J ) ≥ ε 1 , in which case we can apply the same argument leading to (2) and (3).…”