Normality of meromorphic functions whose derivatives have 1-points

Let k be a positive integer and let ${\mathcal F}Let k be a positive integer and let F{\mathcal F} be a family of functions meromorphic in a plane domain D, all of whose zeros have multiplicity at least k + 3. If there exists a subset E of D which has no accumulation points in D such that for each function f ? F{f\in\mathcal F}, f ^(k)(z) − 1 has no zeros in D\E{D\setminus E}, then F{\mathcal F} is normal. The number k + 3 is sharp. The proof uses complex dynamics.