See if you have the statement right.
Meanwhile, a good strategy for any Schwarz problem is to construct a function satisfying the hypotheses of the lemma. Then everything frequently falls nicely onto your lap.
You need an analytic function \to D" alt="h \to D" /> sending 0 to 0.
(Question: why did I scale by one half?)
This may not lead where you want (especially since at the moment the conclusion you seek is unclear), but constructing something like this is usually a good first step.
Verify that satisfies the hypotheses of the lemma and apply it. See what happens.