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If we can show that <math>g^{-1}</math>, and consequently the composition, is analytic, we then have a conformal mapping of <math>D_1</math> onto <math>D_2</math>, proving "any two simply connected regions different from the whole plane <math>\mathbb C</math> can be mapped conformally onto each other."
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{{main|Schwartz's Lemma}}
The '''Schwarz lemma''', named after [[Hermann Amandus Schwarz]], is a result in [[complex analysis]] about [[holomorphic functions]] from the [[open set|open]] [[unit disk]] to itself. The lemma is less celebrated than stronger theorems, such as the [[Riemann mapping theorem]], which it helps to prove. It is however one of the simplest results capturing the rigidity of holomorphic functions.
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