In this article, we formalize differentiability of implicit function theorem in the Mizar system , . In the first half section, properties of Lipschitz continuous linear operators are discussed. Some norm properties of a direct sum decomposition of Lipschitz continuous linear operator are mentioned here.
In the last half section, differentiability of implicit function in implicit function theorem is formalized. The existence and uniqueness of implicit function in  is cited. We referred to , , and  in the formalization.
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