Implicit Function Theorem. Part II

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Summary

In this article, we formalize differentiability of implicit function theorem in the Mizar system [3], [1]. 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 [6] is cited. We referred to [10], [11], and [2] in the formalization.

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  • [9] Hideki Sakurai Hiroyuki Okazaki and Yasunari Shidama. Banach’s continuous inverse theorem and closed graph theorem. Formalized Mathematics 20(4):271–274 2012. doi:10.2478/v10037-012-0032-y.

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