<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p><p>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.</p></abstract>

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.

Implicit Function Theorem. Part II

Formalized Mathematics

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{"article-title":"Implicit Function Theorem. Part II"}

In this article, we formalize differentiability of implicit function theorem in the Mizar system [3], [1]. In the first half section, properties of Lipschitz...

隐函数定理。第二部分

在线发布:2019年7月20日

页面范围： 117 - 131

认可的:2019年5月27日

DOI（操作界面）： https://doi.org/10.2478/forma-2019-0013

关键词
隐函数定理,利普希茨连续性,可微性,隐函数

©2019 Kazuhisa Nakasho等人，由Sciendo出版

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