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http://hdl.handle.net/11320/15401
Tytuł: | Differentiation on Interval |
Autorzy: | Endou, Noboru |
Słowa kluczowe: | differentiation on closed interval chain rule |
Data wydania: | 2023 |
Data dodania: | 9-paź-2023 |
Wydawca: | DeGruyter Open |
Źródło: | Formalized Mathematics, Volume 31, Issue 1, Pages 9-21 |
Abstrakt: | This article generalizes the differential method on intervals, using the Mizar system [2], [3], [12]. Differentiation of real one-variable functions is introduced in Mizar [13], along standard lines (for interesting survey of formalizations of real analysis in various proof-assistants like ACL2 [11], Isabelle/HOL [10], Coq [4], see [5]), but the differentiable interval is restricted to open intervals. However, when considering the relationship with integration [9], since integration is an operation on a closed interval, it would be convenient for differentiation to be able to handle derivates on a closed interval as well. Regarding differentiability on a closed interval, the right and left differentiability have already been formalized [6], but they are the derivatives at the endpoints of an interval and not demonstrated as a differentiation over intervals. Therefore, in this paper, based on these results, although it is limited to real one-variable functions, we formalize the differentiation on arbitrary intervals and summarize them as various basic propositions. In particular, the chain rule [1] is an important formula in relation to differentiation and integration, extending recent formalized results [7], [8] in the latter field of research. |
Afiliacja: | National Institute of Technology, Gifu College, 2236-2 Kamimakuwa, Motosu, Gifu, Japan |
URI: | http://hdl.handle.net/11320/15401 |
DOI: | 10.2478/forma-2023-0002 |
ISSN: | 1426-2630 |
e-ISSN: | 1898-9934 |
metadata.dc.identifier.orcid: | 0000-0002-5922-2332 |
Typ Dokumentu: | Article |
metadata.dc.rights.uri: | https://creativecommons.org/licenses/by-sa/3.0/ |
Właściciel praw: | © 2023 The Author(s) CC BY-SA 3.0 license |
Występuje w kolekcji(ach): | Formalized Mathematics, 2023, Volume 31, Issue 1 |
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