Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

## Darboux's Theorem

Noboru Endou
Shinshu University, Nagano
Katsumi Wasaki
Shinshu University, Nagano
Yasunari Shidama
Shinshu University, Nagano

### Summary.

In this article, we have proved the Darboux's theorem. This theorem is important to prove the Riemann integrability. We can replace an upper bound and a lower bound of a function which is the definition of Riemann integration with convergence of sequence by Darboux's theorem.

#### MML Identifier: INTEGRA3

The terminology and notation used in this paper have been introduced in the following articles [20] [22] [2] [21] [11] [23] [4] [5] [24] [12] [6] [8] [3] [15] [7] [9] [14] [13] [17] [19] [18] [16] [1] [10]

#### Contents (PDF format)

1. Lemmas of Division
2. Darboux's Theorem

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