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%%
%% An UIT Edition example
%%
%% Example 01-00-2 on page 4.
%%
%% Copyright (C) 2010 Herbert Voss
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3
%% of this license or (at your option) any later version.
%%
%% See http://www.latex-project.org/lppl.txt for details.
%%
%%
%% ====
% Show page(s) 1
%%
\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{413.13629pt}
\setlength\parindent{0pt}
\setcounter{equation}{1}
\renewcommand\theequation{1.\arabic{equation}}
\StartShownPreambleCommands
\usepackage{amsmath}
\newcommand\abs[1]{|#1|}
\StopShownPreambleCommands
\begin{document}
\begin{gather}
\left\lvert\frac{\hat v(s)-\hat v(t)}{\abs{\widetilde{D}u}(\mathinner{\left[t,s\right[})}
-\frac{f(\hat u(t)+\dfrac{\widetilde{D}u}{\abs{\widetilde{D}u}}(t)
\abs{\widetilde{D}u}(\mathinner{\left[t,s\right[}))-f(\hat u(t))}
{\abs{\widetilde{D}u}(\mathinner{\left[t,s\right[})}\right\rvert
\le K\left\lvert\frac{\hat u(s)-\hat u(t)}{\abs{\widetilde{D}u}(\mathinner{\left[t,s\right[})}
-\frac{\widetilde{D}u}{\abs{\widetilde{D}u}}(t)\right\rvert
\end{gather}
\end{document}
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