%% 
%%  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}