%% 
%%  Der Mathematiksatz mit LaTeX, 1. Auflage 2009
%% 
%%  Example 1-0-2 on page 4.
%% 
%%  Copyright (C) 2009 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.
%% 

\documentclass[]{ttctexa}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{391.22754pt}
\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}
