<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass{amsart}
\usepackage{amssymb,latexsym}
\usepackage{amsmath}
\usepackage{graphicx}
\usepackage{enumerate}
\usepackage{gensymb}
\usepackage{Gratzer-Color-Scheme}
 
 
\begin{document}
\title{Example file for Gratzer-Color-Scheme}

\author[G.\ Gr\"atzer]{George Gr\"atzer}

\keywords{$\mathcal{C}_1$-diagrams, slim planar semimodular lattice}

\maketitle    

\begin{definition}
%Definition~\ref{D:well}
A diagram of an SPS lattice $L$ is a
\emph{${C}_1$-diagram} if the middle edge of any cover-preserving $7$ is steep
and all other edges are normal.
\end{definition}

\begin{theorem}\label{T:well}
%Theorem~\ref{T:well}
Every slim, planar, semimodular lattice $L$ has a ${C}_1$-diagram.
\end{theorem}

\begin{corollary}
The principal ideals are distributive.
\end{corollary}

\begin{proof}
Let $K$ be represented.
\end{proof}

\begin{lemma}
$K$ is a lattice.
\end{lemma}

\begin{proof}
Obvious.
\end{proof}

\begin{proposition}
$K$ is not a lattice.
\end{proposition}

\end{document}
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