\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l30\_jgraph\_3 (TMMFqL2gH2RzQx31uS9iCNFeEYFELnQHBKU)}
\maketitle
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k22\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k17\_euclid~(k22\_euclid~np\_\_2)=np\_\_1){\unicdcdcdhd}(k18\_euclid~(k22\_euclid~\\
np\_\_2)=np\_\_1)\end{array}
\label{hyp:ehfdpfkghgchbgahigpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((r1\_xxreal\_0~(k18\_euclid~(k22\_euclid~np\_\_2))~(k17\_euclid~(k22\_euclid~\\
np\_\_2))){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_real\_1~(k17\_euclid~(k22\_euclid~np\_\_2)))~\\
(k18\_euclid~(k22\_euclid~np\_\_2)))){\unicdcdcdid}((r1\_xxreal\_0~(k17\_euclid~\\
(k22\_euclid~np\_\_2))~(k18\_euclid~(k22\_euclid~np\_\_2))){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k18\_euclid~(k22\_euclid~np\_\_2))~(k1\_real\_1~(k17\_euclid~(k22\_euclid~\\
np\_\_2)))))\end{array}
\label{hyp:mgcdedpfkghgchbgahigpfdd}
\end{equation}
\begin{theorem}\label{thm:mgddadpfkghgchbgahigpfdd}
$$\begin{array}{c}((r1\_xxreal\_0~(k17\_euclid~(k22\_euclid~np\_\_2))~(k18\_euclid~(k22\_euclid~\\
np\_\_2))){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_real\_1~(k18\_euclid~(k22\_euclid~np\_\_2)))~\\
(k17\_euclid~(k22\_euclid~np\_\_2)))){\unicdcdcdid}((r1\_xxreal\_0~(k18\_euclid~\\
(k22\_euclid~np\_\_2))~(k17\_euclid~(k22\_euclid~np\_\_2))){\unicdcdcdhd}(r1\_xxreal\_0~\\
(k17\_euclid~(k22\_euclid~np\_\_2))~(k1\_real\_1~(k18\_euclid~(k22\_euclid~\\
np\_\_2)))))\end{array}$$
\end{theorem}
\end{document}
