\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l10\_xxreal\_0 (TMXDesRXWKBAfzkWzg5atQGKfZ3ZkekrXVo)}
\maketitle
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1 \in \\
k2\_zfmisc\_1~X2~X3){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X3))\end{array}
\label{hyp:ehidhdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}}}}\label{hyp:ehfdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_tarski}~{k2\_arytm\_2}}~{k1\_numbers}}\label{hyp:ehbdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_xxreal\_0}={{{k4\_tarski}~{k6\_numbers}}~{k1\_numbers}}}\label{hyp:egddpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdadpfihihchfgbgmgpfad}
${\preoh{{{k2\_xxreal\_0} \in {{{k2\_zfmisc\_1}~{({{k1\_tarski}~{k6\_numbers}})}}~{k2\_arytm\_2}}}}}$.
\end{theorem}
\end{document}
