\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{l7\_xxreal\_0 (TMPLMezwonF2cpogYhnPrg1HAQLxnm4oKUB)}
\maketitle
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
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:mgedpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xxreal\_0}={k1\_numbers}}\label{hyp:egcdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mghdpfihihchfgbgmgpfad}
${\preoh{{{k1\_xxreal\_0} \in {k2\_arytm\_2}}}}$.
\end{theorem}
\end{document}
