\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=}
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\newcommand\unicdcdcdjd{\cap}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l27\_arytm\_2 (TMGXKVaXi4t2TmvibdNFRZEJ8ZcNXwXU9ZB)}
\maketitle
Let $ k1\_arytm\_2 : {\iota}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k5\_arytm\_3}})}{\unicdbdjdcd}{({{{r3\_arytm\_3}~{k11\_arytm\_3}}~{X0}})}}}\label{hyp:ehgdedpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X2 .  ((X2 \in k1\_arytm\_2){\unicdcdcdhd}((X0 \in X2){\unicdcdcdhd}(r3\_arytm\_3~\\
X1~X0))){\unicdbdjdcd}(X1 \in X2)))\end{array}
\label{hyp:mgcdgdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in k1\_arytm\_2){\unicdcdcdhd}((X0{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}(\preoh (X1 \in X0){\unicdcdcdhd}(X1{\unicdcdgdad}k11\_arytm\_3))))\end{array}
\label{hyp:mgcdfdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k11\_arytm\_3}}~{k5\_arytm\_3}}\label{hyp:egehpflgbdbdpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:mgcdhdpfbgchjhehngpfcd}
${{\unicdcdadad} X0 .  {{({{X0} \in {k1\_arytm\_2}})}{\unicdbdjdcd}{({{({{X0}={k11\_arytm\_3}})}{\unicdcdcdid}{({{k11\_arytm\_3} \in {X0}})}})}}}$.
\end{theorem}
\end{document}
