\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\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{l22\_arytm\_2 (TManVD4sSaHzJ3dLARuk1CQzgCh5puheaqP)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_arytm\_3){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_arytm\_3)){\unicdbdjdcd}((r3\_arytm\_3~X0~X1){\unicdcdcdid}(r3\_arytm\_3~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchddpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:mgcdcdpfbgchjhehngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (X0 \in ReplSep~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~k5\_arytm\_3)))~({\uniddcgcg} X2 : \iota .  {\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k5\_arytm\_3){\unicdbdjdcd}((X3 \in X2){\unicdbdjdcd}(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_arytm\_3){\unicdbdjdcd}\\
((r3\_arytm\_3~X4~X3){\unicdbdjdcd}(X4 \in X2))){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k5\_arytm\_3){\unicdcdcdhd}\\
((X4 \in X2){\unicdcdcdhd}(\preoh r3\_arytm\_3~X4~X3))))))~({\uniddcgcg} X2 : \iota .  X2)){\unicdcdcdhd}((X1 \in ReplSep~\\
(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(k1\_zfmisc\_1~k5\_arytm\_3)))~\\
({\uniddcgcg} X2 : \iota .  {\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_arytm\_3){\unicdbdjdcd}((X3 \in X2){\unicdbdjdcd}\\
(({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k5\_arytm\_3){\unicdbdjdcd}((r3\_arytm\_3~X4~X3){\unicdbdjdcd}\\
(X4 \in X2))){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~k5\_arytm\_3){\unicdcdcdhd}((X4 \in X2){\unicdcdcdhd}\\
(\preoh r3\_arytm\_3~X4~X3))))))~({\uniddcgcg} X2 : \iota .  X2)){\unicdcdcdhd}((\preoh r1\_tarski~X0~X1){\unicdcdcdhd}\\
(\preoh r1\_tarski~X1~X0)))\end{array}$$
\end{theorem}
\end{document}
