\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{l68\_arytm\_2 (TMb8WMgqiuM8E2JS8j9RNzJ52PczWrDVmc7)}
\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 $ k11\_arytm\_3 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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}((\preoh r3\_arytm\_3~X1~X0){\unicdbdjded}((r3\_arytm\_3~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}\\
X1))))\end{array}
\label{hyp:ehgdidpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}\\
k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(\preoh X2 \in X1)))\end{array}
\label{hyp:ehedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdaddd} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k5\_arytm\_3}})}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X0}})}}}\label{hyp:chdgcdpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:mggdidpfbgchjhehngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
k5\_arytm\_3)))~({\uniddcgcg} X1 : \iota .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}\\
((X2 \in X1){\unicdbdjdcd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~k5\_arytm\_3){\unicdbdjdcd}((r3\_arytm\_3~\\
X3~X2){\unicdbdjdcd}(X3 \in X1))){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k5\_arytm\_3){\unicdcdcdhd}((\\
X3 \in X1){\unicdcdcdhd}(\preoh r3\_arytm\_3~X3~X2))))))~({\uniddcgcg} X1 : \iota .  X1)){\unicdcdcdhd}((X0{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}(\preoh (X1 \in X0){\unicdcdcdhd}(X1{\unicdcdgdad}k11\_arytm\_3))))\end{array}$$
\end{theorem}
\end{document}
