\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{l6\_arytm\_2 (TMX9FcHuiCx4oRSACt2wrbdenoL1VdAAArQ)}
\maketitle
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k1\_arytm\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_tarski~\\
(k2\_xboole\_0~X0~X2)~(k2\_xboole\_0~X1~X2))\end{array}
\label{hyp:ehjdpfihcgpgpgmgfgpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  m1\_subset\_1~(k6\_subset\_1~X0~X1)~(k1\_zfmisc\_1~\\
X0)\end{array}
\label{hyp:egehpflggdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_arytm\_2=k6\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k5\_arytm\_3)))~({\uniddcgcg} X0 : \iota .  {\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}\\
((r3\_arytm\_3~X2~X1){\unicdbdjdcd}(X2 \in X0))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdcdcdhd}\\
((X2 \in X0){\unicdcdcdhd}(\preoh r3\_arytm\_3~X2~X1))))))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_tarski~\\
k5\_arytm\_3)\end{array}
\label{hyp:egbdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mggdpfbgchjhehngpfcd}
$$\begin{array}{c}r1\_tarski~(k2\_xboole\_0~k5\_arytm\_3~k1\_arytm\_2)~(k2\_xboole\_0~k5\_arytm\_3~\\
(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(k1\_zfmisc\_1~k5\_arytm\_3)))~\\
({\uniddcgcg} X0 : \iota .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}\\
(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdbdjdcd}((r3\_arytm\_3~X2~X1){\unicdbdjdcd}\\
(X2 \in X0))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}\\
(\preoh r3\_arytm\_3~X2~X1))))))~({\uniddcgcg} X0 : \iota .  X0)))\end{array}$$
\end{theorem}
\end{document}
