\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{l35\_arytm\_2 (TMYQJJXV1g78dPKqZfQB2HvR3LCz18W2xHS)}
\maketitle
Let $ k1\_arytm\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X0 \in k4\_xboole\_0~X1~(k1\_tarski~\\
X2)){\unicdbdjded}((X0 \in X1){\unicdcdcdhd}(X0{\unicdcdgdad}X2))\end{array}
\label{hyp:ehfdgdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}(({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}(X2 \in X1)){\unicdbdjdcd}(X0=X1))\end{array}
\label{hyp:ehcdidpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k6\_subset\_1}~{X0}}~{X1}}={{{k4\_xboole\_0}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfdhfhcgdhfgehpfbd}
\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}
\begin{theorem}\label{thm:mgddfdpfbgchjhehngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  \preoh (X0 \in k1\_arytm\_2){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k5\_arytm\_3){\unicdbdjdcd}\\
(X1 \in X0))\end{array}$$
\end{theorem}
\end{document}
