\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{l24\_arytm\_2 (TMdwVSqPkVAE4TFwA7huYNJdK9LR83dtCSo)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ r1\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\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 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k5\_arytm\_3}}}}\label{hyp:ggdgddpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}((((X0 \in k5\_arytm\_3){\unicdcdcdhd}(X1 \in k5\_arytm\_3)){\unicdbdjdcd}((r1\_arytm\_2~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k5\_arytm\_3){\unicdcdcdhd}({\unicdcdaddd} X3 .  (\\
m1\_subset\_1~X3~k5\_arytm\_3){\unicdcdcdhd}((X0=X2){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}(r3\_arytm\_3~X2~\\
X3))))))){\unicdcdcdhd}(((X0 \in k5\_arytm\_3){\unicdbdjdcd}((X1 \in k5\_arytm\_3){\unicdcdcdid}((r1\_arytm\_2~\\
X0~X1){\unicdbdjded}(X0 \in X1)))){\unicdcdcdhd}(((X1 \in k5\_arytm\_3){\unicdbdjdcd}((X0 \in k5\_arytm\_3){\unicdcdcdid}((r1\_arytm\_2~\\
X0~X1){\unicdbdjded}(\preoh X1 \in X0)))){\unicdcdcdhd}(\preoh (\preoh (X0 \in k5\_arytm\_3){\unicdcdcdhd}(X1 \in k5\_arytm\_3)){\unicdcdcdhd}\\
((\preoh (X0 \in k5\_arytm\_3){\unicdcdcdhd}(\preoh X1 \in k5\_arytm\_3)){\unicdcdcdhd}((\preoh (\preoh X0 \in k5\_arytm\_3){\unicdcdcdhd}\\
(X1 \in k5\_arytm\_3)){\unicdcdcdhd}(\preoh (r1\_arytm\_2~X0~X1){\unicdbdjded}(r1\_tarski~X0~X1)))))))))\end{array}
\label{hyp:egfdpfbgchjhehngpfcd}
\end{equation}
\begin{theorem}\label{thm:mgcdedpfbgchjhehngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k2\_arytm\_2){\unicdbdjdcd}(((X2=X0){\unicdcdcdhd}(X3=X1)){\unicdbdjdcd}((r1\_arytm\_2~\\
X2~X3){\unicdbdjded}(r3\_arytm\_3~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
