\documentclass{article}
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\newtheorem{definition}{Definition}
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\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t41\_mcart\_1 (TMdgPaRq4YDvMrymrB6b8fppCcK7mfg3xUA)}
\maketitle
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_enumset1~X0~X1~\\
X2~X3=k2\_enumset1~X0~X2~X1~X3\end{array}
\label{hyp:ehgdcdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (k2\_zfmisc\_1~(k1\_tarski~X0)~\\
(k2\_tarski~X1~X2)=k2\_tarski~(k4\_tarski~X0~X1)~(k4\_tarski~X0~X2)){\unicdcdcdhd}\\
(k2\_zfmisc\_1~(k2\_tarski~X0~X1)~(k1\_tarski~X2)=k2\_tarski~(k4\_tarski~\\
X0~X2)~(k4\_tarski~X1~X2))\end{array}
\label{hyp:ehddadpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  k2\_zfmisc\_1~(k2\_tarski~\\
X0~X1)~(k2\_tarski~X2~X3)=k2\_enumset1~(k4\_tarski~X0~X2)~(k4\_tarski~\\
X0~X3)~(k4\_tarski~X1~X2)~(k4\_tarski~X1~X3)\end{array}
\label{hyp:ehcdddpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_xtuple\_0~X0~X1~X2=k4\_tarski~\\
(k4\_tarski~X0~X1)~X2\end{array}
\label{hyp:egedpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_zfmisc\_1~X0~X1~X2=k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)~X2\end{array}
\label{hyp:egddpfkhggngjgdhdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfngdgbgchehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  k3\_zfmisc\_1~\\
(k1\_tarski~X0)~(k2\_tarski~X1~X2)~(k2\_tarski~X3~X4)=k2\_enumset1~\\
(k3\_xtuple\_0~X0~X1~X3)~(k3\_xtuple\_0~X0~X2~X3)~(k3\_xtuple\_0~X0~X1~X4)~\\
(k3\_xtuple\_0~X0~X2~X4)\end{array}$$
\end{theorem}
\end{document}
