\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t37\_sysrel (TMMYkfqDZqWndsQXbVwHXC3uCRhG32HPW2c)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_sysrel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_xboole\_0~X0~(k3\_xboole\_0~X0~X1)=k4\_xboole\_0~\\
X0~X1\end{array}
\label{hyp:ehedhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{r1\_tarski}~{X0}}~{k1\_xboole\_0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehddpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((r1\_tarski~(k4\_relat\_1~(k9\_xtuple\_0~\\
(k1\_sysrel~X0)))~X0){\unicdcdcdhd}(r1\_tarski~(k4\_relat\_1~(k10\_xtuple\_0~(k1\_sysrel~\\
X0)))~X0))\end{array}
\label{hyp:ehddedpfdhjhdhchfgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}((r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_tarski~(k3\_relat\_1~X0~\\
X2)~(k3\_relat\_1~X1~X2)))))\end{array}
\label{hyp:ehddadpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_relat\_1~X2){\unicdbdjdcd}((r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_tarski~(k3\_relat\_1~X2~\\
X0)~(k3\_relat\_1~X2~X1)))))\end{array}
\label{hyp:ehcdjdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}(k1\_sysrel~X0=k4\_relat\_1~(k9\_xtuple\_0~\\
(k1\_sysrel~X0)))\end{array}
\label{hyp:ehcdidpfdhjhdhchfgmg}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X0){\unicdbdjdcd}(v1\_relat\_1~(k4\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ggdgcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k4\_relat\_1}~{X0}})}}}\label{hyp:egehpflgedpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}(k1\_sysrel~X0=k3\_xboole\_0~X0~(k4\_relat\_1~\\
(k9\_xtuple\_0~X0)))\end{array}
\label{hyp:egbdpfdhjhdhchfgmg}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfdhjhdhchfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}(((k3\_relat\_1~X0~(k6\_subset\_1~X0~(\\
k4\_relat\_1~(k9\_xtuple\_0~X0)))=k1\_xboole\_0){\unicdbdjdcd}(k3\_relat\_1~(k4\_relat\_1~\\
(k9\_xtuple\_0~(k1\_sysrel~X0)))~(k6\_subset\_1~X0~(k4\_relat\_1~(k9\_xtuple\_0~\\
(k1\_sysrel~X0))))=k1\_xboole\_0)){\unicdcdcdhd}((k3\_relat\_1~(k6\_subset\_1~\\
X0~(k4\_relat\_1~(k9\_xtuple\_0~X0)))~X0=k1\_xboole\_0){\unicdbdjdcd}(k3\_relat\_1~\\
(k6\_subset\_1~X0~(k4\_relat\_1~(k9\_xtuple\_0~(k1\_sysrel~X0))))~(k4\_relat\_1~\\
(k9\_xtuple\_0~(k1\_sysrel~X0)))=k1\_xboole\_0)))\end{array}$$
\end{theorem}
\end{document}
