\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t30\_sysrel (TMawZBfYzCevZB3akaxRAsNq1kAb9u5M3To)}
\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 $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_sysrel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\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 $ k2\_tarski : {{\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 .  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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}((((k3\_relat\_1~\\
X2~X2=X2){\unicdcdcdhd}((k3\_relat\_1~X2~(k6\_subset\_1~X2~(k1\_sysrel~X2))=k1\_xboole\_0){\unicdcdcdhd}\\
(k4\_tarski~X0~X1 \in X2))){\unicdbdjdcd}((X0=X1){\unicdcdcdid}((X0 \in k6\_subset\_1~(k9\_xtuple\_0~\\
X2)~(k9\_xtuple\_0~(k1\_sysrel~X2))){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~(k1\_sysrel~\\
X2))))){\unicdcdcdhd}(((k3\_relat\_1~X2~X2=X2){\unicdcdcdhd}((k3\_relat\_1~(k6\_subset\_1~X2~\\
(k1\_sysrel~X2))~X2=k1\_xboole\_0){\unicdcdcdhd}(k4\_tarski~X0~X1 \in X2))){\unicdbdjdcd}((X0=\\
X1){\unicdcdcdid}((X1 \in k6\_subset\_1~(k10\_xtuple\_0~X2)~(k9\_xtuple\_0~(k1\_sysrel~\\
X2))){\unicdcdcdhd}(X0 \in k9\_xtuple\_0~(k1\_sysrel~X2))))))\end{array}
\label{hyp:ehcdjdpfdhjhdhchfgmg}
\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 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\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:ehddadpfdhjhdhchfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}((((k3\_relat\_1~\\
X2~X2=X2){\unicdcdcdhd}((k3\_relat\_1~X2~(k6\_subset\_1~X2~(k4\_relat\_1~(k9\_xtuple\_0~\\
X2)))=k1\_xboole\_0){\unicdcdcdhd}(k4\_tarski~X0~X1 \in X2))){\unicdbdjdcd}((X0=X1){\unicdcdcdid}((X0 \in k6\_subset\_1~\\
(k9\_xtuple\_0~X2)~(k9\_xtuple\_0~(k1\_sysrel~X2))){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~\\
(k1\_sysrel~X2))))){\unicdcdcdhd}(((k3\_relat\_1~X2~X2=X2){\unicdcdcdhd}((k3\_relat\_1~(k6\_subset\_1~\\
X2~(k4\_relat\_1~(k9\_xtuple\_0~X2)))~X2=k1\_xboole\_0){\unicdcdcdhd}(k4\_tarski~\\
X0~X1 \in X2))){\unicdbdjdcd}((X0=X1){\unicdcdcdid}((X1 \in k6\_subset\_1~(k10\_xtuple\_0~X2)~(k9\_xtuple\_0~\\
(k1\_sysrel~X2))){\unicdcdcdhd}(X0 \in k9\_xtuple\_0~(k1\_sysrel~X2))))))\end{array}$$
\end{theorem}
\end{document}
