\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t36\_sysrel (TMJqscwAaqi4gqgnn3gjaYjs3UNRTcxpoHm)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_relat\_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\_sysrel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((((r1\_tarski~(k4\_relat\_1~\\
X0)~X1){\unicdcdcdhd}(k3\_relat\_1~(k4\_relat\_1~X0)~(k6\_subset\_1~X1~(k4\_relat\_1~\\
X0))=k1\_xboole\_0)){\unicdbdjdcd}(k5\_relat\_1~X1~X0=k4\_relat\_1~X0)){\unicdcdcdhd}(((r1\_tarski~\\
(k4\_relat\_1~X0)~X1){\unicdcdcdhd}(k3\_relat\_1~(k6\_subset\_1~X1~(k4\_relat\_1~X0))~\\
(k4\_relat\_1~X0)=k1\_xboole\_0)){\unicdbdjdcd}(k6\_relat\_1~X0~X1=k4\_relat\_1~\\
X0)))\end{array}
\label{hyp:ehddfdpfdhjhdhchfgmg}
\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}(k9\_xtuple\_0~(k1\_sysrel~X0)=k10\_xtuple\_0~\\
(k1\_sysrel~X0))\end{array}
\label{hyp:ehcdgdpfdhjhdhchfgmg}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfdhjhdhchfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}(((k3\_relat\_1~(k4\_relat\_1~(k9\_xtuple\_0~\\
(k1\_sysrel~X0)))~(k6\_subset\_1~X0~(k4\_relat\_1~(k9\_xtuple\_0~(k1\_sysrel~\\
X0))))=k1\_xboole\_0){\unicdbdjdcd}((k5\_relat\_1~X0~(k9\_xtuple\_0~(k1\_sysrel~\\
X0))=k4\_relat\_1~(k9\_xtuple\_0~(k1\_sysrel~X0))){\unicdcdcdhd}(k5\_relat\_1~X0~\\
(k10\_xtuple\_0~(k1\_sysrel~X0))=k4\_relat\_1~(k9\_xtuple\_0~(k1\_sysrel~\\
X0))))){\unicdcdcdhd}((k3\_relat\_1~(k6\_subset\_1~X0~(k4\_relat\_1~(k10\_xtuple\_0~\\
(k1\_sysrel~X0))))~(k4\_relat\_1~(k10\_xtuple\_0~(k1\_sysrel~X0)))=\\
k1\_xboole\_0){\unicdbdjdcd}((k6\_relat\_1~(k9\_xtuple\_0~(k1\_sysrel~X0))~X0=k4\_relat\_1~\\
(k9\_xtuple\_0~(k1\_sysrel~X0))){\unicdcdcdhd}(k6\_relat\_1~(k10\_xtuple\_0~(k1\_sysrel~\\
X0))~X0=k4\_relat\_1~(k10\_xtuple\_0~(k1\_sysrel~X0))))))\end{array}$$
\end{theorem}
\end{document}
