\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{t32\_sysrel (TMNvnD2BUwM67xb7ECREs3Dt9Ec5B7Kjsys)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_sysrel : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\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 .  (v1\_relat\_1~X1){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~(k1\_sysrel~\\
X1)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~X1){\unicdcdcdhd}(k4\_tarski~X0~X0 \in X1))){\unicdcdcdhd}((((X0 \in k9\_xtuple\_0~\\
X1){\unicdcdcdhd}(k4\_tarski~X0~X0 \in X1)){\unicdbdjdcd}(X0 \in k9\_xtuple\_0~(k1\_sysrel~X1))){\unicdcdcdhd}\\
(((X0 \in k10\_xtuple\_0~(k1\_sysrel~X1)){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~X1){\unicdcdcdhd}(k4\_tarski~\\
X0~X0 \in X1))){\unicdcdcdhd}((((X0 \in k9\_xtuple\_0~X1){\unicdcdcdhd}(k4\_tarski~X0~X0 \in X1)){\unicdbdjdcd}(X0 \in \\
k10\_xtuple\_0~(k1\_sysrel~X1))){\unicdcdcdhd}(((X0 \in k10\_xtuple\_0~(k1\_sysrel~\\
X1)){\unicdbdjdcd}((X0 \in k10\_xtuple\_0~X1){\unicdcdcdhd}(k4\_tarski~X0~X0 \in X1))){\unicdcdcdhd}((((X0 \in k10\_xtuple\_0~\\
X1){\unicdcdcdhd}(k4\_tarski~X0~X0 \in X1)){\unicdbdjdcd}(X0 \in k10\_xtuple\_0~(k1\_sysrel~X1))){\unicdcdcdhd}\\
(((X0 \in k9\_xtuple\_0~(k1\_sysrel~X1)){\unicdbdjdcd}((X0 \in k10\_xtuple\_0~X1){\unicdcdcdhd}(k4\_tarski~\\
X0~X0 \in X1))){\unicdcdcdhd}(((X0 \in k10\_xtuple\_0~X1){\unicdcdcdhd}(k4\_tarski~X0~X0 \in X1)){\unicdbdjdcd}(X0 \in \\
k9\_xtuple\_0~(k1\_sysrel~X1))))))))))\end{array}
\label{hyp:ehcdhdpfdhjhdhchfgmg}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfdhjhdhchfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((r1\_tarski~(k9\_xtuple\_0~(k1\_sysrel~\\
X0))~(k9\_xtuple\_0~X0)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~(k1\_sysrel~\\
X0))~(k10\_xtuple\_0~X0)){\unicdcdcdhd}((r1\_tarski~(k10\_xtuple\_0~(k1\_sysrel~\\
X0))~(k9\_xtuple\_0~X0)){\unicdcdcdhd}(r1\_tarski~(k9\_xtuple\_0~(k1\_sysrel~X0))~\\
(k10\_xtuple\_0~X0)))))\end{array}$$
\end{theorem}
\end{document}
