\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{t40\_sysrel (TMSK73vxiYttR78G2iLcyMYkUEUAw3j5JMt)}
\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((((\\
k3\_relat\_1~X0~X1=X0){\unicdcdcdhd}(k3\_relat\_1~X1~(k6\_subset\_1~X1~(k4\_relat\_1~\\
(k9\_xtuple\_0~X1)))=k1\_xboole\_0)){\unicdbdjdcd}(r1\_tarski~(k1\_sysrel~X0)~\\
(k1\_sysrel~X1))){\unicdcdcdhd}(((k3\_relat\_1~X1~X0=X0){\unicdcdcdhd}(k3\_relat\_1~(k6\_subset\_1~\\
X1~(k4\_relat\_1~(k9\_xtuple\_0~X1)))~X1=k1\_xboole\_0)){\unicdbdjdcd}(r1\_tarski~\\
(k1\_sysrel~X0)~(k1\_sysrel~X1)))))\end{array}
\label{hyp:ehddjdpfdhjhdhchfgmg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdhjhdhchfgmg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((((\\
k3\_relat\_1~X0~X1=X0){\unicdcdcdhd}((k3\_relat\_1~X1~(k6\_subset\_1~X1~(k4\_relat\_1~\\
(k9\_xtuple\_0~X1)))=k1\_xboole\_0){\unicdcdcdhd}((k3\_relat\_1~X1~X0=X1){\unicdcdcdhd}(k3\_relat\_1~\\
X0~(k6\_subset\_1~X0~(k4\_relat\_1~(k9\_xtuple\_0~X0)))=k1\_xboole\_0)))){\unicdbdjdcd}\\
(k1\_sysrel~X0=k1\_sysrel~X1)){\unicdcdcdhd}(((k3\_relat\_1~X1~X0=X0){\unicdcdcdhd}((k3\_relat\_1~\\
(k6\_subset\_1~X1~(k4\_relat\_1~(k9\_xtuple\_0~X1)))~X1=k1\_xboole\_0){\unicdcdcdhd}\\
((k3\_relat\_1~X0~X1=X1){\unicdcdcdhd}(k3\_relat\_1~(k6\_subset\_1~X0~(k4\_relat\_1~\\
(k9\_xtuple\_0~X0)))~X0=k1\_xboole\_0)))){\unicdbdjdcd}(k1\_sysrel~X0=k1\_sysrel~\\
X1))))\end{array}$$
\end{theorem}
\end{document}
