\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{t31\_relat\_2 (TMVd3u21ceTGEySzCQ2Kq1HnZcL6aDyjhh9)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r8\_relat\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}((k4\_tarski~\\
X0~X1 \in X2){\unicdbdjdcd}((X0 \in k1\_relat\_1~X2){\unicdcdcdhd}(X1 \in k1\_relat\_1~X2)))\end{array}
\label{hyp:ehbdfdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r8\_relat\_2~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}((k4\_tarski~\\
X2~X3 \in X0){\unicdcdcdhd}(k4\_tarski~X3~X4 \in X0))))){\unicdbdjdcd}(k4\_tarski~X2~X4 \in X0)))\end{array}
\label{hyp:egidpfchfgmgbgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v8\_relat\_2~X0){\unicdbdjded}(r8\_relat\_2~X0~(\\
k1\_relat\_1~X0)))\end{array}
\label{hyp:egbdgdpfchfgmgbgehpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddbdpfchfgmgbgehpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v8\_relat\_2~X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  ((k4\_tarski~X1~X2 \in X0){\unicdcdcdhd}(k4\_tarski~X2~X3 \in X0)){\unicdbdjdcd}(k4\_tarski~\\
X1~X3 \in X0)))\end{array}$$
\end{theorem}
\end{document}
