\documentclass{article}
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\newtheorem{theorem}{Theorem}
\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}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t30\_grfunc\_1 (TMRo8W2mB8Y5CW3Na3Fkhr54ihKRAmDu1WX)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_relat\_1 : {{\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.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((k9\_xtuple\_0~X0=\\
k9\_xtuple\_0~X1){\unicdcdcdhd}(k1\_funct\_1~X0~X2=k1\_funct\_1~X1~X2)){\unicdbdjdcd}(k5\_relat\_1~\\
X0~(k1\_tarski~X2)=k5\_relat\_1~X1~(k1\_tarski~X2))))\end{array}
\label{hyp:ehcdjdpfhgchggfhogdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_tarski~X0~X1=k2\_xboole\_0~(k1\_tarski~\\
X0)~(k1\_tarski~X1)\end{array}
\label{hyp:ehbdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  ((k5\_relat\_1~X0~X2=k5\_relat\_1~X1~X2){\unicdcdcdhd}(k5\_relat\_1~X0~\\
X3=k5\_relat\_1~X1~X3)){\unicdbdjdcd}(k5\_relat\_1~X0~(k2\_xboole\_0~X2~X3)=k5\_relat\_1~\\
X1~(k2\_xboole\_0~X2~X3))))\end{array}
\label{hyp:ehbdfdadpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfhgchggfhogdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((k9\_xtuple\_0~\\
X0=k9\_xtuple\_0~X1){\unicdcdcdhd}((k1\_funct\_1~X0~X2=k1\_funct\_1~X1~X2){\unicdcdcdhd}(k1\_funct\_1~\\
X0~X3=k1\_funct\_1~X1~X3))){\unicdbdjdcd}(k5\_relat\_1~X0~(k2\_tarski~X2~X3)=k5\_relat\_1~\\
X1~(k2\_tarski~X2~X3))))\end{array}$$
\end{theorem}
\end{document}
