\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{l18\_glib\_004 (TMLKind8wixHprR5NQYNRjkESuUQhdFfff7)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_glib\_004 : {\iota}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((r1\_tarski~X0~(k9\_xtuple\_0~\\
X1)){\unicdbdjdcd}(k9\_xtuple\_0~(k5\_relat\_1~X1~X0)=X0))\end{array}
\label{hyp:ehgdcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v1\_glib\_003~X0)))))){\unicdbdjdcd}\\
(r1\_tarski~k2\_glib\_004~(k1\_relset\_1~k5\_numbers~X0))\end{array}
\label{hyp:mgbdgdpfhgmgjgcgpfadaded}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v4\_relat\_1~\\
X2~X1)){\unicdbdjdcd}((v1\_relat\_1~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}((v4\_relat\_1~(k5\_relat\_1~\\
X2~X0)~X0){\unicdcdcdhd}(v4\_relat\_1~(k5\_relat\_1~X2~X0)~X1)))\end{array}
\label{hyp:ggdgcdhdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X0){\unicdbdjdcd}(v1\_relat\_1~(k5\_relat\_1~\\
X0~X1))\end{array}
\label{hyp:egehpflgfdpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mgbdidpfhgmgjgcgpfadaded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v1\_glib\_003~X0)))))){\unicdbdjdcd}\\
(k1\_relset\_1~k2\_glib\_004~(k5\_relat\_1~X0~k2\_glib\_004)=k2\_glib\_004)\end{array}$$
\end{theorem}
\end{document}
