\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=}
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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{t43\_glib\_000 (TMQb6nZJYp3VfKuEckbZhqkvNy59N7ZGpQW)}
\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 $ m1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_glib\_000~\\
X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}(v1\_glib\_000~X1))))))\end{array}
\label{hyp:egehpfngbdpfhgmgjgcgpfadadad}
\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}
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))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}(v1\_glib\_000~X1))))){\unicdbdjdcd}((m1\_glib\_000~X1~X0){\unicdbdjded}((r1\_tarski~(\\
k6\_glib\_000~X1)~(k6\_glib\_000~X0)){\unicdcdcdhd}((r1\_tarski~(k7\_glib\_000~X1)~\\
(k7\_glib\_000~X0)){\unicdcdcdhd}({\unicdcdadad} X2 .  (X2 \in k7\_glib\_000~X1){\unicdbdjdcd}((k1\_funct\_1~\\
(k10\_glib\_000~X1)~X2=k1\_funct\_1~(k10\_glib\_000~X0)~X2){\unicdcdcdhd}(k1\_funct\_1~\\
(k11\_glib\_000~X1)~X2=k1\_funct\_1~(k11\_glib\_000~X0)~X2)))))))\end{array}
\label{hyp:egddcdpfhgmgjgcgpfadadad}
\end{equation}
\begin{theorem}\label{thm:ehedddpfhgmgjgcgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_glib\_000~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_glib\_000~X2~X1){\unicdbdjdcd}(m1\_glib\_000~X2~X0)))\end{array}$$
\end{theorem}
\end{document}
