\documentclass{article}
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\newtheorem{proposition}{Proposition}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t11\_glib\_003 (TMdY7xsBL57ewgLgbTxgtXbVJRm7MWS1C9F)}
\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 $ v4\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k25\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_glib\_003 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\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){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((X0 \in X1){\unicdbdjdcd}(k1\_funct\_1~(k5\_relat\_1~X2~X1)~X0=k1\_funct\_1~X2~\\
X0))\end{array}
\label{hyp:ehedjdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((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}(m1\_glib\_000~\\
X1~X0)){\unicdbdjdcd}(k25\_glib\_000~X0~X1=k7\_glib\_000~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdfdpfhgmgjgcgpfadadad}
\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}\\
((v1\_relat\_1~(k5\_glib\_003~X0)){\unicdcdcdhd}((v4\_relat\_1~(k5\_glib\_003~X0)~\\
(k7\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_1~(k5\_glib\_003~X0)){\unicdcdcdhd}(v1\_partfun1~\\
(k5\_glib\_003~X0)~(k7\_glib\_000~X0)))))\end{array}
\label{hyp:egehpflgfdpfhgmgjgcgpfadaddd}
\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}\\
({\unicdcdadad} X1 .  ((v1\_glib\_003~X1){\unicdcdcdhd}(m1\_glib\_000~X1~X0)){\unicdbdjdcd}((v4\_glib\_003~\\
X1~X0){\unicdbdjded}(k5\_glib\_003~X1=k5\_relat\_1~(k5\_glib\_003~X0)~(k25\_glib\_000~\\
X0~X1))))\end{array}
\label{hyp:egbdadpfhgmgjgcgpfadaddd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfhgmgjgcgpfadaddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v1\_glib\_003~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_glib\_003~X1){\unicdcdcdhd}((v4\_glib\_003~X1~X0){\unicdcdcdhd}(m1\_glib\_000~\\
X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2 \in k25\_glib\_000~X0~X1){\unicdbdjdcd}(k1\_funct\_1~(k5\_glib\_003~\\
X1)~X2=k1\_funct\_1~(k5\_glib\_003~X0)~X2)))\end{array}$$
\end{theorem}
\end{document}
