\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{t40\_glib\_003 (TMUD997VE8yKvPTMWXLNu9x6Gms8dN3xiaZ)}
\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 $ v3\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r5\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k13\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k13\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_glib\_003 : {\iota}$ be given.
Let $ k3\_glib\_003 : {\iota}$ be given.
Let $ k4\_glib\_003 : {\iota}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_glib\_003 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\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 .  (r5\_glib\_000~\\
X0~(k13\_glib\_000~X0~k2\_glib\_003~X1)){\unicdcdcdhd}((r5\_glib\_000~X0~(k13\_glib\_000~\\
X0~k3\_glib\_003~X1)){\unicdcdcdhd}(r5\_glib\_000~X0~(k13\_glib\_000~X0~k4\_glib\_003~\\
X1))))\end{array}
\label{hyp:ehhdpfhgmgjgcgpfadaddd}
\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}((\\
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}((r5\_glib\_000~X0~X1){\unicdbdjdcd}\\
(r5\_glib\_000~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchfdpfhgmgjgcgpfadadad}
\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}((\\
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}(r5\_glib\_000~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchfdpfhgmgjgcgpfadadad}
\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}(v3\_glib\_003~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X1 \in k6\_glib\_000~X0){\unicdbdjdcd}(k13\_glib\_003~X0~\\
X1~X2=k13\_glib\_000~X0~k4\_glib\_003~(k1\_funct\_4~(k7\_glib\_003~X0)~\\
(k16\_funcop\_1~X1~X2)))){\unicdcdcdhd}((\preoh X1 \in k6\_glib\_000~X0){\unicdbdjdcd}(k13\_glib\_003~\\
X0~X1~X2=X0)))\end{array}
\label{hyp:egcdcdpfhgmgjgcgpfadaddd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfhgmgjgcgpfadaddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v3\_glib\_003~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  r5\_glib\_000~X0~(k13\_glib\_003~X0~X1~X2))\end{array}$$
\end{theorem}
\end{document}
