\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{t41\_glib\_004 (TMMKExXzvQRejwhVk6Hhs276t9WZ8fWSXk8)}
\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 $ v2\_glib\_000 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_002 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_glib\_002 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_glib\_004 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r5\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_glib\_003 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k24\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_glib\_004 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_uproots : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k10\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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){\unicdcdcdhd}(v1\_glib\_003~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){\unicdcdcdhd}(v1\_glib\_003~\\
X1)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_glib\_000~X2){\unicdcdcdhd}(v1\_glib\_003~\\
X2)))))){\unicdbdjdcd}(((r5\_glib\_000~X0~X1){\unicdcdcdhd}((k5\_glib\_003~X0=k5\_glib\_003~\\
X1){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}((v4\_glib\_003~X0~X2){\unicdcdcdhd}(m1\_glib\_000~X0~X2))))){\unicdbdjdcd}\\
((v1\_glib\_003~X1){\unicdcdcdhd}((v4\_glib\_003~X1~X2){\unicdcdcdhd}(m1\_glib\_000~X1~X2))))))\end{array}
\label{hyp:ehidpfhgmgjgcgpfadaddd}
\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}(((r5\_glib\_000~X0~X1){\unicdcdcdhd}(v3\_glib\_002~\\
X0)){\unicdbdjdcd}(v3\_glib\_002~X1)))\end{array}
\label{hyp:ehedidpfhgmgjgcgpfadadcd}
\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}(k24\_glib\_000~X0~X1=k6\_glib\_000~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdedpfhgmgjgcgpfadadad}
\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 .  (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 .  ((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}((v2\_glib\_000~X0){\unicdcdcdhd}\\
((v1\_glib\_003~X0){\unicdcdcdhd}(v7\_glib\_003~X0)))))))){\unicdbdjdcd}(k4\_glib\_004~X0=\\
k3\_uproots~(k7\_glib\_000~X0)~(k5\_glib\_003~X0))\end{array}
\label{hyp:eggdpfhgmgjgcgpfadaded}
\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}((r5\_glib\_000~X0~X1){\unicdbdjded}((k6\_glib\_000~\\
X0=k6\_glib\_000~X1){\unicdcdcdhd}((k7\_glib\_000~X0=k7\_glib\_000~X1){\unicdcdcdhd}((r1\_funct\_2~\\
(k7\_glib\_000~X0)~(k6\_glib\_000~X0)~(k7\_glib\_000~X1)~(k6\_glib\_000~\\
X1)~(k10\_glib\_000~X0)~(k10\_glib\_000~X1)){\unicdcdcdhd}(r1\_funct\_2~(k7\_glib\_000~\\
X0)~(k6\_glib\_000~X0)~(k7\_glib\_000~X1)~(k6\_glib\_000~X1)~(k11\_glib\_000~\\
X0)~(k11\_glib\_000~X1)))))))\end{array}
\label{hyp:egddedpfhgmgjgcgpfadadad}
\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 .  (m1\_glib\_000~\\
X1~X0){\unicdbdjdcd}((v9\_glib\_000~X1~X0){\unicdbdjded}(k24\_glib\_000~X0~X1=k6\_glib\_000~X0)))\end{array}
\label{hyp:egddddpfhgmgjgcgpfadadad}
\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}((v2\_glib\_000~X0){\unicdcdcdhd}\\
((v1\_glib\_002~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}(v7\_glib\_003~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v9\_glib\_000~X1~X0){\unicdcdcdhd}((v3\_glib\_002~X1){\unicdcdcdhd}((v1\_glib\_003~\\
X1){\unicdcdcdhd}((v4\_glib\_003~X1~X0){\unicdcdcdhd}(m1\_glib\_000~X1~X0))))){\unicdbdjdcd}((v1\_glib\_004~\\
X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  ((v9\_glib\_000~X2~X0){\unicdcdcdhd}((v3\_glib\_002~X2){\unicdcdcdhd}((\\
v1\_glib\_003~X2){\unicdcdcdhd}((v4\_glib\_003~X2~X0){\unicdcdcdhd}(m1\_glib\_000~X2~X0))))){\unicdbdjdcd}\\
(r1\_xxreal\_0~(k4\_glib\_004~X1)~(k4\_glib\_004~X2)))))\end{array}
\label{hyp:egbdjdpfhgmgjgcgpfadaded}
\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}(v2\_glib\_000~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_glib\_000~X1~X0){\unicdbdjdcd}(v2\_glib\_000~X1))\end{array}
\label{hyp:dgdgidpfhgmgjgcgpfadadad}
\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){\unicdcdcdhd}\\
(v7\_glib\_003~X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_glib\_000~X1~X0){\unicdbdjdcd}(((v1\_glib\_003~\\
X1){\unicdcdcdhd}(v4\_glib\_003~X1~X0)){\unicdbdjdcd}((v1\_glib\_003~X1){\unicdcdcdhd}((v4\_glib\_003~X1~\\
X0){\unicdcdcdhd}(v7\_glib\_003~X1)))))\end{array}
\label{hyp:dgdgedpfhgmgjgcgpfadaddd}
\end{equation}
\begin{theorem}\label{thm:ehedbdpfhgmgjgcgpfadaded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}((v2\_glib\_000~X0){\unicdcdcdhd}\\
((v1\_glib\_002~X0){\unicdcdcdhd}((v1\_glib\_003~X0){\unicdcdcdhd}(v7\_glib\_003~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v9\_glib\_000~X1~X0){\unicdcdcdhd}((v3\_glib\_002~X1){\unicdcdcdhd}((v1\_glib\_003~\\
X1){\unicdcdcdhd}((v4\_glib\_003~X1~X0){\unicdcdcdhd}((v1\_glib\_004~X1~X0){\unicdcdcdhd}(m1\_glib\_000~X1~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_finset\_1~X2){\unicdcdcdhd}((v1\_glib\_000~X2){\unicdcdcdhd}(v1\_glib\_003~\\
X2)))))){\unicdbdjdcd}(((r5\_glib\_000~X1~X2){\unicdcdcdhd}(k5\_glib\_003~X1=k5\_glib\_003~\\
X2)){\unicdbdjdcd}((v9\_glib\_000~X2~X0){\unicdcdcdhd}((v3\_glib\_002~X2){\unicdcdcdhd}((v1\_glib\_003~X2){\unicdcdcdhd}\\
((v4\_glib\_003~X2~X0){\unicdcdcdhd}((v1\_glib\_004~X2~X0){\unicdcdcdhd}(m1\_glib\_000~X2~X0)))))))))\end{array}$$
\end{theorem}
\end{document}
