\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{t50\_glib\_002 (TMRkQVBgUgynYdFmJMSXcYp9z3nivnW2XhA)}
\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 $ r5\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_glib\_002 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_glib\_002 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v1\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v6\_glib\_001 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ 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.
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 .  ((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}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
(m3\_glib\_001~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m3\_glib\_001~X5~X1){\unicdbdjdcd}((X4=X5){\unicdbdjdcd}\\
((r1\_glib\_001~X0~X2~X3~X4){\unicdbdjded}(r1\_glib\_001~X1~X2~X3~X5))))))\end{array}
\label{hyp:ehbdjdpfhgmgjgcgpfadadbd}
\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}({\unicdcdadad} X2 .  (m3\_glib\_001~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m3\_glib\_001~X3~X1){\unicdbdjdcd}(((r5\_glib\_000~X0~X1){\unicdcdcdhd}(X2=X3)){\unicdbdjdcd}(((v1\_glib\_001~\\
X2~X0){\unicdbdjdcd}(v1\_glib\_001~X3~X1)){\unicdcdcdhd}(((v1\_glib\_001~X3~X1){\unicdbdjdcd}(v1\_glib\_001~\\
X2~X0)){\unicdcdcdhd}(((v2\_glib\_001~X2~X0){\unicdbdjdcd}(v2\_glib\_001~X3~X1)){\unicdcdcdhd}(((v2\_glib\_001~\\
X3~X1){\unicdbdjdcd}(v2\_glib\_001~X2~X0)){\unicdcdcdhd}(((v3\_glib\_001~X2~X0){\unicdbdjdcd}(v3\_glib\_001~\\
X3~X1)){\unicdcdcdhd}(((v3\_glib\_001~X3~X1){\unicdbdjdcd}(v3\_glib\_001~X2~X0)){\unicdcdcdhd}(((v4\_glib\_001~\\
X2~X0){\unicdbdjdcd}(v4\_glib\_001~X3~X1)){\unicdcdcdhd}(((v4\_glib\_001~X3~X1){\unicdbdjdcd}(v4\_glib\_001~\\
X2~X0)){\unicdcdcdhd}(((v5\_glib\_001~X2~X0){\unicdbdjdcd}(v5\_glib\_001~X3~X1)){\unicdcdcdhd}(((v5\_glib\_001~\\
X3~X1){\unicdbdjdcd}(v5\_glib\_001~X2~X0)){\unicdcdcdhd}(((v6\_glib\_001~X2~X0){\unicdbdjdcd}(v6\_glib\_001~\\
X3~X1)){\unicdcdcdhd}((v6\_glib\_001~X3~X1){\unicdbdjdcd}(v6\_glib\_001~X2~X0)))))))))))))))))\end{array}
\label{hyp:ehbdidbdpfhgmgjgcgpfadadbd}
\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}({\unicdcdadad} X2 .  ((r5\_glib\_000~X0~X1){\unicdcdcdhd}(\\
m3\_glib\_001~X2~X0)){\unicdbdjdcd}(m3\_glib\_001~X2~X1)))\end{array}
\label{hyp:ehbdhdjdpfhgmgjgcgpfadadbd}
\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 .  (r1\_glib\_002~\\
X0~X1){\unicdbdjded}((v3\_glib\_002~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k6\_glib\_000~\\
X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  ((v2\_glib\_001~X3~X0){\unicdcdcdhd}(m3\_glib\_001~X3~X0)){\unicdcdcdhd}(\\
r1\_glib\_001~X0~X1~X2~X3)))))\end{array}
\label{hyp:egedpfhgmgjgcgpfadadcd}
\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}
\begin{theorem}\label{thm:ehfdadpfhgmgjgcgpfadadcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}(v1\_glib\_000~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((r5\_glib\_000~X0~X1){\unicdcdcdhd}(\\
r1\_glib\_002~X0~X2)){\unicdbdjdcd}(r1\_glib\_002~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
