\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{t90\_glib\_000 (TMTtVFKczac2mNyoWo3kRuq8f1Kv3wi4iHn)}
\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 $ k14\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k16\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k21\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k23\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k22\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_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.
Let $ k1\_card\_1 : {{\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){\unicdbdjded}((m1\_glib\_000~\\
X0~X1){\unicdcdcdhd}(m1\_glib\_000~X1~X0))))\end{array}
\label{hyp:ehidhdpfhgmgjgcgpfadadad}
\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}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (r1\_tarski~(k22\_glib\_000~X1~X2~X3)~\\
(k22\_glib\_000~X0~X2~X3)){\unicdcdcdhd}(r1\_tarski~(k23\_glib\_000~X1~X2~X3)~(k23\_glib\_000~\\
X0~X2~X3))))\end{array}
\label{hyp:ehhdhdpfhgmgjgcgpfadadad}
\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}({\unicdcdadad} X2 .  (r1\_tarski~(k18\_glib\_000~X1~X2)~(k18\_glib\_000~\\
X0~X2)){\unicdcdcdhd}((r1\_tarski~(k19\_glib\_000~X1~X2)~(k19\_glib\_000~X0~X2)){\unicdcdcdhd}\\
((r1\_tarski~(k20\_glib\_000~X1~X2)~(k20\_glib\_000~X0~X2)){\unicdcdcdhd}(r1\_tarski~\\
(k21\_glib\_000~X1~X2)~(k21\_glib\_000~X0~X2))))))\end{array}
\label{hyp:ehhdgdpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\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}(k7\_glib\_000~X0=\\
k20\_glib\_000~X0~(k6\_glib\_000~X0))\end{array}
\label{hyp:ehddadpfhgmgjgcgpfadadad}
\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 .  ((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 .  ((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}(m1\_subset\_1~\\
(k20\_glib\_000~X0~X1)~(k1\_zfmisc\_1~(k7\_glib\_000~X0)))\end{array}
\label{hyp:egehpflgcdadpfhgmgjgcgpfadadad}
\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}
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}(k16\_glib\_000~X0=\\
k1\_card\_1~(k7\_glib\_000~X0))\end{array}
\label{hyp:egcdfdpfhgmgjgcgpfadadad}
\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}(k14\_glib\_000~X0=\\
k1\_card\_1~(k6\_glib\_000~X0))\end{array}
\label{hyp:egcdedpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehjdadpfhgmgjgcgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}(v1\_glib\_000~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~\\
X1){\unicdcdcdhd}(v1\_glib\_000~X1))))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (r5\_glib\_000~\\
X0~X1){\unicdbdjdcd}((k14\_glib\_000~X0=k14\_glib\_000~X1){\unicdcdcdhd}((k16\_glib\_000~X0=\\
k16\_glib\_000~X1){\unicdcdcdhd}((k18\_glib\_000~X0~X2=k18\_glib\_000~X1~X2){\unicdcdcdhd}((\\
k19\_glib\_000~X0~X2=k19\_glib\_000~X1~X2){\unicdcdcdhd}((k20\_glib\_000~X0~X2=k20\_glib\_000~\\
X1~X2){\unicdcdcdhd}((k21\_glib\_000~X0~X2=k21\_glib\_000~X1~X2){\unicdcdcdhd}(k23\_glib\_000~\\
X0~X2~X3=k23\_glib\_000~X1~X2~X3)))))))))\end{array}$$
\end{theorem}
\end{document}
