\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{l13\_glib\_000 (TMYQbSoFHYQm1WYM481zoXF5f3MrRH3u1En)}
\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_glib\_000 : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_glib\_000 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k9\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k2\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_glib\_000 : {\iota}$ be given.
Let $ k3\_glib\_000 : {\iota}$ be given.
Let $ k2\_glib\_000 : {\iota}$ be given.
Let $ k1\_glib\_000 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((m1\_subset\_1~X1~X0){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X3~X0){\unicdcdcdhd}(m1\_subset\_1~X4~X0))))){\unicdbdjdcd}(k9\_domain\_1~X0~X1~X2~X3~X4=k2\_enumset1~\\
X1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((m1\_subset\_1~X1~X0){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X3~X0){\unicdcdcdhd}(m1\_subset\_1~X4~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k9\_domain\_1~X0~X1~\\
X2~X3~X4)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgjdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k4\_glib\_000}}~{k5\_numbers}}\label{hyp:egehpflgedpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k3\_glib\_000}}~{k5\_numbers}}\label{hyp:egehpflgddpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k2\_glib\_000}}~{k5\_numbers}}\label{hyp:egehpflgcdpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k5\_glib\_000=k9\_domain\_1~k5\_numbers~k1\_glib\_000~k2\_glib\_000~\\
k3\_glib\_000~k4\_glib\_000\end{array}
\label{hyp:egfdpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (X4=k2\_enumset1~\\
X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  (X5 \in X4){\unicdbdjded}(\preoh (X5{\unicdcdgdad}X0){\unicdcdcdhd}((X5{\unicdcdgdad}X1){\unicdcdcdhd}((X5{\unicdcdgdad}X2){\unicdcdcdhd}\\
(X5{\unicdcdgdad}X3)))))\end{array}
\label{hyp:egcdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_glib\_000}={np\_\_1}}\label{hyp:egbdpfhgmgjgcgpfadadad}
\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)))){\unicdbdjdcd}((v1\_glib\_000~X0){\unicdbdjded}((k1\_glib\_000 \in k1\_relset\_1~\\
k5\_numbers~X0){\unicdcdcdhd}((k2\_glib\_000 \in k1\_relset\_1~k5\_numbers~X0){\unicdcdcdhd}((\\
k3\_glib\_000 \in k1\_relset\_1~k5\_numbers~X0){\unicdcdcdhd}((k4\_glib\_000 \in k1\_relset\_1~\\
k5\_numbers~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k6\_glib\_000~X0)){\unicdcdcdhd}(((v1\_funct\_1~\\
(k8\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_2~(k8\_glib\_000~X0)~(k7\_glib\_000~\\
X0)~(k6\_glib\_000~X0)){\unicdcdcdhd}(m1\_subset\_1~(k8\_glib\_000~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k7\_glib\_000~X0)~(k6\_glib\_000~X0)))))){\unicdcdcdhd}((v1\_funct\_1~\\
(k9\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_2~(k9\_glib\_000~X0)~(k7\_glib\_000~\\
X0)~(k6\_glib\_000~X0)){\unicdcdcdhd}(m1\_subset\_1~(k9\_glib\_000~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k7\_glib\_000~X0)~(k6\_glib\_000~X0)))))))))))))\end{array}
\label{hyp:egbdadpfhgmgjgcgpfadadad}
\end{equation}
\begin{theorem}\label{thm:mgbdddpfhgmgjgcgpfadadad}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}((v1\_glib\_000~X0){\unicdbdjded}((r1\_tarski~k5\_glib\_000~\\
(k1\_relset\_1~k5\_numbers~X0)){\unicdcdcdhd}((\preoh v1\_xboole\_0~(k6\_glib\_000~X0)){\unicdcdcdhd}\\
(((v1\_funct\_1~(k8\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_2~(k8\_glib\_000~X0)~\\
(k7\_glib\_000~X0)~(k6\_glib\_000~X0)){\unicdcdcdhd}(m1\_subset\_1~(k8\_glib\_000~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k7\_glib\_000~X0)~(k6\_glib\_000~X0)))))){\unicdcdcdhd}\\
((v1\_funct\_1~(k9\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_2~(k9\_glib\_000~X0)~\\
(k7\_glib\_000~X0)~(k6\_glib\_000~X0)){\unicdcdcdhd}(m1\_subset\_1~(k9\_glib\_000~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k7\_glib\_000~X0)~(k6\_glib\_000~X0))))))))))\end{array}$$
\end{theorem}
\end{document}
