\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{l16\_glib\_004 (TMGRbfT4PFux1bKU4XXeAj9hCLAqMSh6sJG)}
\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 $ v1\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_glib\_004 : {\iota}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k10\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}$ be given.
Let $ k3\_enumset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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.
Let $ k2\_glib\_003 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ 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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_glib\_000 : {{\iota}{\unicdbdjdcd}{\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\_\_5){\unicdcdcdhd}(m2\_subset\_1~np\_\_5~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_5~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_5~k1\_numbers))\end{array}
\label{hyp:dhahdgfdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\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){\unicdcdcdhd}(m1\_subset\_1~X5~X0)))))){\unicdbdjdcd}\\
(k10\_domain\_1~X0~X1~X2~X3~X4~X5=k3\_enumset1~X1~X2~X3~X4~X5)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfegpgngbgjgogpfbd}
\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}
{{{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}
{{{m1\_subset\_1}~{k1\_glib\_000}}~{k5\_numbers}}\label{hyp:egehpflgbdpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
((\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){\unicdcdcdhd}(m1\_subset\_1~X5~X0)))))){\unicdbdjdcd}\\
(m1\_subset\_1~(k10\_domain\_1~X0~X1~X2~X3~X4~X5)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgbdadpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_glib\_004=k10\_domain\_1~k5\_numbers~k1\_glib\_000~k2\_glib\_000~\\
k3\_glib\_000~k4\_glib\_000~k2\_glib\_003\end{array}
\label{hyp:egedpfhgmgjgcgpfadaded}
\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\_003~X0){\unicdbdjded}((k2\_glib\_003 \in k1\_relset\_1~\\
k5\_numbers~X0){\unicdcdcdhd}((v1\_relat\_1~(k1\_funct\_1~X0~k2\_glib\_003)){\unicdcdcdhd}((\\
v4\_relat\_1~(k1\_funct\_1~X0~k2\_glib\_003)~(k7\_glib\_000~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
(k1\_funct\_1~X0~k2\_glib\_003)){\unicdcdcdhd}(v1\_partfun1~(k1\_funct\_1~X0~k2\_glib\_003)~\\
(k7\_glib\_000~X0)))))))\end{array}
\label{hyp:egedpfhgmgjgcgpfadaddd}
\end{equation}
Assume the following.
\begin{equation}
{{k4\_glib\_000}={np\_\_4}}\label{hyp:egedpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{k3\_glib\_000}={np\_\_3}}\label{hyp:egddpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_glib\_000}={np\_\_2}}\label{hyp:egcdpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_glib\_003}={np\_\_5}}\label{hyp:egbdpfhgmgjgcgpfadaddd}
\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:mgbdgdpfhgmgjgcgpfadaded}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v1\_glib\_003~X0)))))){\unicdbdjdcd}\\
(r1\_tarski~k2\_glib\_004~(k1\_relset\_1~k5\_numbers~X0))\end{array}$$
\end{theorem}
\end{document}
