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\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t38\_glib\_003 (TMPH1wF1CJ28Xv8hSzAcKVAfRu3fXoiwEDx)}
\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 $ v3\_glib\_003 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_glib\_000 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_glib\_003 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_glib\_003 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_funct\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_glib\_000 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k4\_glib\_003 : {\iota}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\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)))){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}(k1\_funct\_1~(k13\_glib\_000~X0~X2~X1)~X2=X1))\end{array}
\label{hyp:ehidpfhgmgjgcgpfadadad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_7){\unicdcdcdhd}(m2\_subset\_1~np\_\_7~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_7~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_7~k1\_numbers))\end{array}
\label{hyp:dhahdghdpfogfhngfgchbgmgdh}
\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 .  ((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}(v3\_glib\_003~X0)))))){\unicdbdjdcd}((v1\_relat\_1~(k13\_glib\_003~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_relat\_1~(k13\_glib\_003~X0~X1~X2)~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
(k13\_glib\_003~X0~X1~X2)){\unicdcdcdhd}((v1\_finset\_1~(k13\_glib\_003~X0~X1~X2)){\unicdcdcdhd}\\
((v1\_glib\_000~(k13\_glib\_003~X0~X1~X2)){\unicdcdcdhd}(v3\_glib\_003~(k13\_glib\_003~\\
X0~X1~X2)))))))\end{array}
\label{hyp:egehpflgbdddpfhgmgjgcgpfadaddd}
\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}(v3\_glib\_003~X0)))))){\unicdbdjdcd}\\
(k7\_glib\_003~X0=k1\_funct\_1~X0~k4\_glib\_003)\end{array}
\label{hyp:egjdpfhgmgjgcgpfadaddd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k16\_funcop\_1~X0~X1=k7\_funcop\_1~(k1\_tarski~\\
X0)~X1\end{array}
\label{hyp:egjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k4\_glib\_003}={np\_\_7}}\label{hyp:egddpfhgmgjgcgpfadaddd}
\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}(v3\_glib\_003~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X1 \in k6\_glib\_000~X0){\unicdbdjdcd}(k13\_glib\_003~X0~\\
X1~X2=k13\_glib\_000~X0~k4\_glib\_003~(k1\_funct\_4~(k7\_glib\_003~X0)~\\
(k16\_funcop\_1~X1~X2)))){\unicdcdcdhd}((\preoh X1 \in k6\_glib\_000~X0){\unicdbdjdcd}(k13\_glib\_003~\\
X0~X1~X2=X0)))\end{array}
\label{hyp:egcdcdpfhgmgjgcgpfadaddd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfhgmgjgcgpfadaddd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_finset\_1~X0){\unicdcdcdhd}((v1\_glib\_000~X0){\unicdcdcdhd}(v3\_glib\_003~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X1 \in k6\_glib\_000~X0){\unicdbdjdcd}(k7\_glib\_003~(k13\_glib\_003~\\
X0~X1~X2)=k1\_funct\_4~(k7\_glib\_003~X0)~(k16\_funcop\_1~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
