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\begin{document}
\title{t24\_classes2 (TMUaBTJqbpodnVw8Gjz6FbwjS49zhKi14dR)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_classes1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_card\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((k9\_xtuple\_0~X0=k1\_xboole\_0){\unicdbdjded}(\\
k10\_xtuple\_0~X0=k1\_xboole\_0))\end{array}
\label{hyp:ehedcdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((v4\_ordinal1~X0){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}\\
({\unicdcdadad} X1 .  (X1 \in k4\_classes1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (v3\_ordinal1~X2){\unicdcdcdhd}\\
((X2 \in X0){\unicdcdcdhd}(X1 \in k4\_classes1~X2))))))\end{array}
\label{hyp:ehddbdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k3\_tarski}~{k1\_xboole\_0}}={k1\_xboole\_0}}\label{hyp:ehcdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k4\_classes1}~{k1\_xboole\_0}}={k1\_xboole\_0}}\label{hyp:ehcdjdpfdgmgbgdhdhfgdhbd}
\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}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v5\_ordinal1~X0))){\unicdbdjdcd}\\
(v3\_ordinal1~(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgedpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k3\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
({\unicdcdaddd} X3 .  (X2 \in X3){\unicdcdcdhd}(X3 \in X0)))\end{array}
\label{hyp:egedpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}(k3\_card\_3~X0=\\
k3\_tarski~(k10\_xtuple\_0~X0))\end{array}
\label{hyp:egedpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=\\
k10\_xtuple\_0~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  (X3 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(X2=k1\_funct\_1~X0~X3))))\end{array}
\label{hyp:egddpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v3\_ordinal1~X1))\end{array}
\label{hyp:dgdgfdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfdgmgbgdhdhfgdhcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}(v1\_funct\_1~X0))){\unicdbdjdcd}\\
(((v4\_ordinal1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}\\
((X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~X0~X1=k4\_classes1~X1)))){\unicdbdjdcd}(\\
k4\_classes1~(k9\_xtuple\_0~X0)=k3\_card\_3~X0))\end{array}$$
\end{theorem}
\end{document}
