\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{t38\_classes2 (TMSWaWyJFbuGY8ZjD8zgTo1B6eiUZ9KYCS1)}
\maketitle
Let $ v2\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_classes1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((X0 \in k4\_classes1~X1){\unicdbdjded}\\
(k9\_setfam\_1~X0 \in k4\_classes1~(k1\_ordinal1~X1)))\end{array}
\label{hyp:ehedcdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}(((r1\_tarski~\\
X0~X1){\unicdcdcdhd}(X1 \in k4\_classes1~X2)){\unicdbdjdcd}(X0 \in k4\_classes1~X2))\end{array}
\label{hyp:ehedbdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (v2\_classes1~X0){\unicdcdcdhd}((r1\_tarski~X1~(k4\_classes1~\\
(k1\_card\_1~X0))){\unicdcdcdhd}((\preoh r2\_tarski~X1~(k4\_classes1~(k1\_card\_1~X0))){\unicdcdcdhd}\\
(\preoh X1 \in k4\_classes1~(k1\_card\_1~X0))))\end{array}
\label{hyp:ehddgdpfdgmgbgdhdhfgdhcd}
\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}
{{{k4\_classes1}~{k1\_xboole\_0}}={k1\_xboole\_0}}\label{hyp:ehcdjdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((v4\_ordinal1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
v3\_ordinal1~X1){\unicdbdjdcd}((X1 \in X0){\unicdbdjdcd}(k1\_ordinal1~X1 \in X0))))\end{array}
\label{hyp:ehcdidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_classes1}~{X0}})}{\unicdbdjdcd}{({{v4\_ordinal1}~{({{k1\_card\_1}~{X0}})}})}}}\label{hyp:ehbdjdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_ordinal1~X0)){\unicdcdcdhd}\\
(v3\_ordinal1~(k1\_ordinal1~X0)))\end{array}
\label{hyp:ggdgcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_card\_1~X0)){\unicdcdcdhd}\\
(v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdgcdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_classes1~X0){\unicdbdjded}((v1\_classes1~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(X1 \in X0){\unicdbdjdcd}(k9\_setfam\_1~X1 \in X0)){\unicdcdcdhd}({\unicdcdadad} X1 .  \preoh (r1\_tarski~X1~X0){\unicdcdcdhd}\\
((\preoh r2\_tarski~X1~X0){\unicdcdcdhd}(\preoh X1 \in X0)))))\end{array}
\label{hyp:egcdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_ordinal1}~{X0}}={{{k2\_xboole\_0}~{X0}}~{({{k1\_tarski}~{X0}})}}}}\label{hyp:egbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_classes1~X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X1 \in X0){\unicdcdcdhd}\\
(r1\_tarski~X2~X1)){\unicdbdjdcd}(X2 \in X0))\end{array}
\label{hyp:egbdpfdgmgbgdhdhfgdhbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdgmgbgdhdhfgdhcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v2\_classes1~X0){\unicdbdjdcd}(v2\_classes1~(k4\_classes1~(k1\_card\_1~\\
X0)))\end{array}$$
\end{theorem}
\end{document}
