\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{t18\_card\_4 (TMTyC6y88u2WLNcbt18hZf9CL6ytpbJ8V3y)}
\maketitle
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r2\_wellord2~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~\\
(k1\_card\_1~X0)~X1)){\unicdcdcdhd}((r2\_wellord2~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~\\
X0~(k1\_card\_1~X1))){\unicdcdcdhd}((r2\_wellord2~(k2\_zfmisc\_1~X0~X1)~(k2\_zfmisc\_1~\\
(k1\_card\_1~X0)~(k1\_card\_1~X1))){\unicdcdcdhd}((k1\_card\_1~(k2\_zfmisc\_1~X0~X1)=\\
k1\_card\_1~(k2\_zfmisc\_1~(k1\_card\_1~X0)~X1)){\unicdcdcdhd}((k1\_card\_1~(k2\_zfmisc\_1~\\
X0~X1)=k1\_card\_1~(k2\_zfmisc\_1~X0~(k1\_card\_1~X1))){\unicdcdcdhd}(k1\_card\_1~\\
(k2\_zfmisc\_1~X0~X1)=k1\_card\_1~(k2\_zfmisc\_1~(k1\_card\_1~X0)~(k1\_card\_1~\\
X1)))))))\end{array}
\label{hyp:ehhdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r2\_wellord2~X0~X1){\unicdbdjded}(k1\_card\_1~X0=k1\_card\_1~\\
X1)\end{array}
\label{hyp:ehfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{({\preoh{{{v1\_finset\_1}~{X0}}}})}{\unicdbdjdcd}{({{{{k2\_card\_2}~{X0}}~{X0}}={X0}})}})}}}\label{hyp:ehbdfdpfdgbgchegpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_finset\_1~X0){\unicdbdjdcd}((\preoh v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}\\
(v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdgidpfdgbgchegpfbd}
\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 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(k2\_card\_2~\\
X0~X1=k1\_card\_1~(k2\_zfmisc\_1~X0~X1)))\end{array}
\label{hyp:egcdpfdgbgchegpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfdgbgchegpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_finset\_1~X0){\unicdbdjdcd}((r2\_wellord2~(k2\_zfmisc\_1~X0~X0)~\\
X0){\unicdcdcdhd}(k1\_card\_1~(k2\_zfmisc\_1~X0~X0)=k1\_card\_1~X0))\end{array}$$
\end{theorem}
\end{document}
