\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{t22\_card\_4 (TMLPG4vFrKxJwHKJ4a1BDMNzdLdiUpG5Red)}
\maketitle
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 .  (v1\_finset\_1~X1){\unicdbdjdcd}((v1\_finset\_1~X0){\unicdcdcdid}((\\
X1=k1\_xboole\_0){\unicdcdcdid}((r2\_wellord2~(k2\_zfmisc\_1~X0~X1)~X0){\unicdcdcdhd}(k1\_card\_1~\\
(k2\_zfmisc\_1~X0~X1)=k1\_card\_1~X0))))\end{array}
\label{hyp:ehbdjdpfdgbgchegpfed}
\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:ehcdcdpfdgbgchegpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_finset\_1~X0){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}(\\
(v1\_finset\_1~X1){\unicdcdcdid}(k2\_card\_2~(k1\_card\_1~X1)~(k1\_card\_1~X0)=k1\_card\_1~\\
X1)))\end{array}$$
\end{theorem}
\end{document}
