\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{t15\_card\_2 (TMGSEeJJJJM4Q8fDNHJPrKiL1QGheGsrAtZ)}
\maketitle
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
{\unicdcdadad} X6 .  {\unicdcdadad} X7 .  ((r2\_wellord2~X0~X1){\unicdcdcdhd}(r2\_wellord2~X2~X3)){\unicdbdjdcd}\\
((X4=X5){\unicdcdcdid}((X6=X7){\unicdcdcdid}((r2\_wellord2~(k2\_xboole\_0~(k2\_zfmisc\_1~\\
X0~(k1\_tarski~X4))~(k2\_zfmisc\_1~X2~(k1\_tarski~X5)))~(k2\_xboole\_0~\\
(k2\_zfmisc\_1~X1~(k1\_tarski~X6))~(k2\_zfmisc\_1~X3~(k1\_tarski~X7)))){\unicdcdcdhd}\\
(k1\_card\_1~(k2\_xboole\_0~(k2\_zfmisc\_1~X0~(k1\_tarski~X4))~(k2\_zfmisc\_1~\\
X2~(k1\_tarski~X5)))=k1\_card\_1~(k2\_xboole\_0~(k2\_zfmisc\_1~X1~(k1\_tarski~\\
X6))~(k2\_zfmisc\_1~X3~(k1\_tarski~X7)))))))\end{array}
\label{hyp:ehbdcdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r2\_wellord2}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfdgbgchegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r2\_wellord2~(k2\_xboole\_0~(k2\_zfmisc\_1~\\
X0~(k1\_tarski~k6\_numbers))~(k2\_zfmisc\_1~X1~(k1\_tarski~np\_\_1)))~\\
(k2\_xboole\_0~(k2\_zfmisc\_1~X1~(k1\_tarski~k6\_numbers))~(k2\_zfmisc\_1~\\
X0~(k1\_tarski~np\_\_1)))){\unicdcdcdhd}(k1\_card\_1~(k2\_xboole\_0~(k2\_zfmisc\_1~\\
X0~(k1\_tarski~k6\_numbers))~(k2\_zfmisc\_1~X1~(k1\_tarski~np\_\_1)))=\\
k1\_card\_1~(k2\_xboole\_0~(k2\_zfmisc\_1~X1~(k1\_tarski~k6\_numbers))~\\
(k2\_zfmisc\_1~X0~(k1\_tarski~np\_\_1))))\end{array}$$
\end{theorem}
\end{document}
