\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{t10\_card\_2 (TMRX8SEm7DWuDXLzfV5p3mdbcu6hR8r7q5m)}
\maketitle
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (X2{\unicdcdgdad}X3){\unicdbdjdcd}((r2\_wellord2~(k10\_ordinal2~X0~X1)~(k2\_xboole\_0~\\
(k2\_zfmisc\_1~X0~(k1\_tarski~X2))~(k2\_zfmisc\_1~X1~(k1\_tarski~X3)))){\unicdcdcdhd}\\
(k1\_card\_1~(k10\_ordinal2~X0~X1)=k1\_card\_1~(k2\_xboole\_0~(k2\_zfmisc\_1~\\
X0~(k1\_tarski~X2))~(k2\_zfmisc\_1~X1~(k1\_tarski~X3)))))))\end{array}
\label{hyp:ehjdpfdgbgchegpfcd}
\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 .  {{{k1\_card\_1}~{({{k1\_card\_1}~{X0}})}}={{k1\_card\_1}~{X0}}}}\label{hyp:ahchpgkgfgdgehjgghjgehjhpflgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(k1\_card\_2~\\
X0~X1=k1\_card\_1~(k10\_ordinal2~X0~X1)))\end{array}
\label{hyp:egbdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_card\_1~X0){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}(k1\_card\_2~\\
X0~X1=k1\_card\_2~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdpfdgbgchegpfcd}
\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:ehbdadpfdgbgchegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (X2{\unicdcdgdad}X3){\unicdbdjdcd}((r2\_wellord2~(k1\_card\_2~X0~X1)~(k2\_xboole\_0~\\
(k2\_zfmisc\_1~X0~(k1\_tarski~X2))~(k2\_zfmisc\_1~X1~(k1\_tarski~X3)))){\unicdcdcdhd}\\
(k1\_card\_2~X0~X1=k1\_card\_1~(k2\_xboole\_0~(k2\_zfmisc\_1~X0~(k1\_tarski~\\
X2))~(k2\_zfmisc\_1~X1~(k1\_tarski~X3)))))))\end{array}$$
\end{theorem}
\end{document}
