\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t35\_card\_2 (TMZTuCuHVjth2SNJd7sGXvKp9PvUKDNHmQL)}
\maketitle
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ k1\_tarski : {{\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 .  (r2\_wellord2~X0~(k2\_zfmisc\_1~X0~(k1\_tarski~\\
X1))){\unicdcdcdhd}(k1\_card\_1~X0=k1\_card\_1~(k2\_zfmisc\_1~X0~(k1\_tarski~X1)))\end{array}
\label{hyp:ehgdpfdgbgchegpfcd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((r1\_xboole\_0~X0~\\
X1){\unicdcdcdhd}((r1\_xboole\_0~X2~X3){\unicdcdcdhd}((r2\_wellord2~X0~X2){\unicdcdcdhd}(r2\_wellord2~X1~\\
X3)))){\unicdbdjdcd}(r2\_wellord2~(k2\_xboole\_0~X0~X1)~(k2\_xboole\_0~X2~X3))\end{array}
\label{hyp:ehddbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\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}
\label{hyp:ehbdadpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X0{\unicdcdgdad}X1){\unicdbdjdcd}(r1\_xboole\_0~\\
(k2\_zfmisc\_1~X2~(k1\_tarski~X0))~(k2\_zfmisc\_1~X3~(k1\_tarski~X1)))\end{array}
\label{hyp:mgcdfdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_card\_1}~{({{k1\_card\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfdgbgchegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_xboole\_0~X0~X1){\unicdbdjdcd}(k1\_card\_1~(k2\_xboole\_0~\\
X0~X1)=k1\_card\_2~(k1\_card\_1~X0)~(k1\_card\_1~X1))\end{array}$$
\end{theorem}
\end{document}
