\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{t93\_card\_2 (TMSd1phQF9HXYAPJrwJptRRGLdrNsUTSbHc)}
\maketitle
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k3\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_card\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_card\_1~X3){\unicdbdjdcd}(\preoh (\preoh (\preoh (X0 \in X1){\unicdcdcdhd}(X2 \in \\
X3)){\unicdcdcdhd}((\preoh (r1\_ordinal1~X0~X1){\unicdcdcdhd}(X2 \in X3)){\unicdcdcdhd}((\preoh (X0 \in X1){\unicdcdcdhd}(r1\_ordinal1~\\
X2~X3)){\unicdcdcdhd}(\preoh (r1\_ordinal1~X0~X1){\unicdcdcdhd}(r1\_ordinal1~X2~X3))))){\unicdcdcdhd}((X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
(\preoh r1\_ordinal1~(k3\_card\_2~X0~X2)~(k3\_card\_2~X1~X3)))))))\end{array}
\label{hyp:ehjdcdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}((X0 \in X1){\unicdbdjded}\\
(\preoh r1\_ordinal1~X1~X0)))\end{array}
\label{hyp:ehedpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{r1\_tarski}~{k1\_xboole\_0}}~{X0}}}\label{hyp:ehcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}((X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k3\_card\_2~k6\_numbers~\\
X0=k6\_numbers))\end{array}
\label{hyp:ehcdgdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
r1\_ordinal1~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_ordinal1~X0~X1){\unicdbdjded}(r1\_tarski~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_card\_1~X0){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}(v1\_card\_1~\\
(k3\_card\_2~X0~X1))\end{array}
\label{hyp:egehpflgddpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({\preoh{{{X1} \in {X0}}}})}}}}\label{hyp:bgogehjgdhjhngngfgehchjhpfchcdpfigjgegegfgog}
\end{equation}
\begin{theorem}\label{thm:ehjdddpfdgbgchegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_card\_1~X2){\unicdbdjdcd}(\preoh ((X0 \in X1){\unicdcdcdid}(r1\_ordinal1~X0~X1)){\unicdcdcdhd}((X2{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}\\
(\preoh (r1\_ordinal1~(k3\_card\_2~X2~X0)~(k3\_card\_2~X2~X1)){\unicdcdcdhd}(r1\_ordinal1~\\
(k3\_card\_2~X0~X2)~(k3\_card\_2~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
