\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{t21\_card\_4 (TMKk4mstqQXEm89HbKbEZNwwayRLsCzdao5)}
\maketitle
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh (\preoh v1\_finset\_1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  \preoh (r1\_tarski~X1~X0){\unicdcdcdhd}\\
(k1\_card\_1~X1=k4\_ordinal1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X1 .  (r1\_tarski~X1~X0){\unicdcdcdhd}\\
(k1\_card\_1~X1=k4\_ordinal1)){\unicdcdcdhd}(v1\_finset\_1~X0))\end{array}
\label{hyp:ehidhdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}((k6\_numbers \in \\
X1){\unicdbdjdcd}((v1\_finset\_1~X0){\unicdcdcdid}(((\preoh r1\_ordinal1~X1~X0){\unicdcdcdhd}(\preoh X1 \in X0)){\unicdcdcdid}((k2\_card\_2~\\
X0~X1=X0){\unicdcdcdhd}(k2\_card\_2~X1~X0=X0))))))\end{array}
\label{hyp:ehbdgdpfdgbgchegpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~\\
X0)~(k1\_card\_1~X1))\end{array}
\label{hyp:ehbdbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_finset\_1~X0){\unicdbdjdcd}((\preoh v1\_finset\_1~(k1\_card\_1~X0)){\unicdcdcdhd}\\
(v1\_card\_1~(k1\_card\_1~X0)))\end{array}
\label{hyp:ggdgidpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_card\_1}~{k4\_ordinal1}}\label{hyp:ggdgedpfdgbgchegpfbd}
\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 .  (X0=k4\_ordinal1){\unicdbdjded}((k1\_xboole\_0 \in X0){\unicdcdcdhd}((v4\_ordinal1~\\
X0){\unicdcdcdhd}((v3\_ordinal1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(((k1\_xboole\_0 \in \\
X1){\unicdcdcdhd}(v4\_ordinal1~X1)){\unicdbdjdcd}(r1\_tarski~X0~X1))))))\end{array}
\label{hyp:egbdbdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfdgbgchegpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_finset\_1~X0){\unicdbdjdcd}(k1\_card\_1~X0=k2\_card\_2~k4\_ordinal1~\\
(k1\_card\_1~X0))\end{array}$$
\end{theorem}
\end{document}
