\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\_fin (TMNH9cKMjKzbjH166ciJ2RK68FHbj8uMgG4)}
\maketitle
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_card\_fin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_finset\_1~X1){\unicdbdjdcd}((\\
r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_xxreal\_0~(k5\_card\_1~X0)~(k5\_card\_1~X1))))\end{array}
\label{hyp:ehedddpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(m1\_subset\_1~(k8\_relset\_1~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgidpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_finset\_1~X0){\unicdcdcdhd}\\
(v7\_ordinal1~X1)){\unicdbdjdcd}(m1\_subset\_1~(k1\_card\_fin~X0~X1~X2~X3)~(k1\_zfmisc\_1~\\
(k9\_funct\_2~X0~(k2\_tarski~X2~X3))))\end{array}
\label{hyp:egehpflgbdpfdgbgchegpfggjgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~(k9\_funct\_2~\\
X0~(k2\_tarski~X2~X3)))){\unicdbdjdcd}((X4=k1\_card\_fin~X0~X1~X2~X3){\unicdbdjded}({\unicdcdadad} X5 .  \\
(X5 \in X4){\unicdbdjded}({\unicdcdaddd} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~X0~(k2\_tarski~\\
X2~X3)){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~(k2\_tarski~\\
X2~X3)))))){\unicdcdcdhd}((X6=X5){\unicdcdcdhd}(k5\_card\_1~(k8\_relset\_1~X0~(k2\_tarski~X2~\\
X3)~X6~(k1\_tarski~X2))=X1)))))))\end{array}
\label{hyp:egbdpfdgbgchegpfggjgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_finset\_1~X1))\end{array}
\label{hyp:dgdgcdpfggjgogdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfdgbgchegpfggjgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_finset\_1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X3~(k5\_card\_1~X2)){\unicdbdjdcd}(v1\_xboole\_0~\\
(k1\_card\_fin~X2~X3~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
