\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{t18\_card\_5 (TMGD3ppaothAGgdkiPB4LduMtzarSthpfXD)}
\maketitle
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\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}((v1\_finset\_1~\\
X0){\unicdbdjdcd}(((\preoh r1\_ordinal1~X1~X0){\unicdcdcdhd}(\preoh X1 \in X0)){\unicdcdcdid}(v1\_finset\_1~X1))))\end{array}
\label{hyp:ehjdcdpfdgbgchegpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{X0}{\unicdcdgdad}{k1\_xboole\_0}})}{\unicdbdjdcd}{({{k1\_xboole\_0} \in {X0}})}})}}}\label{hyp:ehidpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(\preoh (\preoh v1\_finset\_1~\\
X0){\unicdcdcdhd}(((r1\_ordinal1~X1~X0){\unicdcdcdid}(X1 \in X0)){\unicdcdcdhd}(\preoh (k1\_card\_2~X0~X1=X0){\unicdcdcdhd}(\\
k1\_card\_2~X1~X0=X0)))))\end{array}
\label{hyp:ehhdgdpfdgbgchegpfcd}
\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}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_card\_1~X0){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}(k2\_card\_2~\\
X0~X1=k2\_card\_2~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfdgbgchegpfcd}
\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 .  {{({\preoh{{{v1\_finset\_1}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{X0}}}})}}}\label{hyp:dgdgbdpfdgbgchegpffd}
\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:ehbdidpfdgbgchegpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_finset\_1~X1){\unicdcdcdhd}(v1\_card\_1~\\
X1)){\unicdbdjdcd}(((r1\_ordinal1~X1~X0){\unicdcdcdid}(X1 \in X0)){\unicdbdjdcd}((k1\_card\_2~X1~X0=X0){\unicdcdcdhd}(\\
(k1\_card\_2~X0~X1=X0){\unicdcdcdhd}((k2\_card\_2~X1~X0=X0){\unicdcdcdhd}(k2\_card\_2~X0~X1=X0))))))\end{array}$$
\end{theorem}
\end{document}
