\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{t16\_card\_4 (TMKk1HHApaqYMGvLZfFZrCWTq9n4HukAyJb)}
\maketitle
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}((X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}\\
((r1\_ordinal1~X1~(k2\_card\_2~X1~X0)){\unicdcdcdhd}(r1\_ordinal1~X1~(k2\_card\_2~\\
X0~X1)))))\end{array}
\label{hyp:ehjdfdpfdgbgchegpfcd}
\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 .  \\
(v1\_card\_1~X2){\unicdbdjdcd}(((X0 \in X1){\unicdcdcdid}(r1\_ordinal1~X0~X1)){\unicdbdjdcd}((r1\_ordinal1~\\
(k2\_card\_2~X2~X0)~(k2\_card\_2~X2~X1)){\unicdcdcdhd}((r1\_ordinal1~(k2\_card\_2~\\
X2~X0)~(k2\_card\_2~X1~X2)){\unicdcdcdhd}((r1\_ordinal1~(k2\_card\_2~X0~X2)~(k2\_card\_2~\\
X2~X1)){\unicdcdcdhd}(r1\_ordinal1~(k2\_card\_2~X0~X2)~(k2\_card\_2~X1~X2))))))))\end{array}
\label{hyp:ehjdbdpfdgbgchegpfcd}
\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}\\
((r1\_ordinal1~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}X1))))\end{array}
\label{hyp:ehddpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{({\preoh{{{v1\_finset\_1}~{X0}}}})}{\unicdbdjdcd}{({{{{k2\_card\_2}~{X0}}~{X0}}={X0}})}})}}}\label{hyp:ehbdfdpfdgbgchegpfed}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\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 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(k2\_card\_2~\\
X0~X1=k1\_card\_1~(k2\_zfmisc\_1~X0~X1)))\end{array}
\label{hyp:egcdpfdgbgchegpfcd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({\preoh{{{X1} \in {X0}}}})}}}}\label{hyp:bgogehjgdhjhngngfgehchjhpfchcdpfigjgegegfgog}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfdgbgchegpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}((k6\_numbers \in \\
X1){\unicdbdjdcd}((v1\_finset\_1~X0){\unicdcdcdid}(((\preoh r1\_ordinal1~X1~X0){\unicdcdcdhd}(\preoh X1 \in X0)){\unicdcdcdid}((k2\_card\_2~\\
X0~X1=X0){\unicdcdcdhd}(k2\_card\_2~X1~X0=X0))))))\end{array}$$
\end{theorem}
\end{document}
