\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{t29\_card\_fil (TMNV1TGwvm9FvYaXADX6sb1DUk3MHJcmJMi)}
\maketitle
Let $ v6\_card\_fil : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_card\_fil : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_finset\_1~X0){\unicdcdcdhd}(v1\_card\_1~X0)){\unicdbdjdcd}((v1\_card\_5~k4\_ordinal1){\unicdcdcdhd}\\
(v1\_card\_5~(k2\_card\_1~X0)))\end{array}
\label{hyp:ehddadpfdgbgchegpffd}
\end{equation}
Assume the following.
\begin{equation}
{{v5\_card\_fil}~{k4\_ordinal1}}\label{hyp:ehcdgdpfdgbgchegpfggjgmg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_finset\_1}~{k4\_ordinal1}}}}\label{hyp:ggdghdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_card\_1}~{k4\_ordinal1}}\label{hyp:ggdgedpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_finset\_1~X0){\unicdcdcdhd}(v1\_card\_1~X0)){\unicdbdjdcd}((v6\_card\_fil~\\
X0){\unicdbdjded}((v1\_card\_5~X0){\unicdcdcdhd}(v5\_card\_fil~X0)))\end{array}
\label{hyp:egbdfdpfdgbgchegpfggjgmg}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfdgbgchegpfggjgmg}
${{v6\_card\_fil}~{k4\_ordinal1}}$.
\end{theorem}
\end{document}
