\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{l161\_seq\_4 (TMdh3ab1zGgx9rqdsvo5RNKpJJrsazcMoS8)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_finset\_1 : {{\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 $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v4\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_seq\_4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  ((X0~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(k2\_nat\_1~X1~np\_\_1))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(X0~X1))\end{array}
\label{hyp:dhbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}(({\unicdcdadad} X1 .  \\
((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
((k5\_card\_1~X1=X0){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}((v4\_xxreal\_2~X1){\unicdcdcdhd}((\\
k4\_seq\_4~X1 \in X1){\unicdcdcdhd}((v3\_xxreal\_2~X1){\unicdcdcdhd}(k5\_seq\_4~X1 \in X1))))))){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
((k5\_card\_1~X1=k2\_nat\_1~X0~np\_\_1){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}((v4\_xxreal\_2~\\
X1){\unicdcdcdhd}((k4\_seq\_4~X1 \in X1){\unicdcdcdhd}((v3\_xxreal\_2~X1){\unicdcdcdhd}(k5\_seq\_4~X1 \in X1))))))))\end{array}
\label{hyp:mgbdgdadpfdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_finset\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
((k5\_card\_1~X0=k6\_numbers){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}((v4\_xxreal\_2~\\
X0){\unicdcdcdhd}((k4\_seq\_4~X0 \in X0){\unicdcdcdhd}((v3\_xxreal\_2~X0){\unicdcdcdhd}(k5\_seq\_4~X0 \in X0))))))\end{array}
\label{hyp:mgbdfdjdpfdhfgbhpfed}
\end{equation}
\begin{theorem}\label{thm:mgbdgdbdpfdhfgbhpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
((k5\_card\_1~X1=X0){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}((v4\_xxreal\_2~X1){\unicdcdcdhd}((\\
k4\_seq\_4~X1 \in X1){\unicdcdcdhd}((v3\_xxreal\_2~X1){\unicdcdcdhd}(k5\_seq\_4~X1 \in X1)))))))\end{array}$$
\end{theorem}
\end{document}
