\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{t51\_chain\_1 (TMdovo5Hvw838XxGYnWS8La9K7ouGa7Y6Sy)}
\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\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k10\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_abian : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_chain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m2\_subset\_1~X0~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_chain\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k4\_chain\_1~\\
X0~X1~(k2\_nat\_1~X2~np\_\_1)))){\unicdbdjdcd}(k10\_chain\_1~X0~X1~X2~X3=ReplSep~(toset~\\
({\uniddcgcg} X4 : \iota .  m2\_subset\_1~X4~(k1\_zfmisc\_1~(k1\_euclid~X0))~(k4\_chain\_1~\\
X0~X1~X2)))~({\uniddcgcg} X4 : \iota .  (r1\_xxreal\_0~(k2\_nat\_1~X2~np\_\_1)~X0){\unicdcdcdhd}(\\
\preoh v1\_abian~(k5\_card\_1~(k9\_subset\_1~(k4\_chain\_1~X0~X1~(k2\_nat\_1~\\
X2~np\_\_1))~(k9\_chain\_1~X0~X1~X2~X4)~X3))))~({\uniddcgcg} X4 : \iota .  X4)))))\end{array}
\label{hyp:egbdcdpfdgigbgjgogpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfdgigbgjgogpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m2\_subset\_1~X1~k1\_numbers~k5\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_chain\_1~X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k1\_euclid~X1))~(k4\_chain\_1~X1~X2~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k4\_chain\_1~X1~X2~(k2\_nat\_1~X0~np\_\_1)))){\unicdbdjdcd}((X3 \in \\
k10\_chain\_1~X1~X2~X0~X4){\unicdbdjded}((r1\_xxreal\_0~(k2\_nat\_1~X0~np\_\_1)~X1){\unicdcdcdhd}\\
(\preoh v1\_abian~(k5\_card\_1~(k9\_subset\_1~(k4\_chain\_1~X1~X2~(k2\_nat\_1~\\
X0~np\_\_1))~(k9\_chain\_1~X1~X2~X0~X3)~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
