\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{t9\_supinf\_1 (TMHCpQ3VKFThHErcSdavogFyPfuPpeAJsRr)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_setfam\_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 $ k7\_numbers : {\iota}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_setfam\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_supinf\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_setfam\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k1\_zfmisc\_1~k7\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~\\
X1){\unicdbdjdcd}((X1=k5\_setfam\_1~k7\_numbers~X0){\unicdbdjdcd}(m2\_xxreal\_2~(k2\_xxreal\_2~\\
(k6\_supinf\_1~X0))~X1)))\end{array}
\label{hyp:ehidpfdhfhahjgogggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_setfam\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k1\_zfmisc\_1~k7\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v2\_membered~X1)){\unicdbdjdcd}((X1=k5\_setfam\_1~k7\_numbers~\\
X0){\unicdbdjdcd}(m2\_xxreal\_2~(k2\_xxreal\_2~X1)~(k6\_supinf\_1~X0))))\end{array}
\label{hyp:ehhdpfdhfhahjgogggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_setfam\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k1\_zfmisc\_1~k7\_numbers))))){\unicdbdjdcd}(v2\_membered~(\\
k6\_supinf\_1~X0))\end{array}
\label{hyp:egehpflggdpfdhfhahjgogggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v2\_membered}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{({{k2\_xxreal\_2}~{X0}})}})}}}\label{hyp:egehpflgcdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
X1=k2\_xxreal\_2~X0){\unicdbdjded}((m2\_xxreal\_2~X1~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_xxreal\_2~\\
X2~X0){\unicdbdjdcd}(r1\_xxreal\_0~X2~X1)))))\end{array}
\label{hyp:egedpfihihchfgbgmgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfdhfhahjgogggpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_setfam\_1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k1\_zfmisc\_1~k7\_numbers))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(v2\_membered~X1)){\unicdbdjdcd}((X1=k5\_setfam\_1~k7\_numbers~\\
X0){\unicdbdjdcd}(k2\_xxreal\_2~X1=k2\_xxreal\_2~(k6\_supinf\_1~X0))))\end{array}$$
\end{theorem}
\end{document}
