\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{t4\_extreal2 (TMdJmCnDa8mg8u5F6U7XPg1K2KDveM83BEH)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_extreal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_supinf\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_supinf\_2 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}(k1\_xxreal\_3~X0~(k2\_xxreal\_3~X0)=\\
k6\_numbers)\end{array}
\label{hyp:ehhdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{{{k1\_xxreal\_3}~{X0}}~{k6\_numbers}}={X0}})}}}\label{hyp:ehedpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~k6\_numbers~\\
X0){\unicdbdjdcd}(k3\_extreal1~X0=k2\_supinf\_2~X0))\end{array}
\label{hyp:ehedpffgihehchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~\\
(k3\_extreal1~X0))\end{array}
\label{hyp:ehddpffgihehchfgbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~\\
X0){\unicdbdjdcd}(k3\_extreal1~X0=X0))\end{array}
\label{hyp:ehddpffgihehchfgbgmgbd}
\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}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}(k2\_supinf\_2~X0=k2\_xxreal\_3~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_supinf\_2}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k3\_extreal1~\\
X0)~k7\_numbers)\end{array}
\label{hyp:egehpflgddpffgihehchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_supinf\_2}}~{k7\_numbers}}\label{hyp:egehpflgbdpfdhfhahjgogggpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k7\_numbers}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedpffgihehchfgbgmgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(\\
r1\_xxreal\_0~(k3\_extreal1~X0)~k6\_numbers))\end{array}$$
\end{theorem}
\end{document}
