\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t9\_extreal1 (TMQ4CnaLPBUNv7hSPpPWxpAcZAo5CB73GWK)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ k4\_extreal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_supinf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}(k4\_extreal1~(k12\_finseq\_1~\\
k7\_numbers~X0)=X0)\end{array}
\label{hyp:ehidpffgihehchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_finseq\_1~X1~X0){\unicdcdcdhd}(m1\_finseq\_1~\\
X2~X0)){\unicdbdjdcd}(k8\_finseq\_1~X0~X1~X2=k7\_finseq\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X2~X0))){\unicdbdjdcd}(k2\_finseq\_4~X0~X1~X2=k10\_finseq\_1~\\
X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggjgogdhfgbhpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k12\_finseq\_1~X0~X1=k5\_finseq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k7\_numbers){\unicdbdjdcd}(k4\_extreal1~(k8\_finseq\_1~k7\_numbers~X0~(k12\_finseq\_1~\\
k7\_numbers~X1))=k3\_supinf\_2~(k4\_extreal1~X0)~X1))\end{array}
\label{hyp:mgbdbdpffgihehchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k7\_numbers}}}}\label{hyp:ggdgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(m2\_finseq\_1~(k12\_finseq\_1~X0~X1)~X0)\end{array}
\label{hyp:egehpflgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k10\_finseq\_1~X0~X1=k7\_finseq\_1~(k9\_finseq\_1~\\
X0)~(k9\_finseq\_1~X1)\end{array}
\label{hyp:egjdpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpffgihehchfgbgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k7\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k7\_numbers){\unicdbdjdcd}(k4\_extreal1~(k2\_finseq\_4~k7\_numbers~X0~X1)=k3\_supinf\_2~\\
X0~X1))\end{array}$$
\end{theorem}
\end{document}
