\documentclass{article}
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\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t8\_kurato\_2 (TMZQt2Rz51BnrmrZhVY6xPNsF76XsNYx69b)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v9\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k14\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_tbsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v8\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(u1\_struct\_0~(k15\_euclid~X0)=u1\_struct\_0~\\
(k14\_euclid~X0))\end{array}
\label{hyp:ehidpfehpgahchfgbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0)))){\unicdbdjdcd}((v9\_rltopsp1~X1~(k15\_euclid~\\
X0)){\unicdbdjded}((v6\_tbsp\_1~X1~(k14\_euclid~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k14\_euclid~X0)))))))\end{array}
\label{hyp:ehbdbdpfkgpgchegbgogcddg}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v8\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(k4\_metric\_1~X0~X1~X2=k2\_metric\_1~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfngfgehchjgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k14\_euclid~X0)){\unicdcdcdhd}\\
((v1\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}((v6\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
((v7\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}((v8\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
(v9\_metric\_1~(k14\_euclid~X0)))))))\end{array}
\label{hyp:ggdgedpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
((v6\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}((v7\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
((v8\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}((v9\_metric\_1~(k14\_euclid~X0)){\unicdcdcdhd}\\
(l1\_metric\_1~(k14\_euclid~X0)))))))\end{array}
\label{hyp:egehpflgbdedpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_metric\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v6\_tbsp\_1~\\
X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
X2~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(((X3 \in X1){\unicdcdcdhd}(X4 \in \\
X1)){\unicdbdjdcd}(r1\_xxreal\_0~(k2\_metric\_1~X0~X3~X4)~X2))))))))\end{array}
\label{hyp:eghdpfehcgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehidpflgfhchbgehpgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0)))){\unicdbdjdcd}((\preoh v9\_rltopsp1~\\
X1~(k15\_euclid~X0)){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}\\
(\preoh (\preoh r1\_xxreal\_0~X2~k6\_numbers){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(\\
u1\_struct\_0~(k14\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k14\_euclid~X0))){\unicdbdjdcd}(\preoh (X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k4\_metric\_1~\\
(k14\_euclid~X0)~X3~X4)~X2)))))))))\end{array}$$
\end{theorem}
\end{document}
