\documentclass{article}
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\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\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t20\_frechet (TMb8Z2hWPt3PMBwd2XZPwZKKJFnpKrJahgb)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_metric\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_frechet : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_pcomps\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_card\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_frechet : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_yellow\_8 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_metric\_1~X0)){\unicdbdjdcd}(\preoh v2\_struct\_0~\\
(k3\_pcomps\_1~X0))\end{array}
\label{hyp:ggdgcdpfahdgpgngahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}\\
((v7\_metric\_1~X0){\unicdcdcdhd}((v8\_metric\_1~X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~\\
X0)))))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~(k3\_pcomps\_1~X0)))){\unicdbdjdcd}(\\
v4\_card\_3~(k1\_frechet~X0~X1))\end{array}
\label{hyp:ggdgcdpfggchfgdgigfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}\\
((v7\_metric\_1~X0){\unicdcdcdhd}((v8\_metric\_1~X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~\\
X0)))))){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~(k3\_pcomps\_1~X0)))){\unicdbdjdcd}(\\
(v1\_tops\_2~(k1\_frechet~X0~X1)~(k3\_pcomps\_1~X0)){\unicdcdcdhd}(v1\_yellow\_8~\\
(k1\_frechet~X0~X1)~(k3\_pcomps\_1~X0)~X1))\end{array}
\label{hyp:ggdgbdpfggchfgdgigfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_metric\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_pre\_topc}~{({{k3\_pcomps\_1}~{X0}})}})}}}\label{hyp:egehpflgddpfahdgpgngahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_metric\_1~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(u1\_struct\_0~(k3\_pcomps\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_frechet~X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~(u1\_struct\_0~(k3\_pcomps\_1~\\
X0)))))\end{array}
\label{hyp:egehpflgbdpfggchfgdgigfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}((v1\_frechet~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  \\
((v1\_tops\_2~X2~X0){\unicdcdcdhd}((v1\_yellow\_8~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))){\unicdcdcdhd}(v4\_card\_3~X2))))\end{array}
\label{hyp:egcdpfggchfgdgigfgeh}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfggchfgdgigfgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v7\_metric\_1~\\
X0){\unicdcdcdhd}((v8\_metric\_1~X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~X0)))))){\unicdbdjdcd}\\
(v1\_frechet~(k3\_pcomps\_1~X0))\end{array}$$
\end{theorem}
\end{document}
