\documentclass{article}
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\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t24\_metric\_2 (TMTZBTSFfDr1RmF6T6GWC3TNmwVw44qPcuf)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_metric\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_metric\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r4\_metric\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
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\_numbers){\unicdbdjdcd}(k4\_metric\_2~X0~X1=ReplSep~(toset~\\
({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(k2\_zfmisc\_1~(k2\_metric\_2~X0)~(k2\_metric\_2~\\
X0))))~({\uniddcgcg} X2 : \iota .  {\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k2\_metric\_2~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(k2\_metric\_2~X0)){\unicdcdcdhd}((X2=k1\_domain\_1~\\
(k2\_metric\_2~X0)~(k2\_metric\_2~X0)~X3~X4){\unicdcdcdhd}(r4\_metric\_2~X0~X3~X4~X1))))~\\
({\uniddcgcg} X2 : \iota .  X2)))\end{array}
\label{hyp:eghdpfngfgehchjgdgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfngfgehchjgdgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v6\_metric\_1~X0){\unicdcdcdhd}((v8\_metric\_1~\\
X0){\unicdcdcdhd}((v9\_metric\_1~X0){\unicdcdcdhd}(l1\_metric\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_zfmisc\_1~(k2\_metric\_2~\\
X0)~(k2\_metric\_2~X0))){\unicdbdjdcd}((X2 \in k4\_metric\_2~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (\\
m1\_subset\_1~X3~(k2\_metric\_2~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~\\
(k2\_metric\_2~X0)){\unicdcdcdhd}((X2=k1\_domain\_1~(k2\_metric\_2~X0)~(k2\_metric\_2~\\
X0)~X3~X4){\unicdcdcdhd}(r4\_metric\_2~X0~X3~X4~X1)))))))\end{array}$$
\end{theorem}
\end{document}
