\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{t10\_euclmetr (TMU62pGWyhgt9G1LGs77hL3SroafpEdEywv)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_euclmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_conmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_aff\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_analmetr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v2\_conmetr~X0){\unicdbdjded}(v2\_aff\_2~(k3\_analmetr~X0)))\end{array}
\label{hyp:mgbdhdpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v2\_euclmetr~X0){\unicdbdjded}(v2\_aff\_2~(k3\_analmetr~X0)))\end{array}
\label{hyp:egcdpffgfhdgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_analmetr~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_analmetr~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v2\_analmetr~X0)))\end{array}
\label{hyp:dgdgbdpfbgogbgmgngfgehch}
\end{equation}
\begin{theorem}\label{thm:ehbdadpffgfhdgmgngfgehch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((v2\_euclmetr~X0){\unicdbdjded}(v2\_conmetr~X0))\end{array}$$
\end{theorem}
\end{document}
