\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{t18\_euclid\_3 (TMaWchHQn7x1nq3iUmtpMjWVf93BCiHN5j3)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_euclid\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_complex1 : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_euclid\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(k1\_euclid\_3~(k2\_euclid\_3~X0)=X0)\end{array}
\label{hyp:ehcdpffgfhdgmgjgegpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{k1\_euclid\_3}~{k5\_complex1}}={{k4\_struct\_0}~{({{k15\_euclid}~{np\_\_2}})}}}\label{hyp:ehbdgdpffgfhdgmgjgegpfdd}
\end{equation}
\begin{theorem}\label{thm:ehbdidpffgfhdgmgjgegpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((k2\_euclid\_3~X0=k5\_complex1){\unicdbdjdcd}(X0=k4\_struct\_0~(k15\_euclid~\\
np\_\_2)))\end{array}$$
\end{theorem}
\end{document}
