\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{t45\_xxreal\_2 (TMY2UFa5upmzw2KZAH18naacqQ374zsToue)}
\maketitle
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}((\\
(r1\_tarski~X0~X1){\unicdcdcdhd}(v3\_xxreal\_2~X1)){\unicdbdjdcd}(v3\_xxreal\_2~X0)))\end{array}
\label{hyp:ehededpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}((\\
(r1\_tarski~X0~X1){\unicdcdcdhd}(v4\_xxreal\_2~X1)){\unicdbdjdcd}(v4\_xxreal\_2~X0)))\end{array}
\label{hyp:ehedddpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}((v5\_xxreal\_2~X0){\unicdbdjded}((v3\_xxreal\_2~\\
X0){\unicdcdcdhd}(v4\_xxreal\_2~X0)))\end{array}
\label{hyp:egbdbdpfihihchfgbgmgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfihihchfgbgmgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}((\\
(r1\_tarski~X0~X1){\unicdcdcdhd}(v5\_xxreal\_2~X1)){\unicdbdjdcd}(v5\_xxreal\_2~X0)))\end{array}$$
\end{theorem}
\end{document}
