\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{t44\_xxreal\_3 (TMaHSBTMrkFHUd1xMNPMGJUHfK3RxkV4AzP)}
\maketitle
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(\preoh (\preoh (X0=k1\_xxreal\_0){\unicdcdcdhd}(X1=k2\_xxreal\_0)){\unicdcdcdhd}\\
((\preoh (X0=k2\_xxreal\_0){\unicdcdcdhd}(X1=k1\_xxreal\_0)){\unicdcdcdhd}((\preoh (X1=k1\_xxreal\_0){\unicdcdcdhd}\\
(X2=k2\_xxreal\_0)){\unicdcdcdhd}((\preoh (X1=k2\_xxreal\_0){\unicdcdcdhd}(X2=k1\_xxreal\_0)){\unicdcdcdhd}\\
((\preoh (X0=k1\_xxreal\_0){\unicdcdcdhd}(X2=k2\_xxreal\_0)){\unicdcdcdhd}((\preoh (X0=k2\_xxreal\_0){\unicdcdcdhd}\\
(X2=k1\_xxreal\_0)){\unicdcdcdhd}(k1\_xxreal\_3~(k1\_xxreal\_3~X0~X1)~X2{\unicdcdgdad}k1\_xxreal\_3~\\
X0~(k1\_xxreal\_3~X1~X2))))))))))\end{array}
\label{hyp:ehcdjdpfihihchfgbgmgpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{v3\_xxreal\_0}~{k2\_xxreal\_0}}\label{hyp:ggdgedpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}((v3\_xxreal\_0~X0){\unicdbdjded}(\preoh r1\_xxreal\_0~\\
k6\_numbers~X0))\end{array}
\label{hyp:eghdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehededpfihihchfgbgmgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}(((r1\_xxreal\_0~k6\_numbers~X0){\unicdcdcdhd}((r1\_xxreal\_0~\\
k6\_numbers~X1){\unicdcdcdhd}(r1\_xxreal\_0~k6\_numbers~X2))){\unicdbdjdcd}(k1\_xxreal\_3~(\\
k1\_xxreal\_3~X0~X1)~X2=k1\_xxreal\_3~X0~(k1\_xxreal\_3~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
