\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{t53\_xxreal\_2 (TMR2iwgfzdkv2ocpvPiha4R8FqKuZWMPrrk)}
\maketitle
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ v4\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}((m1\_xxreal\_2~k2\_xxreal\_0~X0){\unicdbdjdcd}(\\
r1\_tarski~X0~(k1\_tarski~k2\_xxreal\_0)))\end{array}
\label{hyp:ehfdbdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{v4\_xxreal\_2}~{({{k1\_tarski}~{k2\_xxreal\_0}})}}\label{hyp:ehedidpfihihchfgbgmgpfcd}
\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}
{{\unicdcdadad} X0 .  {{{{k2\_tarski}~{X0}}~{X0}}={{k1\_tarski}~{X0}}}}\label{hyp:ehcdjdpffgogfhngdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}((r1\_tarski~X0~X1){\unicdbdjdcd}(v2\_membered~\\
X0))\end{array}
\label{hyp:ehcdadpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}(\preoh (\preoh X0 \in k1\_numbers){\unicdcdcdhd}((X0{\unicdcdgdad}k1\_xxreal\_0){\unicdcdcdhd}\\
(X0{\unicdcdgdad}k2\_xxreal\_0)))\end{array}
\label{hyp:mgcdcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{({{k1\_tarski}~{X0}})}})}}}\label{hyp:ggdgidpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_xxreal\_2~X1~X0){\unicdbdjdcd}\\
(v1\_xxreal\_0~X1))\end{array}
\label{hyp:egehpfngbdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xxreal\_0}={k1\_numbers}}\label{hyp:egcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k1\_numbers}})}}}\label{hyp:egbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}((v4\_xxreal\_2~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (\\
v1\_xreal\_0~X1){\unicdcdcdhd}(m1\_xxreal\_2~X1~X0)))\end{array}
\label{hyp:egbdadpfihihchfgbgmgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdddpfihihchfgbgmgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_membered~X0){\unicdcdcdhd}(\preoh v1\_xboole\_0~X0)){\unicdbdjdcd}((\preoh {\unicdcdadad} X1 .  \\
(m1\_xxreal\_2~X1~X0){\unicdbdjdcd}(X1=k1\_xxreal\_0)){\unicdbdjdcd}(v4\_xxreal\_2~X0))\end{array}$$
\end{theorem}
\end{document}
