\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{l14\_xxreal\_0 (TMGaY1XXkmRfDzHzu18KUroGLEhqX1bH2yG)}
\maketitle
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{k1\_xxreal\_0} \in {{{k2\_zfmisc\_1}~{({{k1\_tarski}~{k6\_numbers}})}}~{k2\_arytm\_2}}}}}\label{hyp:mgjdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{k1\_xxreal\_0} \in {k2\_arytm\_2}}}}\label{hyp:mghdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k1\_xxreal\_0}}\label{hyp:ggdgbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
((X0 \in k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_arytm\_2)){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}\\
((X0=X2){\unicdcdcdhd}((X1=X3){\unicdcdcdhd}(r1\_arytm\_2~X2~X3))))))){\unicdcdcdhd}((((X0 \in k2\_zfmisc\_1~\\
(k1\_tarski~k6\_numbers)~k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_zfmisc\_1~(k1\_tarski~\\
k6\_numbers)~k2\_arytm\_2)){\unicdbdjdcd}((r1\_xxreal\_0~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (\\
m1\_subset\_1~X2~k2\_arytm\_2){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~k2\_arytm\_2){\unicdcdcdhd}\\
((X0=k4\_tarski~k6\_numbers~X2){\unicdcdcdhd}((X1=k4\_tarski~k6\_numbers~X3){\unicdcdcdhd}\\
(r1\_arytm\_2~X3~X2))))))){\unicdcdcdhd}(\preoh (\preoh (X0 \in k2\_arytm\_2){\unicdcdcdhd}(X1 \in k2\_arytm\_2)){\unicdcdcdhd}\\
((\preoh (X0 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~k2\_arytm\_2){\unicdcdcdhd}(X1 \in \\
k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~k2\_arytm\_2)){\unicdcdcdhd}(\preoh (r1\_xxreal\_0~\\
X0~X1){\unicdbdjded}(\preoh (\preoh (X1 \in k2\_arytm\_2){\unicdcdcdhd}(X0 \in k2\_zfmisc\_1~(k1\_tarski~k6\_numbers)~\\
k2\_arytm\_2)){\unicdcdcdhd}((X0{\unicdcdgdad}k2\_xxreal\_0){\unicdcdcdhd}(X1{\unicdcdgdad}k1\_xxreal\_0)))))))))\end{array}
\label{hyp:egfdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdedpfihihchfgbgmgpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}((r1\_xxreal\_0~k1\_xxreal\_0~X0){\unicdbdjdcd}(\\
X0=k1\_xxreal\_0))\end{array}$$
\end{theorem}
\end{document}
