\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{t1\_xxreal\_0 (TMRGAM8wMGezVBqy5EyuREKLgtriuP9jLdd)}
\maketitle
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_arytm\_3 : {\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 $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_xxreal\_0 : {\iota}$ be given.
Let $ k2\_xxreal\_0 : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}r1\_xboole\_0~k2\_arytm\_2~(k2\_zfmisc\_1~(k1\_tarski~k11\_arytm\_3)~\\
k2\_arytm\_2)\end{array}
\label{hyp:ehfdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}(((r1\_arytm\_2~X0~X1){\unicdcdcdhd}(r1\_arytm\_2~X1~X0)){\unicdbdjdcd}(X0=\\
X1)))\end{array}
\label{hyp:ehedpfbgchjhehngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh (\preoh r1\_xboole\_0~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  \preoh (X2 \in \\
X0){\unicdcdcdhd}(X2 \in X1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X2 .  (X2 \in X0){\unicdcdcdhd}(X2 \in X1)){\unicdcdcdhd}(r1\_xboole\_0~\\
X0~X1))\end{array}
\label{hyp:ehddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1=\\
k4\_tarski~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3))\end{array}
\label{hyp:ehbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k11\_arytm\_3}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdbdpfbgchjhehngpfdd}
\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{{{k2\_xxreal\_0} \in {k2\_arytm\_2}}}}\label{hyp:mgidpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{{r1\_xxreal\_0}~{k1\_xxreal\_0}}~{k2\_xxreal\_0}}}}\label{hyp:mgbdbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xxreal\_0}~{k2\_xxreal\_0}}\label{hyp:ggdgcdpfihihchfgbgmgpfad}
\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}
Assume the following.
\begin{equation}
{{k2\_xxreal\_0}={{{k4\_tarski}~{k6\_numbers}}~{k1\_numbers}}}\label{hyp:egddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xxreal\_0}={k1\_numbers}}\label{hyp:egcdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdpfihihchfgbgmgpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}$$
\end{theorem}
\end{document}
