\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{t37\_jordan22 (TMUJsPZA9qnEHYpKhMVjS1wkjoZUJFMGtzi)}
\maketitle
Let $ v1\_topreal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k2\_jordan21 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_jordan6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_jordan21 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_jordan6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_jordan6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_jordan19 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_jordan19 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_jordan5c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k22\_pscomp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (X1 \in X0){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}((\preoh r1\_jordan6~X0~X1~\\
X2){\unicdcdcdhd}(\preoh r1\_jordan6~X0~X2~X1))))))\end{array}
\label{hyp:ehhdpfkgpgchegbgogbdgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(\preoh (k2\_jordan21~X0 \in k8\_jordan6~X0){\unicdcdcdhd}(k1\_jordan21~\\
X0 \in k8\_jordan6~X0))\end{array}
\label{hyp:ehfdadpfkgpgchegbgogcdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(\preoh (k2\_jordan21~X0 \in k9\_jordan6~X0){\unicdcdcdhd}(k1\_jordan21~\\
X0 \in k9\_jordan6~X0))\end{array}
\label{hyp:ehedjdpfkgpgchegbgogcdbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(r1\_tarski~(k4\_jordan19~X0)~X0)\end{array}
\label{hyp:ehddgdpfkgpgchegbgogcdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(r1\_tarski~(k3\_jordan19~X0)~X0)\end{array}
\label{hyp:ehddfdpfkgpgchegbgogcdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(k2\_jordan21~X0 \in k4\_jordan19~X0)\end{array}
\label{hyp:ehddedpfkgpgchegbgogcdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(k1\_jordan21~X0 \in k3\_jordan19~X0)\end{array}
\label{hyp:ehddddpfkgpgchegbgogcdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}((r1\_jordan6~X0~X1~X2){\unicdbdjded}(\preoh (\preoh (X1 \in k8\_jordan6~X0){\unicdcdcdhd}((X2 \in \\
k9\_jordan6~X0){\unicdcdcdhd}(X2{\unicdcdgdad}k18\_pscomp\_1~X0))){\unicdcdcdhd}((\preoh (X1 \in k8\_jordan6~X0){\unicdcdcdhd}\\
((X2 \in k8\_jordan6~X0){\unicdcdcdhd}(r1\_jordan5c~(k8\_jordan6~X0)~(k18\_pscomp\_1~\\
X0)~(k22\_pscomp\_1~X0)~X1~X2))){\unicdcdcdhd}(\preoh (X1 \in k9\_jordan6~X0){\unicdcdcdhd}((X2 \in k9\_jordan6~\\
X0){\unicdcdcdhd}((X2{\unicdcdgdad}k18\_pscomp\_1~X0){\unicdcdcdhd}(r1\_jordan5c~(k9\_jordan6~X0)~(k22\_pscomp\_1~\\
X0)~(k18\_pscomp\_1~X0)~X1~X2)))))))))\end{array}
\label{hyp:egbdadpfkgpgchegbgoggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal2~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v2\_compts\_1~\\
X0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:dgdgbdpfehpgahchfgbgmgcd}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfkgpgchegbgogcdcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(((k2\_jordan21~X0 \in k9\_jordan6~X0){\unicdcdcdhd}(k1\_jordan21~\\
X0 \in k8\_jordan6~X0)){\unicdcdcdid}((k1\_jordan21~X0 \in k9\_jordan6~X0){\unicdcdcdhd}(k2\_jordan21~\\
X0 \in k8\_jordan6~X0)))\end{array}$$
\end{theorem}
\end{document}
