\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{t20\_jordan18 (TMH4DdFrM3bm5USUbcRkusiPBy4x3pYt1Cd)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ v2\_compts\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_jordan2c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_jordan18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_jordan18 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_topreal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_topreal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v2\_compts\_1~X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}((X0 \in k1\_jordan2c~\\
np\_\_2~X1){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k18\_euclid~X0)~(k18\_euclid~(k2\_jordan18~\\
X0~X1))){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k18\_euclid~(k1\_jordan18~X0~X1))~(k18\_euclid~\\
X0)))))\end{array}
\label{hyp:ehbdidpfkgpgchegbgogbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v2\_compts\_1~X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}((X0 \in k1\_jordan2c~\\
np\_\_2~X1){\unicdbdjdcd}((k1\_jordan18~X0~X1 \in X1){\unicdcdcdhd}((k1\_jordan18~X0~X1 \in k4\_topreal1~\\
X0){\unicdcdcdhd}((k2\_jordan18~X0~X1 \in X1){\unicdcdcdhd}(k2\_jordan18~X0~X1 \in k6\_topreal1~X0))))))\end{array}
\label{hyp:ehbdhdpfkgpgchegbgogbdid}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(m1\_subset\_1~(k4\_topreal1~X0)~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))))\end{array}
\label{hyp:egehpflgedpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((X1=k4\_topreal1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}((X2 \in X1){\unicdbdjded}((k17\_euclid~X2=\\
k17\_euclid~X0){\unicdcdcdhd}(r1\_xxreal\_0~(k18\_euclid~X0)~(k18\_euclid~X2)))))))\end{array}
\label{hyp:egbdadpfehpgahchfgbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfkgpgchegbgogbdid}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v2\_compts\_1~X1~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(\preoh (X0 \in k1\_jordan2c~\\
np\_\_2~X1){\unicdcdcdhd}(k2\_jordan18~X0~X1=k1\_jordan18~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
