\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{t98\_jordan (TMauqQvbMoiWJqxT2BvCSc7ortTJKqEW54d)}
\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 $ k3\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_connsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_jordan1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ 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}(v1\_jordan1~X0)\end{array}
\label{hyp:mgcdadgdpfkgpgchegbgog}
\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\_jordan1~X0){\unicdbdjded}((k3\_subset\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}((k3\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0=k4\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X1~X2){\unicdcdcdhd}((r1\_xboole\_0~X1~X2){\unicdcdcdhd}((k7\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_pre\_topc~(k15\_euclid~np\_\_2)~\\
X1)~X1=k7\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X2)~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0))))){\unicdbdjdcd}(((X3=X1){\unicdcdcdhd}(X4=X2)){\unicdbdjdcd}((v3\_connsp\_1~\\
X3~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0))){\unicdcdcdhd}(v3\_connsp\_1~X4~(k1\_pre\_topc~(k15\_euclid~\\
np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0))))))))))))))\end{array}
\label{hyp:egcdpfkgpgchegbgogbd}
\end{equation}
\begin{theorem}\label{thm:ehjdidpfkgpgchegbgog}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_topreal2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}((k3\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0=k4\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X1~X2){\unicdcdcdhd}((r1\_xboole\_0~X1~X2){\unicdcdcdhd}((k7\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_pre\_topc~(k15\_euclid~np\_\_2)~\\
X1)~X1=k7\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k2\_pre\_topc~\\
(k15\_euclid~np\_\_2)~X2)~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0))))){\unicdbdjdcd}(((X3=X1){\unicdcdcdhd}(X4=X2)){\unicdbdjdcd}((v3\_connsp\_1~\\
X3~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0))){\unicdcdcdhd}(v3\_connsp\_1~X4~(k1\_pre\_topc~(k15\_euclid~\\
np\_\_2)~(k3\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0))))))))))))\end{array}$$
\end{theorem}
\end{document}
