\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{t74\_jordan2c (TMHQ7ZcyJSzGd88qTT3wwHejpHvsFz89ogy)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
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 $ k14\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_topmetr : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X2~X1)){\unicdbdjdcd}(r1\_tarski~(k2\_xboole\_0~X0~X2)~X1)\end{array}
\label{hyp:ehidpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(\\
k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k14\_euclid~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  ((v1\_funct\_1~X6){\unicdcdcdhd}((v1\_funct\_2~X6~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~\\
X0))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X6~k5\_topmetr~(k15\_euclid~X0)){\unicdcdcdhd}((k1\_funct\_1~\\
X6~k6\_numbers=X2){\unicdcdcdhd}((k1\_funct\_1~X6~np\_\_1=X3){\unicdcdcdhd}((X4 \in k9\_metric\_1~\\
(k14\_euclid~X0)~X5~X1){\unicdcdcdhd}((X3 \in k9\_metric\_1~(k14\_euclid~X0)~X5~X1){\unicdcdcdhd}\\
({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}((v1\_funct\_2~X7~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~\\
X0))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X7~k5\_topmetr~(k15\_euclid~X0)){\unicdcdcdhd}((k1\_funct\_1~\\
X7~k6\_numbers=X2){\unicdcdcdhd}((k1\_funct\_1~X7~np\_\_1=X4){\unicdcdcdhd}(r1\_tarski~(k2\_relset\_1~\\
(u1\_struct\_0~(k15\_euclid~X0))~X7)~(k2\_xboole\_0~(k2\_relset\_1~(\\
u1\_struct\_0~(k15\_euclid~X0))~X6)~(k9\_metric\_1~(k14\_euclid~X0)~\\
X5~X1))))))))))))))))))\end{array}
\label{hyp:ehhdddpfkgpgchegbgogcddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdedpfkgpgchegbgogcddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(\\
k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~(k14\_euclid~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}((v1\_funct\_2~X7~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}(m1\_subset\_1~X7~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~X0))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X7~k5\_topmetr~(k15\_euclid~\\
X0)){\unicdcdcdhd}((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~X0))~\\
X7)~X6){\unicdcdcdhd}((k1\_funct\_1~X7~k6\_numbers=X2){\unicdcdcdhd}((k1\_funct\_1~X7~np\_\_1=\\
X3){\unicdcdcdhd}((X4 \in k9\_metric\_1~(k14\_euclid~X0)~X5~X1){\unicdcdcdhd}((X3 \in k9\_metric\_1~\\
(k14\_euclid~X0)~X5~X1){\unicdcdcdhd}((r1\_tarski~(k9\_metric\_1~(k14\_euclid~X0)~\\
X5~X1)~X6){\unicdcdcdhd}({\unicdcdadad} X8 .  ((v1\_funct\_1~X8){\unicdcdcdhd}((v1\_funct\_2~X8~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}(m1\_subset\_1~X8~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k15\_euclid~X0))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X8~k5\_topmetr~(k15\_euclid~\\
X0)){\unicdcdcdhd}((r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~X0))~\\
X8)~X6){\unicdcdcdhd}((k1\_funct\_1~X8~k6\_numbers=X2){\unicdcdcdhd}(k1\_funct\_1~X8~np\_\_1=\\
X4)))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
