\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{t40\_jordan2c (TMaG3EV8iDiG99uLMEQ3xF4hFSkhFFzZZGG)}
\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 $ 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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\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\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0)))){\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}(\preoh (X2 \in X1){\unicdcdcdhd}((\\
X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}((r1\_tarski~(k1\_rltopsp1~(k15\_euclid~X0)~X2~\\
X3)~X1){\unicdcdcdhd}((r1\_tarski~(k1\_rltopsp1~(k15\_euclid~X0)~X3~X4)~X1){\unicdcdcdhd}({\unicdcdadad} X5 .  \\
((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k1\_pre\_topc~(k15\_euclid~X0)~X1))){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k1\_pre\_topc~\\
(k15\_euclid~X0)~X1))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X5~k5\_topmetr~(k1\_pre\_topc~\\
(k15\_euclid~X0)~X1)){\unicdcdcdhd}((X2=k1\_funct\_1~X5~k6\_numbers){\unicdcdcdhd}(X4=k1\_funct\_1~\\
X5~np\_\_1)))))))))))))\end{array}
\label{hyp:ehddidpfkgpgchegbgogcddg}
\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~(u1\_struct\_0~(k15\_euclid~X0))){\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 .  ((\preoh v1\_xboole\_0~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~X0)~X4))){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k1\_pre\_topc~(k15\_euclid~X0)~X4))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~\\
X6){\unicdcdcdhd}((v1\_funct\_2~X6~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k1\_pre\_topc~\\
(k15\_euclid~X0)~X4))){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~\\
X0)~X4))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X5~k5\_topmetr~(k1\_pre\_topc~(k15\_euclid~\\
X0)~X4)){\unicdcdcdhd}((X1=k1\_funct\_1~X5~k6\_numbers){\unicdcdcdhd}((X2=k1\_funct\_1~X5~np\_\_1){\unicdcdcdhd}\\
((v5\_pre\_topc~X6~k5\_topmetr~(k1\_pre\_topc~(k15\_euclid~X0)~X4)){\unicdcdcdhd}\\
((X2=k1\_funct\_1~X6~k6\_numbers){\unicdcdcdhd}((X3=k1\_funct\_1~X6~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X7 .  \\
((v1\_funct\_1~X7){\unicdcdcdhd}((v1\_funct\_2~X7~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k1\_pre\_topc~(k15\_euclid~X0)~X4))){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k1\_pre\_topc~\\
(k15\_euclid~X0)~X4))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X7~k5\_topmetr~(k1\_pre\_topc~\\
(k15\_euclid~X0)~X4)){\unicdcdcdhd}((X1=k1\_funct\_1~X7~k6\_numbers){\unicdcdcdhd}(X3=k1\_funct\_1~\\
X7~np\_\_1))))))))))))))))\end{array}
\label{hyp:ehddhdpfkgpgchegbgogcddg}
\end{equation}
\begin{theorem}\label{thm:ehedadpfkgpgchegbgogcddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
m1\_subset\_1~X5~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~\\
(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(\\
u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}\\
((X5 \in X1){\unicdcdcdhd}((X6 \in X1){\unicdcdcdhd}((X7 \in X1){\unicdcdcdhd}((X8 \in X1){\unicdcdcdhd}((r1\_tarski~(k1\_rltopsp1~\\
(k15\_euclid~X0)~X2~X3)~X1){\unicdcdcdhd}((r1\_tarski~(k1\_rltopsp1~(k15\_euclid~\\
X0)~X3~X4)~X1){\unicdcdcdhd}((r1\_tarski~(k1\_rltopsp1~(k15\_euclid~X0)~X4~X5)~X1){\unicdcdcdhd}\\
((r1\_tarski~(k1\_rltopsp1~(k15\_euclid~X0)~X5~X6)~X1){\unicdcdcdhd}((r1\_tarski~\\
(k1\_rltopsp1~(k15\_euclid~X0)~X6~X7)~X1){\unicdcdcdhd}((r1\_tarski~(k1\_rltopsp1~\\
(k15\_euclid~X0)~X7~X8)~X1){\unicdcdcdhd}({\unicdcdadad} X9 .  ((v1\_funct\_1~X9){\unicdcdcdhd}((v1\_funct\_2~\\
X9~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~\\
X0)~X1))){\unicdcdcdhd}(m1\_subset\_1~X9~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~X0)~X1))))))){\unicdbdjdcd}\\
(\preoh (v5\_pre\_topc~X9~k5\_topmetr~(k1\_pre\_topc~(k15\_euclid~X0)~X1)){\unicdcdcdhd}\\
((X2=k1\_funct\_1~X9~k6\_numbers){\unicdcdcdhd}(X8=k1\_funct\_1~X9~np\_\_1)))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
