\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{t18\_jordan7 (TMXgv4XTh1DamLpnM3V132onA8LpV9s3btF)}
\maketitle
Let $ v1\_xboole\_0 : {{\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 $ 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 $ k1\_numbers : {\iota}$ be given.
Let $ r1\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v2\_funct\_1 : {{\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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_jordan5c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_tops\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\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~np\_\_2)~X0))){\unicdcdcdhd}\\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}\\
(((r1\_topreal1~(k15\_euclid~np\_\_2)~X1~X2~X0){\unicdcdcdhd}((v3\_tops\_2~X5~k5\_topmetr~\\
(k1\_pre\_topc~(k15\_euclid~np\_\_2)~X0)){\unicdcdcdhd}((k1\_funct\_1~X5~k6\_numbers=\\
X1){\unicdcdcdhd}((k1\_funct\_1~X5~np\_\_1=X2){\unicdcdcdhd}((k1\_funct\_1~X5~X6=X3){\unicdcdcdhd}((r1\_xxreal\_0~\\
k6\_numbers~X6){\unicdcdcdhd}((r1\_xxreal\_0~X6~np\_\_1){\unicdcdcdhd}((k1\_funct\_1~X5~X7=X4){\unicdcdcdhd}\\
((r1\_xxreal\_0~k6\_numbers~X7){\unicdcdcdhd}((r1\_xxreal\_0~X7~np\_\_1){\unicdcdcdhd}(r1\_xxreal\_0~\\
X6~X7))))))))))){\unicdbdjdcd}(r1\_jordan5c~X0~X1~X2~X3~X4)))))))))\end{array}
\label{hyp:ehidpfkgpgchegbgogfddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~k5\_topmetr)~\\
(u1\_struct\_0~(k15\_euclid~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~\\
X0))))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X2~k5\_topmetr~(k15\_euclid~X0)){\unicdcdcdhd}((v2\_funct\_1~\\
X2){\unicdcdcdhd}((k2\_relset\_1~(u1\_struct\_0~(k15\_euclid~X0))~X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  \\
((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~\\
(k1\_pre\_topc~(k15\_euclid~X0)~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k1\_pre\_topc~\\
(k15\_euclid~X0)~X1))))))){\unicdbdjdcd}(\preoh (X3=X2){\unicdcdcdhd}(v3\_tops\_2~X3~k5\_topmetr~\\
(k1\_pre\_topc~(k15\_euclid~X0)~X1)))))))))\end{array}
\label{hyp:ehbdgdpfkgpgchegbgoghd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfkgpgchegbgoghd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_funct\_1~\\
X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
k5\_topmetr)~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}\\
(((r1\_topreal1~(k15\_euclid~np\_\_2)~X1~X2~X0){\unicdcdcdhd}((v5\_pre\_topc~X5~k5\_topmetr~\\
(k15\_euclid~np\_\_2)){\unicdcdcdhd}((v2\_funct\_1~X5){\unicdcdcdhd}((k2\_relset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X5=X0){\unicdcdcdhd}((k1\_funct\_1~X5~k6\_numbers=X1){\unicdcdcdhd}(\\
(k1\_funct\_1~X5~np\_\_1=X2){\unicdcdcdhd}((k1\_funct\_1~X5~X6=X3){\unicdcdcdhd}((r1\_xxreal\_0~\\
k6\_numbers~X6){\unicdcdcdhd}((r1\_xxreal\_0~X6~np\_\_1){\unicdcdcdhd}((k1\_funct\_1~X5~X7=X4){\unicdcdcdhd}\\
((r1\_xxreal\_0~k6\_numbers~X7){\unicdcdcdhd}((r1\_xxreal\_0~X7~np\_\_1){\unicdcdcdhd}(r1\_xxreal\_0~\\
X6~X7))))))))))))){\unicdbdjdcd}(r1\_jordan5c~X0~X1~X2~X3~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
