\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{t5\_jordan16 (TMdpdc3xFwLAVkJMJ7o1MRVLzTTDRn6jVyF)}
\maketitle
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 $ r1\_jordan5c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ k5\_jordan6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k1\_numbers : {\iota}$ be given.
Let $ v3\_tops\_2 : {{\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 $ r1\_xxreal\_0 : {{\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}((X3 \in X0){\unicdbdjdcd}(r1\_jordan5c~X0~X1~X2~X3~X3)))))\end{array}
\label{hyp:ehjdpfkgpgchegbgogfddg}
\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}({\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}(k5\_jordan6~X0~X1~X2~X3~X4=ReplSep~(toset~({\uniddcgcg} X5 : \iota .  \\
m1\_subset\_1~X5~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X5 : \iota .  \\
(r1\_jordan5c~X0~X1~X2~X3~X5){\unicdcdcdhd}(r1\_jordan5c~X0~X1~X2~X5~X4))~({\uniddcgcg} X5 : \\
\iota .  X5))))))\end{array}
\label{hyp:ehcdgdpfkgpgchegbgoggd}
\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}({\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}((r1\_jordan5c~X0~X1~X2~X3~X4){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}((X4 \in X0){\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~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}(((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))))))))){\unicdbdjdcd}\\
(r1\_xxreal\_0~X6~X7))))))))))))\end{array}
\label{hyp:egddpfkgpgchegbgogfddg}
\end{equation}
\begin{theorem}\label{thm:ehfdpfkgpgchegbgogbdgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))){\unicdbdjdcd}((r1\_jordan5c~X0~X3~X4~X1~X2){\unicdbdjdcd}((X1 \in k5\_jordan6~X0~X3~X4~\\
X1~X2){\unicdcdcdhd}(X2 \in k5\_jordan6~X0~X3~X4~X1~X2)))))))\end{array}$$
\end{theorem}
\end{document}
