\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{t17\_jordan1c (TMXXko9Adda8pFnUTbvMqkVPcQXHEvEekRu)}
\maketitle
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\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 $ k14\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_jordan2c : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_metric\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_tops\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k14\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~X0)))){\unicdbdjdcd}((X1 \in k1\_tops\_1~(k15\_euclid~X0)~\\
X2){\unicdbdjded}({\unicdcdaddd} X3 .  (v1\_xreal\_0~X3){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X3~k6\_numbers){\unicdcdcdhd}\\
(r1\_tarski~(k9\_metric\_1~(k14\_euclid~X0)~X1~X3)~X2))))))\end{array}
\label{hyp:ehfdpfhgpgcgpgbgcheggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l1\_pre\_topc~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}(((v3\_pre\_topc~X3~X1){\unicdbdjdcd}(k1\_tops\_1~X1~X3=X3)){\unicdcdcdhd}((k1\_tops\_1~\\
X0~X2=X2){\unicdbdjdcd}(v3\_pre\_topc~X2~X0))))))\end{array}
\label{hyp:ehcdddpfehpgahdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\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}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (l1\_pre\_topc~X0){\unicdcdcdhd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}(v8\_pre\_topc~X0)))\end{array}
\label{hyp:chdgbdpfdgpgngahehdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{v6\_membered}~{k4\_ordinal1}}\label{hyp:ggdggdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_pre\_topc~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(v3\_pre\_topc~\\
(k1\_jordan2c~np\_\_2~X0)~(k15\_euclid~np\_\_2))\end{array}
\label{hyp:ggdggdpfkgpgchegbgogcddg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_rltopsp1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{X0}})}})}}}\label{hyp:egehpfmgbdpfchmgehpgahdhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~X0))))){\unicdbdjdcd}(m1\_subset\_1~(k1\_jordan2c~\\
X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~X0))))\end{array}
\label{hyp:egehpflgbdpfkgpgchegbgogcddg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v5\_rltopsp1~(k15\_euclid~X0)){\unicdcdcdhd}\\
(l1\_rltopsp1~(k15\_euclid~X0)))\end{array}
\label{hyp:egehpflgbdfdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k1\_numbers}})}}}\label{hyp:egbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v6\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v7\_ordinal1~X1))\end{array}
\label{hyp:dgdgbdhdpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfkgpgchegbgogbddg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_pre\_topc~X0~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~(k14\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (X1 \in k1\_jordan2c~\\
np\_\_2~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~\\
X2~k6\_numbers){\unicdcdcdhd}(r1\_tarski~(k9\_metric\_1~(k14\_euclid~np\_\_2)~X1~\\
X2)~(k1\_jordan2c~np\_\_2~X0))))))\end{array}$$
\end{theorem}
\end{document}
