\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{t30\_jordan6 (TMbYGFj5jhVxYJRZgWHeaMD3XwZQCCmSy2w)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_jordan6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k7\_jordan6 : {{\iota}{\unicdbdjdcd}{\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 $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdbdjdcd}((X1=ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X2 : \\
\iota .  k18\_euclid~X2=X0)~({\uniddcgcg} X2 : \iota .  X2)){\unicdbdjdcd}(v4\_pre\_topc~X1~(k15\_euclid~\\
np\_\_2))))\end{array}
\label{hyp:ehjdpfkgpgchegbgoggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdbdjdcd}((X1=ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X2 : \\
\iota .  k17\_euclid~X2=X0)~({\uniddcgcg} X2 : \iota .  X2)){\unicdbdjdcd}(v4\_pre\_topc~X1~(k15\_euclid~\\
np\_\_2))))\end{array}
\label{hyp:ehgdpfkgpgchegbgoggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k7\_jordan6~X0)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpflghdpfkgpgchegbgoggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k6\_jordan6~X0)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:egehpflggdpfkgpgchegbgoggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k7\_jordan6~X0=ReplSep~(toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X1 : \\
\iota .  k18\_euclid~X1=X0)~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:eghdpfkgpgchegbgoggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k6\_jordan6~X0=ReplSep~(toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X1 : \\
\iota .  k17\_euclid~X1=X0)~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:eggdpfkgpgchegbgoggd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfkgpgchegbgoggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v4\_pre\_topc~(k6\_jordan6~X0)~(k15\_euclid~\\
np\_\_2)){\unicdcdcdhd}(v4\_pre\_topc~(k7\_jordan6~X0)~(k15\_euclid~np\_\_2)))\end{array}$$
\end{theorem}
\end{document}
