\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{t47\_jgraph\_2 (TMTU83KqGwt3vWwba9yrDWQEzLqmoDem87f)}
\maketitle
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(v4\_pre\_topc~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k18\_euclid~X0)~\\
(k1\_real\_1~(k17\_euclid~X0)))~({\uniddcgcg} X0 : \iota .  X0))~(k15\_euclid~np\_\_2)){\unicdcdcdhd}\\
(m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k18\_euclid~X0)~\\
(k1\_real\_1~(k17\_euclid~X0)))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_zfmisc\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:mgfdcdpfkghgchbgahigpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v4\_pre\_topc~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k1\_real\_1~(k17\_euclid~\\
X0))~(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  X0))~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(\\
m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k1\_real\_1~(k17\_euclid~\\
X0))~(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))\end{array}
\label{hyp:mgedjdpfkghgchbgahigpfcd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfkghgchbgahigpfcd}
$$\begin{array}{c}((v4\_pre\_topc~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k1\_real\_1~(k17\_euclid~\\
X0))~(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  X0))~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(\\
m1\_subset\_1~(ReplSep~(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k1\_real\_1~(k17\_euclid~\\
X0))~(k18\_euclid~X0))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))))){\unicdcdcdhd}((v4\_pre\_topc~(ReplSep~(toset~({\uniddcgcg} X0 : \\
\iota .  m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~({\uniddcgcg} X0 : \\
\iota .  r1\_xxreal\_0~(k18\_euclid~X0)~(k1\_real\_1~(k17\_euclid~X0)))~\\
({\uniddcgcg} X0 : \iota .  X0))~(k15\_euclid~np\_\_2)){\unicdcdcdhd}(m1\_subset\_1~(ReplSep~\\
(toset~({\uniddcgcg} X0 : \iota .  m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))))~\\
({\uniddcgcg} X0 : \iota .  r1\_xxreal\_0~(k18\_euclid~X0)~(k1\_real\_1~(k17\_euclid~\\
X0)))~({\uniddcgcg} X0 : \iota .  X0))~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))))\end{array}$$
\end{theorem}
\end{document}
