\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\_topreal4 (TMH9ChzjbqqcKgqcm4TpQN1amQFSwUMkzVD)}
\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 $ v1\_topreal4 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_topreal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_topreal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\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}((r1\_topreal4~X0~X1~X2){\unicdbdjdcd}((X1 \in X0){\unicdcdcdhd}(X2 \in X0)))))\end{array}
\label{hyp:ehddpfehpgahchfgbgmged}
\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}((r1\_topreal4~X0~X1~X2){\unicdbdjdcd}(r1\_topreal1~(k15\_euclid~np\_\_2)~\\
X1~X2~X0))))\end{array}
\label{hyp:ehcdpfehpgahchfgbgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~\\
X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))))){\unicdbdjdcd}(((r1\_topreal1~(k15\_euclid~\\
np\_\_2)~X0~X1~X3){\unicdcdcdhd}((r1\_topreal1~(k15\_euclid~np\_\_2)~X0~X1~X4){\unicdcdcdhd}((X2=\\
k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~X4){\unicdcdcdhd}(k9\_subset\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~X4=k2\_tarski~X0~X1)))){\unicdbdjdcd}(v1\_topreal2~\\
X2))))))\end{array}
\label{hyp:mgddjdpfehpgahchfgbgmgcd}
\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}((v1\_topreal4~X0){\unicdbdjded}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2)))){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}\\
((X1 \in X0){\unicdcdcdhd}((X2 \in X0){\unicdcdcdhd}((r1\_topreal4~X3~X1~X2){\unicdcdcdhd}((r1\_topreal4~X4~X1~\\
X2){\unicdcdcdhd}((k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~X4=k2\_tarski~\\
X1~X2){\unicdcdcdhd}(X0=k4\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X3~X4))))))))))))\end{array}
\label{hyp:egcdpfehpgahchfgbgmged}
\end{equation}
\begin{theorem}\label{thm:ehfdpfehpgahchfgbgmged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2)))){\unicdbdjdcd}((v1\_topreal4~X0){\unicdbdjdcd}(v1\_topreal2~X0))\end{array}$$
\end{theorem}
\end{document}
