\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{t29\_topreal9 (TMMYzoKxuQkGxsM8oPFDKpLsJPzzmZoaTBZ)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\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~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(\\
{\unicdcdadad} X4 .  (X4=k3\_rlvect\_1~(k15\_euclid~X0)~(k1\_rlvect\_1~(k15\_euclid~\\
X0)~X2~(k9\_real\_1~np\_\_1~X1))~(k1\_rlvect\_1~(k15\_euclid~X0)~X3~X1)){\unicdbdjdcd}\\
((\preoh (X4=X2){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(X2{\unicdcdgdad}X3))){\unicdcdcdhd}((((X1=k6\_numbers){\unicdcdcdid}\\
(X2=X3)){\unicdbdjdcd}(X4=X2)){\unicdcdcdhd}((\preoh (X4=X3){\unicdcdcdhd}((X1{\unicdcdgdad}np\_\_1){\unicdcdcdhd}(X2{\unicdcdgdad}X3))){\unicdcdcdhd}(((X1=\\
np\_\_1){\unicdcdcdid}(X2=X3)){\unicdbdjdcd}(X4=X3)))))))))\end{array}
\label{hyp:ehedpfehpgahchfgbgmgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(X1 \in k4\_topreal9~X0~X1~X2)))\end{array}
\label{hyp:ehcdhdpfehpgahchfgbgmgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in k4\_topreal9~\\
X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X4 .  (v1\_xreal\_0~X4){\unicdcdcdhd}((X3=k3\_rlvect\_1~(k15\_euclid~\\
X0)~(k1\_rlvect\_1~(k15\_euclid~X0)~X1~(k9\_real\_1~np\_\_1~X4))~(k1\_rlvect\_1~\\
(k15\_euclid~X0)~X2~X4)){\unicdcdcdhd}(r1\_xxreal\_0~k6\_numbers~X4))))))\end{array}
\label{hyp:ehcdgdpfehpgahchfgbgmgjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k1\_tarski~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
(X2=X0))\end{array}
\label{hyp:egbdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfehpgahchfgbgmgjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(k4\_topreal9~X0~X1~X1=k1\_tarski~\\
X1))\end{array}$$
\end{theorem}
\end{document}
