\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{t9\_topreal9 (TMKCEeesbfvcFUNA93Zb7FKTJyvRUBvCBkm)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k12\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xreal\_0~X2){\unicdbdjdcd}(k3\_topreal9~\\
X0~X1~X2=ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~(u1\_struct\_0~\\
(k15\_euclid~X0))))~({\uniddcgcg} X3 : \iota .  k12\_euclid~(k5\_algstr\_0~(k15\_euclid~\\
X0)~X3~X1)=X2)~({\uniddcgcg} X3 : \iota .  X3))))\end{array}
\label{hyp:egddpfehpgahchfgbgmgjd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfehpgahchfgbgmgjd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~\\
X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(\\
(X2 \in k3\_topreal9~X0~X3~X1){\unicdbdjded}(k12\_euclid~(k5\_algstr\_0~(k15\_euclid~\\
X0)~X2~X3)=X1)))))\end{array}$$
\end{theorem}
\end{document}
