\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{l5\_toprealb (TMbAVmXdmUaKa8L1bG9rNMWbCpKAMviAsf8)}
\maketitle
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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 $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ c2\_\_binop\_2 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_numbers}}~{k1\_numbers}}\label{hyp:mgbdjdpfbgchjhehngpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~k6\_numbers~\\
X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~np\_\_1)){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(k9\_real\_1~\\
np\_\_1~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k9\_real\_1~np\_\_1~X0)~np\_\_1)))\end{array}
\label{hyp:mgbdgdpfcgpgchdhfhlgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{k6\_numbers}}~{np\_\_1}}\label{hyp:mgbdcdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{c2\_\_binop\_2}={k6\_numbers}}\label{hyp:egfgpfdgcdpfpfcgjgogpgahpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:mgfdpfehpgahchfgbgmgcg}
${{{r1\_xxreal\_0}~{({{{k9\_real\_1}~{np\_\_1}}~{k6\_numbers}})}}~{np\_\_1}}$.
\end{theorem}
\end{document}
