\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t5\_urysohn3 (TMMHWU7p7D1zThiEB7edEsmNF2zq8G8J4Bi)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_urysohn1 : {\iota}$ be given.
Let $ k1\_urysohn1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_urysohn3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(m2\_subset\_1~np\_\_0~k1\_numbers~k5\_numbers){\unicdcdcdhd}((m1\_subset\_1~np\_\_0~\\
k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_0~k1\_numbers))\end{array}
\label{hyp:dhahdgadpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m2\_subset\_1~(k2\_urysohn3~\\
X0)~k1\_numbers~k5\_numbers)\end{array}
\label{hyp:egehpflgcdpffhchjhdhpgigogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((X0 \in k2\_urysohn1){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X1=k2\_urysohn3~\\
X0){\unicdbdjded}(((X0 \in k1\_urysohn1~k6\_numbers){\unicdbdjdcd}(X1=k6\_numbers)){\unicdcdcdhd}(((X1=\\
k6\_numbers){\unicdbdjdcd}(X0 \in k1\_urysohn1~k6\_numbers)){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X0 \in k1\_urysohn1~(k2\_nat\_1~X2~np\_\_1)){\unicdbdjdcd}\\
((X0 \in k1\_urysohn1~X2){\unicdcdcdid}(X1=k2\_nat\_1~X2~np\_\_1)))))))))\end{array}
\label{hyp:egddpffhchjhdhpgigogdd}
\end{equation}
\begin{theorem}\label{thm:ehfdpffhchjhdhpgigogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((X0 \in k2\_urysohn1){\unicdbdjdcd}(\\
X0 \in k1\_urysohn1~(k2\_urysohn3~X0)))\end{array}$$
\end{theorem}
\end{document}
