\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{t19\_urysohn3 (TMQQct3ueQxCeNRQGbzrhxZLfWPVUrm9Zws)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
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 $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m2\_urysohn3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k6\_urysohn3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v10\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_pre\_topc~\\
X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((r1\_xboole\_0~\\
X1~X2){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X3 .  (m2\_urysohn3~X3~X0~X1~X2){\unicdbdjdcd}\\
((v5\_pre\_topc~(k6\_urysohn3~X0~X1~X2~X3)~X0~k3\_topmetr){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(\\
k1\_seq\_1~(k6\_urysohn3~X0~X1~X2~X3)~X4)){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_seq\_1~\\
(k6\_urysohn3~X0~X1~X2~X3)~X4)~np\_\_1){\unicdcdcdhd}(((X4 \in X1){\unicdbdjdcd}(k1\_seq\_1~(k6\_urysohn3~\\
X0~X1~X2~X3)~X4=k6\_numbers)){\unicdcdcdhd}((X4 \in X2){\unicdbdjdcd}(k1\_seq\_1~(k6\_urysohn3~\\
X0~X1~X2~X3)~X4=np\_\_1))))))))))))\end{array}
\label{hyp:ehbdidpffhchjhdhpgigogdd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))){\unicdbdjdcd}({\unicdcdaddd} X3 .  \\
m2\_urysohn3~X3~X0~X1~X2)\end{array}
\label{hyp:fgihjgdhehfgogdgfgpfngcdpffhchjhdhpgigogdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(\\
k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}((m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdcdcdhd}(m2\_urysohn3~X3~X0~X1~X2)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k6\_urysohn3~X0~X1~X2~X3)){\unicdcdcdhd}((v1\_funct\_2~(k6\_urysohn3~X0~X1~X2~X3)~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}(m1\_subset\_1~(k6\_urysohn3~\\
X0~X1~X2~X3)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k3\_topmetr))))))\end{array}
\label{hyp:egehpflggdpffhchjhdhpgigogdd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpffhchjhdhpgigogdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}((v10\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v4\_pre\_topc~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v4\_pre\_topc~\\
X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}\\
k1\_xboole\_0){\unicdcdcdhd}((r1\_xboole\_0~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~X0)~(u1\_struct\_0~k3\_topmetr)){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
k3\_topmetr)))))){\unicdbdjdcd}(\preoh (v5\_pre\_topc~X3~X0~k3\_topmetr){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~(\\
k1\_seq\_1~X3~X4)){\unicdcdcdhd}((r1\_xxreal\_0~(k1\_seq\_1~X3~X4)~np\_\_1){\unicdcdcdhd}(((X4 \in \\
X1){\unicdbdjdcd}(k1\_seq\_1~X3~X4=k6\_numbers)){\unicdcdcdhd}((X4 \in X2){\unicdbdjdcd}(k1\_seq\_1~X3~X4=np\_\_1))))))))))))\end{array}$$
\end{theorem}
\end{document}
