\documentclass{article}
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\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{t17\_urysohn2 (TMLRRsk3nTAJ5Ac9HHHrA4GCLniK3EAc73y)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_xxreal\_2 : {{\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 $ k1\_numbers : {\iota}$ be given.
Let $ k1\_integra2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_measure5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v2\_measure5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_measure5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_measure5 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((v3\_measure5~X0){\unicdbdjdcd}((r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdid}(v3\_measure5~\\
(k1\_integra2~X0~X1)))))\end{array}
\label{hyp:ehjdpffhchjhdhpgigogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((v2\_measure5~X0){\unicdbdjdcd}((X1=k6\_numbers){\unicdcdcdid}(v2\_measure5~(k1\_integra2~\\
X0~X1)))))\end{array}
\label{hyp:ehidpffhchjhdhpgigogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((v1\_measure5~X0){\unicdbdjdcd}((X1=k6\_numbers){\unicdcdcdid}(v1\_measure5~(k1\_integra2~\\
X0~X1)))))\end{array}
\label{hyp:ehhdpffhchjhdhpgigogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(v6\_xxreal\_2~(k1\_integra2~X0~k6\_numbers))\end{array}
\label{hyp:ehgdpffhchjhdhpgigogcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers))){\unicdbdjdcd}\\
(\preoh (\preoh v1\_measure5~X0){\unicdcdcdhd}((\preoh v2\_measure5~X0){\unicdcdcdhd}((\preoh v3\_measure5~X0){\unicdcdcdhd}\\
(\preoh v4\_measure5~X0))))\end{array}
\label{hyp:ehbdpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((v4\_measure5~X0){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~X1){\unicdcdcdid}(v3\_measure5~\\
(k1\_integra2~X0~X1)))))\end{array}
\label{hyp:ehbdcdpffhchjhdhpgigogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((v4\_measure5~X0){\unicdbdjdcd}((r1\_xxreal\_0~X1~k6\_numbers){\unicdcdcdid}(v4\_measure5~\\
(k1\_integra2~X0~X1)))))\end{array}
\label{hyp:ehbdbdpffhchjhdhpgigogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((v3\_measure5~X0){\unicdbdjdcd}((r1\_xxreal\_0~k6\_numbers~X1){\unicdcdcdid}(v4\_measure5~\\
(k1\_integra2~X0~X1)))))\end{array}
\label{hyp:ehbdadpffhchjhdhpgigogcd}
\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}{\unicdcdaddd} X0 .  (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xxreal\_0~\\
X0){\unicdcdcdhd}(v1\_xreal\_0~X0)))\end{array}
\label{hyp:chdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_membered~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(m1\_subset\_1~\\
(k1\_integra2~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgbdpfjgogehfghgchbgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(v3\_membered~\\
X0)\end{array}
\label{hyp:dgdgidpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}((v4\_measure5~\\
X0){\unicdbdjdcd}(v6\_xxreal\_2~X0))\end{array}
\label{hyp:dgdgedpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}((v3\_measure5~\\
X0){\unicdbdjdcd}(v6\_xxreal\_2~X0))\end{array}
\label{hyp:dgdgddpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}((v2\_measure5~\\
X0){\unicdbdjdcd}(v6\_xxreal\_2~X0))\end{array}
\label{hyp:dgdgcdpfngfgbgdhfhchfgfd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}((v1\_measure5~\\
X0){\unicdbdjdcd}(v6\_xxreal\_2~X0))\end{array}
\label{hyp:dgdgbdpfngfgbgdhfhchfgfd}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpffhchjhdhpgigogcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v6\_xxreal\_2~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~k1\_numbers)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k1\_numbers){\unicdbdjdcd}\\
((v6\_xxreal\_2~(k1\_integra2~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~(k1\_integra2~\\
X0~X1)~(k1\_zfmisc\_1~k1\_numbers))))\end{array}$$
\end{theorem}
\end{document}
