\documentclass{article}
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\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\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t175\_member\_1 (TMcBem6oDfcALVERiqcBF3eVQiSgpXeq9RH)}
\maketitle
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k20\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_member\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}(k4\_member\_1~\\
(k5\_xboole\_0~X0~X1)=k5\_xboole\_0~(k4\_member\_1~X0)~(k4\_member\_1~\\
X1)))\end{array}
\label{hyp:ehidpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}(k20\_member\_1~\\
X0~X1=k4\_member\_1~(k18\_member\_1~X0~X1)))\end{array}
\label{hyp:ehbdhdbdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(k18\_member\_1~(k5\_xboole\_0~X0~X1)~X2=k5\_xboole\_0~\\
(k18\_member\_1~X0~X2)~(k18\_member\_1~X1~X2))))\end{array}
\label{hyp:ehbdfdjdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v2\_membered~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
v2\_membered~(k18\_member\_1~X0~X1))\end{array}
\label{hyp:ggdghdddpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v2\_membered~X0){\unicdcdcdhd}(v2\_membered~X1)){\unicdbdjdcd}(\\
v2\_membered~(k5\_xboole\_0~X0~X1))\end{array}
\label{hyp:ggdgfdadpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k5\_xboole\_0}~{X0}}~{X1}}={{{k5\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgfdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdhdfdpfngfgngcgfgchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xreal\_0~X2){\unicdbdjdcd}(k20\_member\_1~(k5\_xboole\_0~X0~X1)~X2=k5\_xboole\_0~\\
(k20\_member\_1~X0~X2)~(k20\_member\_1~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
