\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}
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\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{t47\_member\_1 (TMVixQZrryQhnAf6hYQZX35TK1rkSaGBAoG)}
\maketitle
Let $ v1\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k3\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_membered~X0){\unicdcdcdhd}(v1\_membered~X1)){\unicdbdjdcd}(\\
v1\_membered~(k9\_member\_1~X0~X1))\end{array}
\label{hyp:ggdgcdddpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}((X2 \in X0){\unicdbdjdcd}(X2 \in X1))))\end{array}
\label{hyp:eghdpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_membered~X1){\unicdbdjdcd}(k9\_member\_1~\\
X0~X1=ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k2\_numbers))~\\
({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k2\_numbers))~(\\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  (X2 \in X0){\unicdcdcdhd}(X3 \in X1))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  k3\_binop\_2~X2~X3)))\end{array}
\label{hyp:eggdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_membered~X0){\unicdcdcdhd}(v1\_membered~X1)){\unicdbdjdcd}(\\
k9\_member\_1~X0~X1=k9\_member\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgjdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfngfgngcgfgchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_membered~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_membered~X3){\unicdbdjdcd}(((r1\_tarski~\\
X0~X1){\unicdcdcdhd}(r1\_tarski~X2~X3)){\unicdbdjdcd}(r1\_tarski~(k9\_member\_1~X0~X2)~(k9\_member\_1~\\
X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
