\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}
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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{t79\_member\_1 (TMP6UxpZKamShhQgoisAG14eZ5edLizBv4D)}
\maketitle
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xxreal\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_numbers : {\iota}$ be given.
Let $ k3\_member\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k7\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k7\_numbers)){\unicdbdjdcd}(k3\_member\_1~X0~X1=k4\_xxreal\_3~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}(k12\_member\_1~\\
X0~X1=ReplSep2~(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~k7\_numbers))~\\
({\uniddcgcg} X2 : \iota .  toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k7\_numbers))~(\\
{\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \iota .  (X2 \in X0){\unicdcdcdhd}(X3 \in X1))~({\uniddcgcg} X2 : \iota .  {\uniddcgcg} X3 : \\
\iota .  k3\_member\_1~X2~X3)))\end{array}
\label{hyp:egjdpfngfgngcgfgchpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xxreal\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k7\_numbers}})}}}\label{hyp:egbdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehhdjdpfngfgngcgfgchpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v2\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v2\_membered~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xxreal\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_xxreal\_0~X3){\unicdbdjdcd}(((X2 \in X0){\unicdcdcdhd}(X3 \in \\
X1)){\unicdbdjdcd}(k4\_xxreal\_3~X2~X3 \in k12\_member\_1~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
