\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{t22\_sgraph1 (TMdWL1YM2c87M2vWSiL8sqhqzgsjkiWTALb)}
\maketitle
Let $ m1\_sgraph1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ g1\_sgraph1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_subset\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_sgraph1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_sgraph1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_sgraph1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_sgraph1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1 \in k2\_sgraph1~X0){\unicdbdjded}(((v1\_finset\_1~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0))){\unicdcdcdhd}({\unicdcdaddd} X2 .  {\unicdcdaddd} X3 .  (X2 \in \\
X0){\unicdcdcdhd}((X3 \in X0){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}(X1=k2\_tarski~X2~X3)))))\end{array}
\label{hyp:ehidpfdhhgchbgahigbd}
\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 .  {\unicdcdadad} X1 .  (m1\_sgraph1~X1~X0){\unicdbdjdcd}(((v1\_finset\_1~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~(u1\_struct\_0~X1)~(k1\_zfmisc\_1~X0))){\unicdcdcdhd}((v1\_finset\_1~\\
(u1\_sgraph1~X1)){\unicdcdcdhd}(m1\_subset\_1~(u1\_sgraph1~X1)~(k1\_zfmisc\_1~(\\
k2\_sgraph1~(u1\_struct\_0~X1))))))\end{array}
\label{hyp:ehcdbdpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_sgraph1~X1~X0){\unicdbdjdcd}((v1\_sgraph1~X1){\unicdcdcdhd}(l1\_sgraph1~\\
X1))\end{array}
\label{hyp:egehpfngbdpfdhhgchbgahigbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_subset\_1}~{X0}}={k1\_xboole\_0}}}\label{hyp:egcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_sgraph1~X0){\unicdbdjdcd}((v1\_sgraph1~X0){\unicdbdjdcd}(X0=g1\_sgraph1~\\
(u1\_struct\_0~X0)~(u1\_sgraph1~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdhhgchbgahigbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfdhhgchbgahigbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_sgraph1~X1~X0){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}g1\_sgraph1~k1\_xboole\_0~\\
(k1\_subset\_1~(k2\_sgraph1~k1\_xboole\_0))){\unicdcdcdhd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_sgraph1~X2))){\unicdbdjdcd}(\preoh (\preoh v1\_xboole\_0~\\
X2){\unicdcdcdhd}(X1=g1\_sgraph1~X2~X3))))\end{array}$$
\end{theorem}
\end{document}
