\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{t32\_sgraph1 (TMXmiNisWiSu3nvrjha13DEuk5f4H5qPbRP)}
\maketitle
Let $ m1\_sgraph1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_sgraph1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_sgraph1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_sgraph1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}(k5\_sgraph1~X0~X1~X2~X3=ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m2\_finseq\_2~\\
X4~(u1\_struct\_0~X1)~(k3\_finseq\_2~(u1\_struct\_0~X1))))~({\uniddcgcg} X4 : \\
\iota .  r3\_sgraph1~X0~X1~X2~X3~X4)~({\uniddcgcg} X4 : \iota .  X4))))\end{array}
\label{hyp:egbdadpfdhhgchbgahigbd}
\end{equation}
\begin{theorem}\label{thm:ehddcdpfdhhgchbgahigbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_sgraph1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (X4 \in k5\_sgraph1~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X5 .  (m2\_finseq\_2~\\
X5~(u1\_struct\_0~X1)~(k3\_finseq\_2~(u1\_struct\_0~X1))){\unicdcdcdhd}((X4=X5){\unicdcdcdhd}\\
(r3\_sgraph1~X0~X1~X2~X3~X5))))))\end{array}$$
\end{theorem}
\end{document}
