\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{t43\_graphsp (TMQft1cCrB7ufsXUJJm3isX4VgzRkCAwCYd)}
\maketitle
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\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 $ r2\_graphsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_2~X0~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_finseq\_2~X1~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r2\_graphsp~X0~X1~X2~X3){\unicdbdjded}\\
((k4\_finseq\_1~X0=k4\_finseq\_1~X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~\\
k1\_numbers~k5\_numbers){\unicdbdjdcd}(((X4 \in k4\_finseq\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~\\
X2~X4){\unicdcdcdhd}(r1\_xxreal\_0~X4~X3))){\unicdbdjdcd}(k1\_seq\_1~X0~X4=k1\_seq\_1~X1~X4))))))))\end{array}
\label{hyp:egbdgdpfhgchbgahigdhah}
\end{equation}
\begin{theorem}\label{thm:ehedddpfhgchbgahigdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_2~\\
X2~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_2~\\
X3~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_finseq\_2~\\
X4~k1\_numbers~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}(((r2\_graphsp~X2~X3~X0~\\
X1){\unicdcdcdhd}(r2\_graphsp~X3~X4~X0~X1)){\unicdbdjdcd}(r2\_graphsp~X2~X4~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
