\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{t13\_arrow (TMYdf3GmR5tjJYUCM6AwQjUoM2Ku5SDm9KV)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_arrow : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_arrow : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_arrow : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(\\
k2\_arrow~X0)~(k3\_arrow~X0)){\unicdbdjdcd}(((r1\_arrow~X3~X1~X2){\unicdcdcdhd}(r1\_arrow~X3~\\
X2~X1)){\unicdbdjdcd}(X1=X2)))))\end{array}
\label{hyp:ehgdpfbgchchpghh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(\\
k2\_arrow~X0)){\unicdbdjdcd}((r1\_arrow~X3~X1~X2){\unicdcdcdid}(r1\_arrow~X3~X2~X1)))))\end{array}
\label{hyp:ehedpfbgchchpghh}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfbgchchpghh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k2\_arrow~\\
X0)~(k3\_arrow~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_arrow~X0)){\unicdbdjdcd}\\
(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
X0){\unicdbdjdcd}(\preoh (\preoh r1\_arrow~X1~X4~X3){\unicdcdcdhd}(r1\_arrow~X2~X4~X3)))){\unicdbdjded}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~X0){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}((\preoh (\preoh r1\_arrow~\\
X1~X4~X3){\unicdcdcdhd}(r1\_arrow~X2~X4~X3)){\unicdcdcdhd}(\preoh (\preoh r1\_arrow~X2~X4~X3){\unicdcdcdhd}(r1\_arrow~\\
X1~X4~X3))))))))\end{array}$$
\end{theorem}
\end{document}
