\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{t12\_arrow (TMK1oi8QSBWJzsbXE9HVkdBTyc8iSaA9HLz)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ r1\_arrow : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k3\_arrow}~{X0}})}}}})}}}\label{hyp:ggdgcdpfbgchchpghh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v1\_xboole\_0}~{({{k2\_arrow}~{X0}})}}}})}}}\label{hyp:ggdgbdpfbgchchpghh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjdcd}(m1\_subset\_1~X2~X0))\end{array}
\label{hyp:egehpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k3\_arrow~X0)~(k1\_zfmisc\_1~\\
(k2\_arrow~X0)))\end{array}
\label{hyp:egehpflgddpfbgchchpghh}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfbgchchpghh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(\\
k2\_arrow~X0)~(k3\_arrow~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~(k2\_arrow~\\
X0)~(k3\_arrow~X0)){\unicdbdjdcd}((\preoh (\preoh (\preoh r1\_arrow~X3~X2~X1){\unicdcdcdhd}(r1\_arrow~X4~X2~X1)){\unicdcdcdhd}\\
((\preoh (\preoh r1\_arrow~X4~X2~X1){\unicdcdcdhd}(r1\_arrow~X3~X2~X1)){\unicdcdcdhd}((\preoh (\preoh r1\_arrow~X3~X1~\\
X2){\unicdcdcdhd}(r1\_arrow~X4~X1~X2)){\unicdcdcdhd}((\preoh (\preoh r1\_arrow~X4~X1~X2){\unicdcdcdhd}(r1\_arrow~X3~X1~\\
X2)){\unicdcdcdhd}(\preoh (\preoh (\preoh r1\_arrow~X3~X2~X1){\unicdcdcdhd}(r1\_arrow~X4~X2~X1)){\unicdcdcdhd}(\preoh (\preoh r1\_arrow~\\
X4~X2~X1){\unicdcdcdhd}(r1\_arrow~X3~X2~X1))))))){\unicdcdcdhd}(\preoh (\preoh (\preoh r1\_arrow~X3~X2~X1){\unicdcdcdhd}(r1\_arrow~\\
X4~X2~X1)){\unicdcdcdhd}((\preoh (\preoh r1\_arrow~X4~X2~X1){\unicdcdcdhd}(r1\_arrow~X3~X2~X1)){\unicdcdcdhd}(\preoh (\preoh (\preoh r1\_arrow~\\
X3~X2~X1){\unicdcdcdhd}(r1\_arrow~X4~X2~X1)){\unicdcdcdhd}((\preoh (\preoh r1\_arrow~X4~X2~X1){\unicdcdcdhd}(r1\_arrow~\\
X3~X2~X1)){\unicdcdcdhd}((\preoh (\preoh r1\_arrow~X3~X1~X2){\unicdcdcdhd}(r1\_arrow~X4~X1~X2)){\unicdcdcdhd}(\preoh (\preoh r1\_arrow~\\
X4~X1~X2){\unicdcdcdhd}(r1\_arrow~X3~X1~X2))))))))))))\end{array}$$
\end{theorem}
\end{document}
