\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{l54\_arytm\_2 (TMU12dBpR9mDuVJUga6zBGfwWLN8Rdwkgua)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_arytm\_2 : {\iota}$ be given.
Let $ k7\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_arytm\_3 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k1\_arytm\_2 : {\iota}$ be given.
Let $ k5\_arytm\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_arytm\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_arytm\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}((k7\_arytm\_2~X0~X1=k11\_arytm\_3){\unicdbdjdcd}(X0=k11\_arytm\_3)))\end{array}
\label{hyp:ehfdpfbgchjhehngpfcd}
\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){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2){\unicdbdjdcd}\\
((k5\_arytm\_2~X0~X1=X0){\unicdbdjdcd}((X0=k11\_arytm\_3){\unicdcdcdid}(X1=k11\_arytm\_3))))\end{array}
\label{hyp:mgfdddpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2){\unicdbdjdcd}\\
(k3\_arytm\_2~(k4\_arytm\_2~X0)=X0)\end{array}
\label{hyp:mgcdbdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}((k3\_arytm\_2~X0=k11\_arytm\_3){\unicdbdjded}\\
(X0=k11\_arytm\_3))\end{array}
\label{hyp:mgbdjdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_arytm\_2}}}}\label{hyp:ggdgbdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_arytm\_2){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k1\_arytm\_2)){\unicdbdjdcd}(m2\_subset\_1~(k5\_arytm\_2~X0~X1)~(k1\_zfmisc\_1~\\
k5\_arytm\_3)~k1\_arytm\_2)\end{array}
\label{hyp:egehpflgfdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}(m2\_subset\_1~(k3\_arytm\_2~\\
X0)~(k1\_zfmisc\_1~k5\_arytm\_3)~k1\_arytm\_2)\end{array}
\label{hyp:egehpflgddpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_arytm\_2}}~{({{k1\_zfmisc\_1}~{({{k1\_zfmisc\_1}~{k5\_arytm\_3}})}})}}\label{hyp:egehpflgbdpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}(((X1=k11\_arytm\_3){\unicdbdjdcd}(k7\_arytm\_2~X0~X1=X0)){\unicdcdcdhd}(\\
((X0=k11\_arytm\_3){\unicdbdjdcd}(k7\_arytm\_2~X0~X1=X1)){\unicdcdcdhd}(\preoh (X1{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}\\
((X0{\unicdcdgdad}k11\_arytm\_3){\unicdcdcdhd}(k7\_arytm\_2~X0~X1{\unicdcdgdad}k4\_arytm\_2~(k5\_arytm\_2~\\
(k3\_arytm\_2~X0)~(k3\_arytm\_2~X1))))))))\end{array}
\label{hyp:egidpfbgchjhehngpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k2\_arytm\_2){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k2\_arytm\_2)){\unicdbdjdcd}(k7\_arytm\_2~X0~X1=k7\_arytm\_2~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflghdpfbgchjhehngpfcd}
\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}
\begin{theorem}\label{thm:mgfdedpfbgchjhehngpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_arytm\_2){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_arytm\_2){\unicdbdjdcd}((k7\_arytm\_2~X0~X1=X0){\unicdbdjdcd}(X1=k11\_arytm\_3)))\end{array}$$
\end{theorem}
\end{document}
