\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{t38\_arytm\_3 (TMJBqiie1yrFmUUFgvoLgNCu4bVQYT2DkKN)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_arytm\_3 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k7\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}((\preoh X0 \in k4\_ordinal1){\unicdbdjdcd}\\
((X0=k4\_tarski~(k6\_arytm\_3~X0)~(k7\_arytm\_3~X0)){\unicdcdcdhd}(k7\_arytm\_3~\\
X0{\unicdcdgdad}np\_\_1)))\end{array}
\label{hyp:ehddgdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}(m1\_subset\_1~(k7\_arytm\_3~\\
X0)~k4\_ordinal1)\end{array}
\label{hyp:egehpflghdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k4\_ordinal1){\unicdbdjdcd}(((X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k7\_arytm\_3~X0){\unicdbdjded}(X1=\\
np\_\_1))){\unicdcdcdhd}((\preoh X0 \in k4\_ordinal1){\unicdbdjdcd}((X1=k7\_arytm\_3~X0){\unicdbdjded}({\unicdcdaddd} X2 .  \\
((v3\_ordinal1~X2){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdcdcdhd}(X0=k4\_tarski~X2~X1))))))\end{array}
\label{hyp:egjdpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehddidpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_arytm\_3){\unicdbdjdcd}((X0 \in k4\_ordinal1){\unicdbdjded}(\\
k7\_arytm\_3~X0=np\_\_1))\end{array}$$
\end{theorem}
\end{document}
