\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t16\_arytm\_3 (TMKQFEgKUpWqRbbzBtU1hTeviVCYkkaXxz7)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
r2\_arytm\_3~X0~X0)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k4\_ordinal1){\unicdbdjdcd}((X2=k3\_arytm\_3~X0~X1){\unicdbdjded}((r2\_arytm\_3~X2~X0){\unicdcdcdhd}(\\
(r2\_arytm\_3~X2~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v3\_ordinal1~X3){\unicdcdcdhd}(v7\_ordinal1~\\
X3)){\unicdbdjdcd}(((r2\_arytm\_3~X3~X0){\unicdcdcdhd}(r2\_arytm\_3~X3~X1)){\unicdbdjdcd}(r2\_arytm\_3~X3~\\
X2))))))))\end{array}
\label{hyp:egfdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v3\_ordinal1~X1){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~k4\_ordinal1){\unicdbdjdcd}((X2=k2\_arytm\_3~X0~X1){\unicdbdjded}((r2\_arytm\_3~X0~X2){\unicdcdcdhd}(\\
(r2\_arytm\_3~X1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  ((v3\_ordinal1~X3){\unicdcdcdhd}(v7\_ordinal1~\\
X3)){\unicdbdjdcd}(((r2\_arytm\_3~X0~X3){\unicdcdcdhd}(r2\_arytm\_3~X1~X3)){\unicdbdjdcd}(r2\_arytm\_3~X2~\\
X3))))))))\end{array}
\label{hyp:egedpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjded}{({{X0} \in {k4\_ordinal1}})}}}\label{hyp:egbdcdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}((k3\_arytm\_3~\\
X0~X0=X0){\unicdcdcdhd}(k2\_arytm\_3~X0~X0=X0))\end{array}$$
\end{theorem}
\end{document}
