\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t2\_arytm\_3 (TMRoTgwzBjHM8iw4TAYpqz2hEK8vvQdDJ98)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k11\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
k11\_ordinal2~X0~X1=np\_\_1){\unicdbdjdcd}((X0=np\_\_1){\unicdcdcdhd}(X1=np\_\_1))))\end{array}
\label{hyp:ehddhdpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 .  {\unicdcdaddd} X2 .  ((v5\_ordinal1~X2){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_ordinal2~X2)))){\unicdcdcdhd}((k9\_xtuple\_0~\\
X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(k1\_funct\_1~X2~\\
X3=X0~X3))))\end{array}
\label{hyp:dhddpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v5\_ordinal1~X0))){\unicdbdjdcd}\\
(v3\_ordinal1~(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgedpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_arytm\_3~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (\\
v3\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}(((X0=k11\_ordinal2~\\
X2~X3){\unicdcdcdhd}(X1=k11\_ordinal2~X2~X4)){\unicdbdjdcd}(X2=np\_\_1)))))))\end{array}
\label{hyp:egcdpfbgchjhehngpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfbgchjhehngpfdd}
${{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{r1\_arytm\_3}~{np\_\_1}}~{X0}})}}}$.
\end{theorem}
\end{document}
