\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t43\_arytm\_3 (TMVkkoWmjXCQWwvVWF2uosUQj8PYJvkR4pi)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ r1\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_arytm\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_arytm\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((k6\_arytm\_3~\\
(k8\_arytm\_3~X1~X0)=k4\_arytm\_3~X1~X0){\unicdcdcdhd}(k7\_arytm\_3~(k8\_arytm\_3~\\
X1~X0)=k4\_arytm\_3~X0~X1))))\end{array}
\label{hyp:ehedcdpfbgchjhehngpfdd}
\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}((r1\_arytm\_3~X0~X1){\unicdbdjdcd}(k4\_arytm\_3~\\
X0~X1=X0)))\end{array}
\label{hyp:ehcdddpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_arytm\_3~X0~X1){\unicdbdjdcd}(r1\_arytm\_3~X1~X0))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfbgchjhehngpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehedddpfbgchjhehngpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k4\_ordinal1){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k4\_ordinal1){\unicdbdjdcd}((r1\_arytm\_3~X0~X1){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}((k6\_arytm\_3~\\
(k8\_arytm\_3~X0~X1)=X0){\unicdcdcdhd}(k7\_arytm\_3~(k8\_arytm\_3~X0~X1)=X1)))))\end{array}$$
\end{theorem}
\end{document}
