\documentclass{article}
\newtheorem{axiom}{Axiom}
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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\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t13\_binarith (TMM3nbZo9TLC2j9QDiSz7YL2hou3ZjaPzXN)}
\maketitle
Let $ k2\_binarith : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Let $ k7\_margrel1 : {\iota}$ be given.
Let $ v1\_xboolean : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xboolean : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xboolean : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboolean : {\iota}$ be given.
Let $ k1\_xboolean : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}(k10\_xboolean~k8\_margrel1~X0=k3\_xboolean~\\
X0)\end{array}
\label{hyp:ehhdpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboolean~X0){\unicdbdjdcd}(((X0=k7\_margrel1){\unicdbdjdcd}(k3\_xboolean~\\
X0=k8\_margrel1)){\unicdcdcdhd}(((k3\_xboolean~X0=k8\_margrel1){\unicdbdjdcd}(X0=k7\_margrel1)){\unicdcdcdhd}\\
(((X0=k8\_margrel1){\unicdbdjdcd}(k3\_xboolean~X0=k7\_margrel1)){\unicdcdcdhd}((k3\_xboolean~\\
X0=k7\_margrel1){\unicdbdjdcd}(X0=k8\_margrel1)))))\end{array}
\label{hyp:ehbdbdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k8\_margrel1}={k2\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_margrel1}={k1\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k6\_margrel1){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k6\_margrel1)){\unicdbdjdcd}(k2\_binarith~X0~X1=k10\_xboolean~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfcgjgogbgchjgehig}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboolean}~{k1\_xboolean}}\label{hyp:ggdgbdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k8\_margrel1}}~{k6\_margrel1}}\label{hyp:egehpflgidpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k7\_margrel1}}~{k6\_margrel1}}\label{hyp:egehpflghdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_xboolean}={np\_\_1}}\label{hyp:egcdpfihcgpgpgmgfgbgog}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfcgjgogbgchjgehig}
${{{{k2\_binarith}~{k8\_margrel1}}~{k7\_margrel1}}={k8\_margrel1}}$.
\end{theorem}
\end{document}
