\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{t42\_xboole\_1 (TMRogbJjsUdaYctHrosmxVsJXiDqhbFeCoT)}
\maketitle
Let $ k4\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{({{{k2\_xboole\_0}~{X0}}~{X1}})}}}}\label{hyp:ehhdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_xboole\_0~X0~(k2\_xboole\_0~X0~X1)=k2\_xboole\_0~\\
X0~X1\end{array}
\label{hyp:ehgdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_xboole\_0~(k2\_xboole\_0~X0~\\
X1)~X2=k2\_xboole\_0~X0~(k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:ehedpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k4\_xboole\_0}~{k1\_xboole\_0}}~{X0}}={k1\_xboole\_0}}}\label{hyp:ehedpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k4\_xboole\_0~(k4\_xboole\_0~X0~\\
X1)~X2=k4\_xboole\_0~X0~(k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:ehedbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_xboole\_0~(k2\_xboole\_0~X0~X1)~X1=k4\_xboole\_0~\\
X0~X1\end{array}
\label{hyp:ehedadpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{{k4\_xboole\_0}~{X0}}~{k1\_xboole\_0}}={X0}}}\label{hyp:ehddpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k2\_xboole\_0~X0~(k4\_xboole\_0~X1~X0)=k2\_xboole\_0~\\
X0~X1\end{array}
\label{hyp:ehddjdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~(k4\_xboole\_0~X1~X0)){\unicdbdjdcd}(X0=\\
k1\_xboole\_0)\end{array}
\label{hyp:ehddidpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{({{{k4\_xboole\_0}~{X0}}~{X1}})}}~{X0}}}}\label{hyp:ehddgdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  r1\_tarski~(k2\_xboole\_0~(k3\_xboole\_0~\\
X0~X1)~(k3\_xboole\_0~X0~X2))~(k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:ehddbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  r1\_tarski~(k3\_xboole\_0~X0~X1)~\\
(k2\_xboole\_0~X0~X2)\end{array}
\label{hyp:ehcdjdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_xboole\_0~(k2\_xboole\_0~(k3\_xboole\_0~\\
X0~X1)~(k3\_xboole\_0~X1~X2))~(k3\_xboole\_0~X2~X0)=k3\_xboole\_0~(k3\_xboole\_0~\\
(k2\_xboole\_0~X0~X1)~(k2\_xboole\_0~X1~X2))~(k2\_xboole\_0~X2~X0)\end{array}
\label{hyp:ehcdfdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k2\_xboole\_0~X0~(k3\_xboole\_0~\\
X1~X2)=k3\_xboole\_0~(k2\_xboole\_0~X0~X1)~(k2\_xboole\_0~X0~X2)\end{array}
\label{hyp:ehcdedpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k3\_xboole\_0~X0~(k2\_xboole\_0~\\
X1~X2)=k2\_xboole\_0~(k3\_xboole\_0~X0~X1)~(k3\_xboole\_0~X0~X2)\end{array}
\label{hyp:ehcdddpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{({{{k3\_xboole\_0}~{X0}}~{X1}})}}={X0}}}}\label{hyp:ehcdcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{{k2\_xboole\_0}~{X0}}~{X1}}={X1}})}}}}\label{hyp:ehbdcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_tarski~\\
X0~(k2\_xboole\_0~X2~X1))\end{array}
\label{hyp:ehbdadpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k4\_xboole\_0~X0~(k3\_xboole\_0~\\
X1~X2)=k2\_xboole\_0~(k4\_xboole\_0~X0~X1)~(k4\_xboole\_0~X0~X2)\end{array}
\label{hyp:mgddgdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k4\_xboole\_0~X0~X1=k1\_xboole\_0){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:mgddcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X0}}={X0}}}}\label{hyp:jgegfgngahpgehfgogdgfgpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k4\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(\preoh X3 \in X1)))\end{array}
\label{hyp:egfdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfihcgpgpgmgfgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k4\_xboole\_0~(k2\_xboole\_0~X0~\\
X1)~X2=k2\_xboole\_0~(k4\_xboole\_0~X0~X2)~(k4\_xboole\_0~X1~X2)\end{array}$$
\end{theorem}
\end{document}
