\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{t71\_cohsp\_1 (TMGtgoDKg7JMe98PHipZMS6zRSPBb95jPKs)}
\maketitle
Let $ k13\_cohsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_coh\_sp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{r1\_tarski}~{X0}}~{({{k1\_zfmisc\_1}~{({{k3\_tarski}~{X0}})}})}}}\label{hyp:ehidcdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_classes1~X0){\unicdcdcdhd}(v1\_coh\_sp~\\
X0))){\unicdbdjdcd}(k3\_tarski~(k13\_cohsp\_1~X0)=k3\_tarski~X0)\end{array}
\label{hyp:ehgdgdpfdgpgigdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{({{k1\_tarski}~{X0}})}}~{X1}})}{\unicdbdjded}{({{X0} \in {X1}})}}}}\label{hyp:ehddbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_tarski}~{({{k1\_tarski}~{X0}})}}={X0}}}\label{hyp:ehcdfdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{k1\_zfmisc\_1}~{k1\_xboole\_0}}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_classes1~X0){\unicdcdcdhd}(v1\_coh\_sp~\\
X0))){\unicdbdjdcd}(k1\_xboole\_0 \in X0)\end{array}
\label{hyp:ehbdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k1\_tarski}~{X0}})}}}}}\label{hyp:ggdgcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_classes1~(k1\_tarski~k1\_xboole\_0)){\unicdcdcdhd}(v1\_coh\_sp~(k1\_tarski~\\
k1\_xboole\_0))\end{array}
\label{hyp:ggdgbdpfdgpgigdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_classes1~X0){\unicdcdcdhd}(v1\_coh\_sp~\\
X0))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k13\_cohsp\_1~X0)){\unicdcdcdhd}((v1\_classes1~(k13\_cohsp\_1~\\
X0)){\unicdcdcdhd}(v1\_coh\_sp~(k13\_cohsp\_1~X0))))\end{array}
\label{hyp:ggdgbdddpfdgpgigdhahpfbd}
\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}
\begin{theorem}\label{thm:ehhdbdpfdgpgigdhahpfbd}
${{{k13\_cohsp\_1}~{({{k1\_tarski}~{k1\_xboole\_0}})}}={{k1\_tarski}~{k1\_xboole\_0}}}$.
\end{theorem}
\end{document}
