\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{t4\_simplex0 (TMTaHe9915v5twAK94JssELTYEHiXN7VCEm)}
\maketitle
Let $ k1\_simplex0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ u2\_e\_siec : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\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}
\begin{array}{c}{\unicdcdadad} X0 .  (u1\_struct\_0~(k5\_e\_siec~X0)=k1\_tarski~X0){\unicdcdcdhd}((u1\_e\_siec~\\
(k5\_e\_siec~X0)=k1\_xboole\_0){\unicdcdcdhd}(u2\_e\_siec~(k5\_e\_siec~X0)=k1\_xboole\_0))\end{array}
\label{hyp:ehjdpffgpfdhjgfgdg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{r1\_tarski}~{({{k1\_tarski}~{X0}})}}~{({{k1\_zfmisc\_1}~{X0}})}}}\label{hyp:ehgdidpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~(k9\_setfam\_1~X0)){\unicdcdcdhd}((v1\_classes1~(k9\_setfam\_1~\\
X0)){\unicdcdcdhd}(v1\_coh\_sp~(k9\_setfam\_1~X0)))\end{array}
\label{hyp:ehcdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_classes1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (X1 \in X0){\unicdbdjdcd}(r1\_tarski~\\
(k9\_setfam\_1~X1)~X0))\end{array}
\label{hyp:ehbdpfdhjgngahmgfgihad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{({{k1\_tarski}~{X0}})}}~{X1}})}{\unicdbdjded}{({{X0} \in {X1}})}}}}\label{hyp:mgbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_classes1~X1){\unicdbdjdcd}((X1=k1\_simplex0~X0){\unicdbdjded}\\
((r1\_tarski~X0~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  ((r1\_tarski~X0~X2){\unicdcdcdhd}(v1\_classes1~\\
X2)){\unicdbdjdcd}(r1\_tarski~X1~X2))))\end{array}
\label{hyp:egbdpfdhjgngahmgfgihad}
\end{equation}
\begin{theorem}\label{thm:ehedpfdhjgngahmgfgihad}
${{\unicdcdadad} X0 .  {{{k1\_simplex0}~{({{k1\_tarski}~{X0}})}}={{k9\_setfam\_1}~{X0}}}}$.
\end{theorem}
\end{document}
