\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{t6\_pcomps\_1 (TMdRZhgxKef7asAFmiNeMpv2hFbxEvkTR2N)}
\maketitle
Let $ v1\_compts\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_compts\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{v8\_struct\_0}~{({{k1\_compts\_1}~{X0}})}})}}}\label{hyp:ggdgedpfdgpgngahehdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_finset\_1}~{({{k1\_tarski}~{X0}})}}}\label{hyp:ggdgbdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_pre\_topc~(k1\_compts\_1~X0)){\unicdcdcdhd}(v2\_pre\_topc~(k1\_compts\_1~\\
X0))\end{array}
\label{hyp:ggdgbdpfdgpgngahehdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{l1\_pre\_topc}~{({{k1\_compts\_1}~{X0}})}}}\label{hyp:egehpflgbdpfdgpgngahehdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}(((v8\_struct\_0~X0){\unicdcdcdhd}(v2\_pre\_topc~\\
X0)){\unicdbdjdcd}((v2\_pre\_topc~X0){\unicdcdcdhd}(v1\_compts\_1~X0)))\end{array}
\label{hyp:dgdgddpfdgpgngahehdhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfahdgpgngahdhpfbd}
${{\unicdcdadad} X0 .  {{v1\_compts\_1}~{({{k1\_compts\_1}~{({{k1\_tarski}~{X0}})}})}}}$.
\end{theorem}
\end{document}
