\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{t8\_coh\_sp (TMJY6c62NkreD2iTZhWH4LDpX68yYLzQmKk)}
\maketitle
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.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_classes1~X1){\unicdcdcdhd}\\
(v1\_coh\_sp~X1))){\unicdbdjdcd}((X0 \in X1){\unicdbdjded}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X2 \in X0){\unicdcdcdhd}\\
(X3 \in X0)){\unicdbdjdcd}(k2\_tarski~X2~X3 \in X1)))\end{array}
\label{hyp:ehgdpfdgpgigpfdhah}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{r1\_tarski}~{X0}}~{({{k3\_tarski}~{X1}})}})}}}}\label{hyp:mgedcdpfkhggngjgdhdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehidpfdgpgigpfdhah}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v1\_classes1~X1){\unicdcdcdhd}\\
(v1\_coh\_sp~X1))){\unicdbdjdcd}(({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X2 \in X0){\unicdcdcdhd}(X3 \in X0)){\unicdbdjdcd}\\
(k2\_tarski~X2~X3 \in X1)){\unicdbdjdcd}(r1\_tarski~X0~(k3\_tarski~X1)))\end{array}$$
\end{theorem}
\end{document}
