\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{t3\_coh\_sp (TMYtwjMv61u6YLyNAWUFDnznrmRxh4agtqA)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_coh\_sp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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}
{{{k1\_zfmisc\_1}~{k1\_xboole\_0}}={{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:ehbdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddpfdgpgigpfdhah}
$$\begin{array}{c}(\preoh v1\_xboole\_0~(k1\_tarski~k1\_xboole\_0)){\unicdcdcdhd}((v1\_classes1~(k1\_tarski~\\
k1\_xboole\_0)){\unicdcdcdhd}(v1\_coh\_sp~(k1\_tarski~k1\_xboole\_0)))\end{array}$$
\end{theorem}
\end{document}
