\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{t42\_setwiseo (TMciUYvwqfFHuck7uD2JJwjYzCu1So7NfPs)}
\maketitle
Let $ r3\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_setwiseo : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{v1\_setwiseo}~{({{k9\_setwiseo}~{X0}})}}~{({{k5\_finsub\_1}~{X0}})}}}\label{hyp:ehedbdpfdhfgehhhjgdhfgpg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}((v1\_setwiseo~X1~X0){\unicdbdjded}\\
(r3\_binop\_1~X0~(k4\_binop\_1~X0~X1)~X1)))\end{array}
\label{hyp:ehbdedpfdhfgehhhjgdhfgpg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~(k5\_finsub\_1~X0)){\unicdcdcdhd}(v4\_finsub\_1~(k5\_finsub\_1~\\
X0))\end{array}
\label{hyp:ggdgcdpfggjgogdhfhcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_funct\_1~(k9\_setwiseo~X0)){\unicdcdcdhd}((v1\_funct\_2~(k9\_setwiseo~\\
X0)~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k5\_finsub\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k9\_setwiseo~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k5\_finsub\_1~\\
X0)))))\end{array}
\label{hyp:egehpflgjdpfdhfgehhhjgdhfgpg}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfdhfgehhhjgdhfgpg}
$$\begin{array}{c}{\unicdcdadad} X0 .  r3\_binop\_1~(k5\_finsub\_1~X0)~(k4\_binop\_1~(k5\_finsub\_1~\\
X0)~(k9\_setwiseo~X0))~(k9\_setwiseo~X0)\end{array}$$
\end{theorem}
\end{document}
