\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{t24\_mcart\_1 (TMW3PySVtPEP7MVapsVVJurV8URnr7svz61)}
\maketitle
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k1\_xtuple\_0~(k4\_tarski~X0~X1)=X0){\unicdcdcdhd}(k2\_xtuple\_0~\\
(k4\_tarski~X0~X1)=X1)\end{array}
\label{hyp:ehhdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
(\preoh {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}(X2=k4\_tarski~\\
(k1\_xtuple\_0~X2)~(k2\_xtuple\_0~X2))))\end{array}
\label{hyp:ehcdcdpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ({\unicdcdaddd} X1 .  {\unicdcdaddd} X2 .  X0=k4\_tarski~X1~X2){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_xtuple\_0~\\
X0){\unicdcdcdhd}(X0{\unicdcdgdad}k2\_xtuple\_0~X0))\end{array}
\label{hyp:ehcdadpfngdgbgchehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfngdgbgchehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  \preoh (X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
(\preoh {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k2\_zfmisc\_1~X0~X1)){\unicdbdjdcd}((X2{\unicdcdgdad}k1\_xtuple\_0~\\
X2){\unicdcdcdhd}(X2{\unicdcdgdad}k2\_xtuple\_0~X2))))\end{array}$$
\end{theorem}
\end{document}
