\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{t43\_pcs\_0 (TMKXTUfZ2jC6BvJ5FMamxcwZhaxp6Wt8PYj)}
\maketitle
Let $ l1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k24\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_pcs\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_pcs\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k24\_pcs\_0~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)))\end{array}
\label{hyp:egehpflgcdedpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_pcs\_0~\\
X0~X1~X2){\unicdbdjded}(k4\_tarski~X1~X2 \in u1\_pcs\_0~X0))))\end{array}
\label{hyp:eghdpfahdgdhpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1))){\unicdbdjdcd}((X2=k24\_pcs\_0~X0~X1){\unicdbdjded}(\\
{\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (k4\_tarski~X3~X4 \in X2){\unicdbdjded}((X3 \in X1){\unicdcdcdhd}((X4 \in X1){\unicdcdcdhd}\\
({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  ((X5 \in X3){\unicdcdcdhd}(X6 \in X4)){\unicdbdjdcd}(k4\_tarski~X5~X6 \in u1\_pcs\_0~\\
X0)))))))\end{array}
\label{hyp:egedgdpfahdgdhpfad}
\end{equation}
\begin{theorem}\label{thm:ehedddpfahdgdhpfad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pcs\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~\\
X2~X3 \in k24\_pcs\_0~X0~X1){\unicdbdjded}((X2 \in X1){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(((X4 \in X2){\unicdcdcdhd}(X5 \in X3)){\unicdbdjdcd}(r1\_pcs\_0~X0~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
