\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{t15\_dilworth (TMUMLp7pUYQGfkdpp4VjAXfDRBvHNNokvSe)}
\maketitle
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_dilworth : {{\iota}{\unicdbdjdcd}{{\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 $ v2\_dilworth : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_dilworth~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X2 \in X1){\unicdcdcdhd}\\
((X3 \in X1){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}((\preoh r1\_orders\_2~X0~X2~X3){\unicdcdcdhd}(\preoh r1\_orders\_2~X0~\\
X3~X2)))))))))\end{array}
\label{hyp:ehgdpfegjgmghhpgchehig}
\end{equation}
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 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}((v2\_dilworth~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(((X2 \in X1){\unicdcdcdhd}(X3 \in X1)){\unicdbdjdcd}((X2=X3){\unicdcdcdid}((\preoh r1\_orders\_2~X0~X2~X3){\unicdcdcdhd}\\
(\preoh r1\_orders\_2~X0~X3~X2))))))))\end{array}
\label{hyp:egcdpfegjgmghhpgchehig}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfegjgmghhpgchehig}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_dilworth~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v2\_dilworth~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((X3 \in X2){\unicdcdcdhd}((X4 \in X2){\unicdcdcdhd}((X3 \in X1){\unicdcdcdhd}\\
(X4 \in X1)))){\unicdbdjdcd}(X3=X4))))\end{array}$$
\end{theorem}
\end{document}
