\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\_mycielsk (TMNnQ9jEyo5HunBBofRjiLwGE9KTcghg3vS)}
\maketitle
Let $ v1\_necklace : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_dilworth : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_dilworth : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_dilworth : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_necklace : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_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 $ v1\_dilworth : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_dilworth : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_dilworth~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((v1\_dilworth~\\
X1~(k3\_necklace~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
(k3\_necklace~X0))))))\end{array}
\label{hyp:ehcdbdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_necklace~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_dilworth~X1~(k3\_necklace~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_necklace~X0))))){\unicdbdjdcd}((v2\_dilworth~X1~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))))\end{array}
\label{hyp:ehcdadpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_necklace~X0){\unicdcdcdhd}((v4\_dilworth~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}((v1\_orders\_2~(k3\_necklace~X0)){\unicdcdcdhd}(v3\_dilworth~(k3\_necklace~\\
X0)))\end{array}
\label{hyp:ggdgbdadpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~(k3\_necklace~X0)){\unicdcdcdhd}\\
(l1\_orders\_2~(k3\_necklace~X0)))\end{array}
\label{hyp:egehpflgddpfogfgdglgmgbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_dilworth~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}(v7\_ordinal1~\\
(k2\_dilworth~X0))\end{array}
\label{hyp:egehpflgcdpfegjgmghhpgchehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_dilworth~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}((X1=k2\_dilworth~X0){\unicdbdjded}(({\unicdcdaddd} X2 .  ((v1\_finset\_1~\\
X2){\unicdcdcdhd}((v2\_dilworth~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))){\unicdcdcdhd}(k5\_card\_1~X2=X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}(\\
(v2\_dilworth~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}(r1\_xxreal\_0~(k5\_card\_1~X2)~X1)))))\end{array}
\label{hyp:eggdpfegjgmghhpgchehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_dilworth~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}((X1=k1\_dilworth~X0){\unicdbdjded}(({\unicdcdaddd} X2 .  ((v1\_finset\_1~\\
X2){\unicdcdcdhd}((v1\_dilworth~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))){\unicdcdcdhd}(k5\_card\_1~X2=X1)){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_finset\_1~X2){\unicdcdcdhd}(\\
(v1\_dilworth~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))))){\unicdbdjdcd}(r1\_xxreal\_0~(k5\_card\_1~X2)~X1)))))\end{array}
\label{hyp:egedpfegjgmghhpgchehig}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfngjhdgjgfgmgdhlg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_necklace~X0){\unicdcdcdhd}((v4\_dilworth~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}(k2\_dilworth~X0=k1\_dilworth~(k3\_necklace~X0))\end{array}$$
\end{theorem}
\end{document}
