\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t34\_mycielsk (TMJdJqtwEzQyURcLFajL2DcQ6d65N9AHQKs)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_dilworth : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_mycielsk : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_dilworth : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_dilworth : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_struct\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_mycielsk : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_dilworth~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}(((v1\_dilworth~(k2\_struct\_0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~(k2\_struct\_0~\\
X0)~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k2\_dilworth~X0=np\_\_1))\end{array}
\label{hyp:ehcdadpfegjgmghhpgchehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(v1\_dilworth~(k2\_struct\_0~(k5\_mycielsk~\\
X0))~(k5\_mycielsk~X0))\end{array}
\label{hyp:ggdgbdedpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_mycielsk~X1~X0){\unicdbdjdcd}\\
((v1\_orders\_2~X1){\unicdcdcdhd}(l1\_orders\_2~X1)))\end{array}
\label{hyp:egehpfngbdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{m1\_mycielsk}~{({{k5\_mycielsk}~{X0}})}}~{X0}})}}}\label{hyp:egehpflgfdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k2\_struct\_0~X0)~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpflgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v8\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{v4\_dilworth}~{X0}})}})}}}\label{hyp:dgdggdpfegjgmghhpgchehig}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_mycielsk~X1~X0){\unicdbdjdcd}\\
(v8\_struct\_0~X1))\end{array}
\label{hyp:dgdgfdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_mycielsk~X1~X0){\unicdbdjdcd}(\preoh v2\_struct\_0~X1))\end{array}
\label{hyp:dgdgedpfngjhdgjgfgmgdhlg}
\end{equation}
\begin{theorem}\label{thm:ehddedpfngjhdgjgfgmgdhlg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}(k2\_dilworth~\\
(k5\_mycielsk~X0)=np\_\_1)\end{array}$$
\end{theorem}
\end{document}
