\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{t35\_mycielsk (TMaXxCBtasxESuZtQgp9tiq51Y2o7qsKWVx)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_mycielsk : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_mycielsk : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_dilworth : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_dilworth : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_mycielsk : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_mycielsk : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
k1\_card\_1~X0=k1\_card\_1~X1){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehedadpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k1\_dilworth}~{({{k5\_mycielsk}~{X0}})}}={X0}})}}}\label{hyp:ehddddpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_dilworth~X0){\unicdcdcdhd}((v1\_mycielsk~X0){\unicdcdcdhd}(l1\_orders\_2~\\
X0))){\unicdbdjdcd}(r1\_xxreal\_0~(k1\_dilworth~X0)~(k2\_mycielsk~X0))\end{array}
\label{hyp:ehbdfdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v8\_struct\_0~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}(r1\_xxreal\_0~\\
(k2\_mycielsk~X0)~(k5\_card\_1~(u1\_struct\_0~X0)))\end{array}
\label{hyp:ehbdddpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{k5\_card\_1}~{X0}}={{k1\_card\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_card\_1}~{({{k1\_card\_1}~{X0}})}}={{k1\_card\_1}~{X0}}}}\label{hyp:ahchpgkgfgdgehjgghjgehjhpflgbdpfdgbgchegpfbd}
\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 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{m1\_mycielsk}~{({{k5\_mycielsk}~{X0}})}}~{X0}})}}}\label{hyp:egehpflgfdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_finset\_1}~{X0}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{({{k5\_card\_1}~{X0}})}}~{k4\_ordinal1}})}}}\label{hyp:egehpflgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_mycielsk~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}(v7\_ordinal1~\\
(k2\_mycielsk~X0))\end{array}
\label{hyp:egehpflgcdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_orders\_2~X1){\unicdcdcdhd}(\\
l1\_orders\_2~X1)){\unicdbdjdcd}((m1\_mycielsk~X1~X0){\unicdbdjded}(u1\_struct\_0~X1=X0)))\end{array}
\label{hyp:eghdpfngjhdgjgfgmgdhlg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\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}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_finset\_1}~{X0}})}}}\label{hyp:dgdgfdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v8\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{v3\_dilworth}~{X0}})}})}}}\label{hyp:dgdgedpfegjgmghhpgchehig}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_orders\_2}~{X0}})}{\unicdbdjdcd}{({{({{v8\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_mycielsk}~{X0}})}})}}}\label{hyp:dgdgbdpfngjhdgjgfgmgdhlg}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfngjhdgjgfgmgdhlg}
${{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k2\_mycielsk}~{({{k5\_mycielsk}~{X0}})}}={X0}})}}}$.
\end{theorem}
\end{document}
