\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{t76\_card\_2 (TMbpQ9NW73j4xYDqGBA2YjByjTfTx59SFFW)}
\maketitle
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{({\preoh{{{v1\_finset\_1}~{X0}}}})}{\unicdbdjdcd}{({{{{k1\_card\_2}~{X0}}~{X0}}={X0}})}})}}}\label{hyp:ehhdfdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}((X0 \in X1){\unicdbdjded}\\
((r1\_ordinal1~X0~X1){\unicdcdcdhd}(X0{\unicdcdgdad}X1))))\end{array}
\label{hyp:ehddpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v3\_ordinal1~X2){\unicdbdjdcd}((r1\_ordinal1~X0~X1){\unicdbdjdcd}(r1\_ordinal1~(k10\_ordinal2~\\
X2~X0)~(k10\_ordinal2~X2~X1)))))\end{array}
\label{hyp:ehddddpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_ordinal1~X0~(k10\_ordinal2~X0~X1)){\unicdcdcdhd}(r1\_ordinal1~X1~(k10\_ordinal2~\\
X0~X1))))\end{array}
\label{hyp:ehcdedpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(r1\_ordinal1~(k1\_card\_1~\\
X0)~(k1\_card\_1~X1))\end{array}
\label{hyp:ehbdbdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_ordinal1~X0~X1){\unicdbdjded}(r1\_tarski~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfpgchegjgogbgmgbd}
\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 .  {\unicdcdadad} X1 .  ((v1\_card\_1~X0){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}(v1\_card\_1~\\
(k1\_card\_2~X0~X1))\end{array}
\label{hyp:egehpflgbdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
v3\_ordinal1~(k10\_ordinal2~X0~X1))\end{array}
\label{hyp:egehpflgbdadpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(k1\_card\_2~\\
X0~X1=k1\_card\_1~(k10\_ordinal2~X0~X1)))\end{array}
\label{hyp:egbdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_card\_1~X0){\unicdcdcdhd}(v1\_card\_1~X1)){\unicdbdjdcd}(k1\_card\_2~\\
X0~X1=k1\_card\_2~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdpfdgbgchegpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_card\_1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgbdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdgdpfdgbgchegpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_card\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_card\_1~X1){\unicdbdjdcd}(\preoh (\preoh v1\_finset\_1~\\
X0){\unicdcdcdhd}(((r1\_ordinal1~X1~X0){\unicdcdcdid}(X1 \in X0)){\unicdcdcdhd}(\preoh (k1\_card\_2~X0~X1=X0){\unicdcdcdhd}(\\
k1\_card\_2~X1~X0=X0)))))\end{array}$$
\end{theorem}
\end{document}
