\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{t42\_card\_2 (TMVy4Xc1W4u8jj5hUtMWwN1o4bwaa8jQuU5)}
\maketitle
Let $ k1\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_card\_1}~{({{k1\_tarski}~{X0}})}}={np\_\_1}}}\label{hyp:ehddadpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (k1\_card\_1~X0=k1\_card\_1~(k1\_tarski~X1)){\unicdbdjded}\\
({\unicdcdaddd} X2 .  X0=k1\_tarski~X2)\end{array}
\label{hyp:ehcdjdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfdgbgchegpfcd}
${{\unicdcdadad} X0 .  {{({{{k1\_card\_1}~{X0}}={np\_\_1}})}{\unicdbdjded}{({{\unicdcdaddd} X1 .  {{X0}={{k1\_tarski}~{X1}}}})}}}$.
\end{theorem}
\end{document}
