\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{l13\_ordinal1 (TMGNt2y9yTcexbkEmJRVGtnprLwRK23CwDp)}
\maketitle
Let $ v1\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v2\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v2\_ordinal1~X0){\unicdbdjded}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \preoh (X1 \in X0){\unicdcdcdhd}\\
((X2 \in X0){\unicdcdcdhd}((\preoh X1 \in X2){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(\preoh X2 \in X1)))))\end{array}
\label{hyp:egddpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_ordinal1}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {{({{X1} \in {X0}})}{\unicdbdjdcd}{({{{r1\_tarski}~{X1}}~{X0}})}}})}}}\label{hyp:egcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdddpfpgchegjgogbgmgbd}
${{({{v1\_ordinal1}~{k1\_xboole\_0}})}{\unicdcdcdhd}{({{v2\_ordinal1}~{k1\_xboole\_0}})}}$.
\end{theorem}
\end{document}
