\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{t24\_ordinal2 (TMa7ippZghq9SL7WuUgraHjUozsMVhmr5t7)}
\maketitle
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{r1\_tarski}~{({{k1\_setfam\_1}~{X1}})}}~{X0}})}}}}\label{hyp:ehddpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdaddd} X1 .  (X1 \in X0){\unicdcdcdhd}(r1\_xboole\_0~\\
X1~X0))\end{array}
\label{hyp:ehbdpfihchfghgfhmgbgch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X0 \in X1){\unicdbdjdcd}(X0 \in k3\_ordinal2~\\
X1))\end{array}
\label{hyp:ehbdjdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X0 \in X1){\unicdbdjdcd}(k2\_ordinal2~\\
X1 \in X1))\end{array}
\label{hyp:ehbdhdpfpgchegjgogbgmgcd}
\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~X1){\unicdcdcdid}(X1 \in X0)))\end{array}
\label{hyp:ehbdgdpfpgchegjgogbgmgbd}
\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 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:mgbdddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v3\_ordinal1}~{({{k3\_ordinal2}~{X0}})}}}\label{hyp:egehpflgddpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v3\_ordinal1}~{({{k2\_ordinal2}~{X0}})}}}\label{hyp:egehpflgcdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k2\_ordinal1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
((X2 \in X0){\unicdcdcdhd}(v3\_ordinal1~X2)))\end{array}
\label{hyp:egjdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_ordinal2}~{X0}}={{k1\_setfam\_1}~{({{k2\_ordinal1}~{X0}})}}}}\label{hyp:egcdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((X1=k1\_setfam\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}(X2 \in X3))))){\unicdcdcdhd}((X0=\\
k1\_xboole\_0){\unicdbdjdcd}((X1=k1\_setfam\_1~X0){\unicdbdjded}(X1=k1\_xboole\_0)))\end{array}
\label{hyp:egbdpfdhfgehggbgngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({\preoh{{{X1} \in {X0}}}})}}}}\label{hyp:bgogehjgdhjhngngfgehchjhpfchcdpfigjgegegfgog}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfpgchegjgogbgmgcd}
${{\unicdcdadad} X0 .  {{{r1\_ordinal1}~{({{k2\_ordinal2}~{X0}})}}~{({{k3\_ordinal2}~{X0}})}}}$.
\end{theorem}
\end{document}
