\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{t47\_ordinal2 (TMVRzky67eEzdS8NHgN2uPDuYUiX5GWwWXm)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{X0} \in {{k1\_ordinal1}~{X0}}}}\label{hyp:ehgdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((\preoh (\preoh v4\_ordinal1~X0){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(v3\_ordinal1~X1){\unicdbdjdcd}(X0{\unicdcdgdad}k1\_ordinal1~X1))){\unicdcdcdhd}(\preoh ({\unicdcdaddd} X1 .  (v3\_ordinal1~\\
X1){\unicdcdcdhd}(X0=k1\_ordinal1~X1)){\unicdcdcdhd}(v4\_ordinal1~X0)))\end{array}
\label{hyp:ehcdjdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(k10\_ordinal2~\\
X0~(k1\_ordinal1~X1)=k1\_ordinal1~(k10\_ordinal2~X0~X1)))\end{array}
\label{hyp:ehcdidpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{{k10\_ordinal2}~{X0}}~{k1\_xboole\_0}}={X0}})}}}\label{hyp:ehcdhdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}o .  ({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(({\unicdcdadad} X2 .  \\
(v3\_ordinal1~X2){\unicdbdjdcd}((X2 \in X1){\unicdbdjdcd}(X0~X2))){\unicdbdjdcd}(X0~X1))){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
v3\_ordinal1~X1){\unicdbdjdcd}(X0~X1))\end{array}
\label{hyp:dhcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}(v7\_ordinal1~\\
(k1\_ordinal1~X0))\end{array}
\label{hyp:ggdghdpfpgchegjgogbgmgbd}
\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}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdggdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehedhdpfpgchegjgogbgmgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdaddd} X1 .  (v3\_ordinal1~X1){\unicdcdcdhd}({\unicdcdaddd} X2 .  \\
(v3\_ordinal1~X2){\unicdcdcdhd}((v4\_ordinal1~X1){\unicdcdcdhd}((v7\_ordinal1~X2){\unicdcdcdhd}(X0=k10\_ordinal2~\\
X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
