\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{t10\_wellord2 (TMPynDSo3B5Jocjo72BWhrEfhvMWqnzX6dv)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r4\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_wellord2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_wellord1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in X1){\unicdbdjdcd}(X0=k1\_wellord1~(k1\_wellord2~X1)~X0)))\end{array}
\label{hyp:ehjdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(r1\_tarski~(k1\_wellord1~\\
X1~X0)~(k1\_relat\_1~X1))\end{array}
\label{hyp:ehjdpfhhfgmgmgpgchegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_tarski~X1~X0){\unicdbdjdcd}(v2\_wellord1~\\
(k1\_wellord2~X1)))\end{array}
\label{hyp:ehidpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjdcd}(k2\_wellord1~(k1\_wellord2~\\
X1)~X0=k1\_wellord2~X0)\end{array}
\label{hyp:ehhdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v2\_wellord1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \preoh (\\
X1 \in k1\_relat\_1~X0){\unicdcdcdhd}(r4\_wellord1~X0~(k2\_wellord1~X0~(k1\_wellord1~\\
X0~X1)))))\end{array}
\label{hyp:ehedgdpfhhfgmgmgpgchegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((r4\_wellord1~\\
X0~X1){\unicdbdjdcd}(r4\_wellord1~X1~X0)))\end{array}
\label{hyp:ehedadpfhhfgmgmgpgchegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(\preoh X0 \in X1){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdcdcdhd}(\preoh X1 \in X0))))\end{array}
\label{hyp:ehbdedpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k1\_wellord2}~{X0}})}}}\label{hyp:egehpflgbdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((X1=k1\_wellord2~X0){\unicdbdjded}\\
((k1\_relat\_1~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X2 \in X0){\unicdcdcdhd}(X3 \in X0)){\unicdbdjdcd}\\
((k4\_tarski~X2~X3 \in X1){\unicdbdjded}(r1\_tarski~X2~X3)))))\end{array}
\label{hyp:egbdpfhhfgmgmgpgchegcd}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfhhfgmgmgpgchegcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
r4\_wellord1~(k1\_wellord2~X0)~(k1\_wellord2~X1)){\unicdbdjdcd}(X0=X1)))\end{array}$$
\end{theorem}
\end{document}
