\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}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t6\_ordinal6 (TMKiw7K4dF1bLB96JhtETVeGutag2qPwubr)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_wellord2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdbdjdcd}((r3\_wellord1~X0~X1~X2){\unicdbdjded}((\\
k9\_xtuple\_0~X2=k1\_relat\_1~X0){\unicdcdcdhd}((k10\_xtuple\_0~X2=k1\_relat\_1~\\
X1){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (k4\_tarski~X3~X4 \in \\
X0){\unicdbdjded}((X3 \in k1\_relat\_1~X0){\unicdcdcdhd}((X4 \in k1\_relat\_1~X0){\unicdcdcdhd}(k4\_tarski~(k1\_funct\_1~\\
X2~X3)~(k1\_funct\_1~X2~X4) \in X1))))))))))\end{array}
\label{hyp:eghdpfhhfgmgmgpgchegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=\\
k10\_xtuple\_0~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  (X3 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(X2=k1\_funct\_1~X0~X3))))\end{array}
\label{hyp:egddpfggfhogdgehpfbd}
\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:ehgdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((r3\_wellord1~(k1\_wellord2~X0)~(k1\_wellord2~X1)~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
{\unicdcdadad} X4 .  ((X3 \in X0){\unicdcdcdhd}(X4 \in X0)){\unicdbdjdcd}((r1\_tarski~X3~X4){\unicdbdjded}(r1\_tarski~\\
(k1\_funct\_1~X2~X3)~(k1\_funct\_1~X2~X4)))))\end{array}$$
\end{theorem}
\end{document}
