\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{t22\_ordinal6 (TMbdEsTa4Ky6fbz4Rr6tF2ecvnSF36UmYN7)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\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 $ r3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_wellord2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\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}
\label{hyp:ehgdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  r3\_wellord1~(k1\_wellord2~(k1\_ordinal6~X0))~(k1\_wellord2~\\
(k2\_ordinal1~X0))~(k2\_ordinal6~X0)\end{array}
\label{hyp:ehcdbdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (k9\_xtuple\_0~(k2\_ordinal6~X0)=k1\_ordinal6~X0){\unicdcdcdhd}(k10\_xtuple\_0~\\
(k2\_ordinal6~X0)=k2\_ordinal1~X0)\end{array}
\label{hyp:ehbdidpfpgchegjgogbgmggd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_ordinal1~X3){\unicdcdcdhd}(v1\_ordinal2~X3)))){\unicdbdjdcd}(((\\
X3=k2\_ordinal6~X0){\unicdcdcdhd}((X1 \in k9\_xtuple\_0~X3){\unicdcdcdhd}(X2 \in k9\_xtuple\_0~X3))){\unicdbdjdcd}\\
((r1\_tarski~X1~X2){\unicdbdjded}(r1\_tarski~(k1\_funct\_1~X3~X1)~(k1\_funct\_1~X3~\\
X2))))\end{array}$$
\end{theorem}
\end{document}
