\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{t49\_ordinal6 (TMRBb4ZP1qUKcX9WVBAp7haghR1y62hxjSU)}
\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 $ v3\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_ordinal6 : {{\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 $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}}}}\label{hyp:ehfdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}(v3\_ordinal6~X1)))){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k7\_ordinal6~X1)){\unicdbdjdcd}\\
(r1\_tarski~X0~(k1\_funct\_1~(k7\_ordinal6~X1)~X0)))\end{array}
\label{hyp:ehedidpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v3\_ordinal6~\\
X2)))){\unicdbdjdcd}(((X0 \in k9\_xtuple\_0~X2){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~(k7\_ordinal6~\\
X2))){\unicdbdjdcd}(r1\_abian~(k1\_funct\_1~(k7\_ordinal6~X2)~X1)~(k1\_funct\_1~\\
X2~X0)))))\end{array}
\label{hyp:ehedhdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_ordinal6}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {{({{X1} \in {X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X1}})}}})}}}\label{hyp:ehbdpfpgchegjgogbgmggd}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}(v3\_ordinal6~X0)))){\unicdbdjdcd}((v1\_relat\_1~(k7\_ordinal6~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
(k7\_ordinal6~X0)){\unicdcdcdhd}((v5\_ordinal1~(k7\_ordinal6~X0)){\unicdcdcdhd}(v1\_ordinal2~\\
(k7\_ordinal6~X0)))))\end{array}
\label{hyp:egehpflghdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v5\_ordinal1}~{X0}})}{\unicdbdjded}{({{v3\_ordinal1}~{({{k9\_xtuple\_0}~{X0}})}})}}}\label{hyp:eghdpfpgchegjgogbgmgbd}
\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){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((r1\_abian~\\
X0~X1){\unicdbdjded}((X0 \in k9\_xtuple\_0~X1){\unicdcdcdhd}(X0=k1\_funct\_1~X1~X0)))\end{array}
\label{hyp:egddpfbgcgjgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_ordinal6}~{X0}})}}}\label{hyp:dgdgbdpfpgchegjgogbgmggd}
\end{equation}
\begin{theorem}\label{thm:ehedjdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v3\_ordinal6~X1)))){\unicdbdjdcd}((X0 \in k10\_xtuple\_0~\\
X1){\unicdbdjdcd}(r1\_ordinal1~(k9\_xtuple\_0~(k7\_ordinal6~X1))~(k9\_xtuple\_0~\\
X0))))\end{array}$$
\end{theorem}
\end{document}
