\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{t45\_ordinal6 (TMQYHU5rNxn1UrD64rEMCrZ4xsmmM7XmkkW)}
\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 $ v2\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v3\_ordinal1~X2){\unicdbdjdcd}(((v2\_ordinal2~X0){\unicdcdcdhd}((r1\_ordinal1~X1~X2){\unicdcdcdhd}(X2 \in \\
k9\_xtuple\_0~X0))){\unicdbdjdcd}(r1\_ordinal1~(k1\_funct\_1~X0~X1)~(k1\_funct\_1~\\
X0~X2)))))\end{array}
\label{hyp:ehjdpfpgchegjgogbgmged}
\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}(v1\_ordinal2~X1)))){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k3\_ordinal6~X1)){\unicdbdjdcd}\\
(r1\_abian~(k1\_funct\_1~(k3\_ordinal6~X1)~X0)~X1))\end{array}
\label{hyp:ehcdjdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(((v2\_ordinal2~\\
X0){\unicdcdcdhd}(X1 \in k9\_xtuple\_0~X0)){\unicdbdjdcd}(r1\_ordinal1~X1~(k1\_funct\_1~X0~X1))))\end{array}
\label{hyp:ehbdadpfpgchegjgogbgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(v3\_ordinal1~\\
(k1\_funct\_1~X0~X1))\end{array}
\label{hyp:ggdgcdpfpgchegjgogbgmgcd}
\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}(v1\_ordinal2~X0)))){\unicdbdjdcd}((v1\_relat\_1~(k3\_ordinal6~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
(k3\_ordinal6~X0)){\unicdcdcdhd}((v5\_ordinal1~(k3\_ordinal6~X0)){\unicdcdcdhd}((v1\_ordinal2~\\
(k3\_ordinal6~X0)){\unicdcdcdhd}(v2\_ordinal2~(k3\_ordinal6~X0))))))\end{array}
\label{hyp:ggdgbdedpfpgchegjgogbgmggd}
\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}(v1\_ordinal2~X0)))){\unicdbdjdcd}((v1\_relat\_1~(k3\_ordinal6~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
(k3\_ordinal6~X0)){\unicdcdcdhd}((v5\_ordinal1~(k3\_ordinal6~X0)){\unicdcdcdhd}(v1\_ordinal2~\\
(k3\_ordinal6~X0)))))\end{array}
\label{hyp:egehpflgddpfpgchegjgogbgmggd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}((v1\_ordinal2~X0){\unicdcdcdhd}(v2\_ordinal6~X0))))){\unicdbdjdcd}((v1\_relat\_1~X0){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_ordinal2~X0){\unicdcdcdhd}((v2\_ordinal2~\\
X0){\unicdcdcdhd}(v3\_ordinal2~X0))))))\end{array}
\label{hyp:dgdgedpfpgchegjgogbgmggd}
\end{equation}
\begin{theorem}\label{thm:ehedfdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}((v2\_ordinal6~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}((X1 \in k9\_xtuple\_0~(k3\_ordinal6~X0)){\unicdbdjdcd}(r1\_ordinal1~(k1\_funct\_1~\\
X0~X1)~(k1\_funct\_1~(k3\_ordinal6~X0)~X1)))))\end{array}$$
\end{theorem}
\end{document}
