\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{t43\_ordinal3 (TMXV81D36Va431Q8xJq5PHnPmFoWXsNW84W)}
\maketitle
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_ordinal1~X1){\unicdcdcdhd}((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_ordinal2~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v3\_ordinal1~\\
X2){\unicdbdjdcd}(((k9\_xtuple\_0~X0=k9\_xtuple\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~\\
X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}(((X3 \in k9\_xtuple\_0~X0){\unicdcdcdhd}(X4=\\
k1\_funct\_1~X0~X3)){\unicdbdjdcd}(k1\_funct\_1~X1~X3=k10\_ordinal2~X2~X4))))){\unicdbdjdcd}\\
((k1\_xboole\_0=k9\_xtuple\_0~X0){\unicdcdcdid}(k4\_ordinal2~X1=k10\_ordinal2~\\
X2~(k4\_ordinal2~X0))))))\end{array}
\label{hyp:ehddjdpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_ordinal2~X1))))){\unicdbdjdcd}((v5\_ordinal1~\\
(k1\_ordinal3~X0~X1)){\unicdcdcdhd}((v1\_relat\_1~(k1\_ordinal3~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~\\
(k1\_ordinal3~X0~X1)){\unicdcdcdhd}(v1\_ordinal2~(k1\_ordinal3~X0~X1)))))\end{array}
\label{hyp:egehpflgbdpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v5\_ordinal1~X1){\unicdcdcdhd}(\\
(v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_ordinal2~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v5\_ordinal1~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_ordinal2~\\
X2)))){\unicdbdjdcd}((X2=k1\_ordinal3~X0~X1){\unicdbdjded}((k9\_xtuple\_0~X2=k9\_xtuple\_0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}((X3 \in k9\_xtuple\_0~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X2~X3=k10\_ordinal2~X0~(k1\_funct\_1~X1~X3))))))))\end{array}
\label{hyp:egbdpfpgchegjgogbgmgdd}
\end{equation}
\begin{theorem}\label{thm:ehedddpfpgchegjgogbgmgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((k1\_xboole\_0{\unicdcdgdad}\\
k9\_xtuple\_0~X0){\unicdbdjdcd}(k4\_ordinal2~(k1\_ordinal3~X1~X0)=k10\_ordinal2~\\
X1~(k4\_ordinal2~X0))))\end{array}$$
\end{theorem}
\end{document}
