\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{l28\_ordinal4 (TMN6jMkR3cqSwfdGtbFEZD8u2m1RAfxCFZF)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{X0}{\unicdcdgdad}{k1\_xboole\_0}})}{\unicdbdjdcd}{({{k1\_xboole\_0} \in {X0}})}})}}}\label{hyp:ehidpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((k12\_ordinal2~X0~np\_\_1=X0){\unicdcdcdhd}(k12\_ordinal2~\\
np\_\_1~X0=np\_\_1))\end{array}
\label{hyp:ehedgdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\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}
{{v1\_xboole\_0}~{k1\_xboole\_0}}\label{hyp:ggdgbdpfihcgpgpgmgfgpfad}
\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}(((X0=\\
k1\_xboole\_0){\unicdbdjdcd}((r1\_ordinal2~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  (v3\_ordinal1~\\
X2){\unicdcdcdhd}((X2 \in k9\_xtuple\_0~X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}(((r1\_ordinal1~\\
X2~X3){\unicdcdcdhd}(X3 \in k9\_xtuple\_0~X1)){\unicdbdjdcd}(k1\_funct\_1~X1~X3=k1\_xboole\_0))))))){\unicdcdcdhd}\\
((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}((r1\_ordinal2~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (v3\_ordinal1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}(\preoh (X2 \in X0){\unicdcdcdhd}((X0 \in X3){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(v3\_ordinal1~X4){\unicdbdjdcd}(\preoh (X4 \in k9\_xtuple\_0~X1){\unicdcdcdhd}({\unicdcdadad} X5 .  (v3\_ordinal1~\\
X5){\unicdbdjdcd}(((r1\_ordinal1~X4~X5){\unicdcdcdhd}(X5 \in k9\_xtuple\_0~X1)){\unicdbdjdcd}((X2 \in k1\_funct\_1~\\
X1~X5){\unicdcdcdhd}(k1\_funct\_1~X1~X5 \in X3))))))))))))))\end{array}
\label{hyp:egjdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v3\_ordinal1~X1))\end{array}
\label{hyp:dgdgfdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:mgcdidpfpgchegjgogbgmged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_ordinal2~\\
X1)))){\unicdbdjdcd}(((k9\_xtuple\_0~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}\\
((X2 \in X0){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k12\_ordinal2~np\_\_1~X2)))){\unicdbdjdcd}(r1\_ordinal2~\\
np\_\_1~X1))))\end{array}$$
\end{theorem}
\end{document}
