\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{t27\_ordinal4 (TMFJFZvqF7LYGttzBuQQgnzrjqJTHgcZvFX)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k12\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {{k1\_ordinal1}~{X1}}})}{\unicdbdjded}{({{({{X0} \in {X1}})}{\unicdcdcdid}{({{X0}={X1}})}})}}}}\label{hyp:ehidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{X0} \in {{k1\_ordinal1}~{X0}}}}\label{hyp:ehgdpfpgchegjgogbgmgbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v3\_ordinal1~X2){\unicdbdjdcd}(((np\_\_1 \in X0){\unicdcdcdhd}(X1 \in X2)){\unicdbdjdcd}(k12\_ordinal2~X0~X1 \in \\
k12\_ordinal2~X0~X2))))\end{array}
\label{hyp:ehcdedpfpgchegjgogbgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in k1\_ordinal1~X1){\unicdbdjded}(r1\_ordinal1~X0~X1)))\end{array}
\label{hyp:ehcdcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}(\preoh (r1\_ordinal1~X0~np\_\_1){\unicdcdcdhd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}\\
(X0{\unicdcdgdad}np\_\_1)))\end{array}
\label{hyp:ehbdgdpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{v3\_ordinal1}~{X1}})}{\unicdbdjdcd}{({{({{X0} \in {X1}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}})}}}}\label{hyp:ehbdddpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{np\_\_1}={{k1\_ordinal1}~{k1\_xboole\_0}}}\label{hyp:mgbdedpfpgchegjgogbgmgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k1\_ordinal1~X0)){\unicdcdcdhd}\\
(v3\_ordinal1~(k1\_ordinal1~X0)))\end{array}
\label{hyp:ggdgcdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
v3\_ordinal1~(k12\_ordinal2~X0~X1))\end{array}
\label{hyp:egehpflgbdcdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v3\_ordinal1~X1)){\unicdbdjdcd}(\\
(r1\_ordinal1~X0~X1){\unicdcdcdid}(r1\_ordinal1~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdhdpfpgchegjgogbgmged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v3\_ordinal1~X2){\unicdbdjdcd}((r1\_ordinal1~X1~X2){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}(r1\_ordinal1~\\
(k12\_ordinal2~X0~X1)~(k12\_ordinal2~X0~X2))))))\end{array}$$
\end{theorem}
\end{document}
