\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{t22\_ordinal4 (TMRtZarq7T7zaoAHpo57dDhtt6ELeKmZr7C)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k12\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_ordinal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
v4\_ordinal1~X0){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X2 .  ((v5\_ordinal1~\\
X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_ordinal2~X2)))){\unicdbdjdcd}\\
(((k9\_xtuple\_0~X2=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}((X3 \in X0){\unicdbdjdcd}\\
(k1\_funct\_1~X2~X3=k12\_ordinal2~X1~X3)))){\unicdbdjdcd}(k12\_ordinal2~X1~X0=\\
k8\_ordinal2~X2))))))\end{array}
\label{hyp:ehedfdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(k12\_ordinal2~\\
X0~(k1\_ordinal1~X1)=k11\_ordinal2~X0~(k12\_ordinal2~X0~X1)))\end{array}
\label{hyp:ehededpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{{k12\_ordinal2}~{X0}}~{k1\_xboole\_0}}={np\_\_1}})}}}\label{hyp:ehedddpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(k11\_ordinal2~X0~X1=k1\_xboole\_0){\unicdcdcdhd}((X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(X1{\unicdcdgdad}k1\_xboole\_0))))\end{array}
\label{hyp:ehddbdpfpgchegjgogbgmgdd}
\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 : \iota{\unicdbdjdcd}o .  ((X0~k1\_xboole\_0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}((X0~X1){\unicdbdjdcd}(X0~(k1\_ordinal1~X1)))){\unicdcdcdhd}({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}(((v4\_ordinal1~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}((X2 \in X1){\unicdbdjdcd}\\
(X0~X2)))){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}(X0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}(X0~X1))\end{array}
\label{hyp:dhbdpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\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){\unicdbdjded}(r1\_tarski~X0~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(X1{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}((v4\_ordinal1~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_ordinal2~X2)))){\unicdbdjdcd}\\
(\preoh (k9\_xtuple\_0~X2=X1){\unicdcdcdhd}(({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}\\
(k1\_funct\_1~X2~X3=k12\_ordinal2~X0~X3))){\unicdcdcdhd}({\unicdcdaddd} X3 .  (v3\_ordinal1~\\
X3){\unicdcdcdhd}(r1\_ordinal2~X3~X2))))))))\end{array}
\label{hyp:mgcdjdpfpgchegjgogbgmged}
\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 .  {\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 .  (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}
{{k1\_xboole\_0}={{the}~{({{\uniddcgcg} X0 : {\iota} .  {{v1\_xboole\_0}~{X0}}})}}}\label{hyp:egcdpfihcgpgpgmgfgpfad}
\end{equation}
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}(({\unicdcdaddd} X1 .  (v3\_ordinal1~X1){\unicdcdcdhd}(r1\_ordinal2~\\
X1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((X1=k8\_ordinal2~X0){\unicdbdjded}(\\
r1\_ordinal2~X1~X0))))\end{array}
\label{hyp:egbdadpfpgchegjgogbgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X0}})}}}\label{hyp:dgdgddpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpfpgchegjgogbgmged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(X0{\unicdcdgdad}k1\_xboole\_0){\unicdcdcdhd}(k12\_ordinal2~X0~X1=k1\_xboole\_0)))\end{array}$$
\end{theorem}
\end{document}
