\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{l79\_ordinal6 (TMU6hXnudLn5eqS4t9HCPrzxiao4sUvfuW5)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_classes1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_wellord2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_wellord2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k6\_ordinal6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v2\_classes1~X1){\unicdcdcdhd}(\\
X0 \in X1)){\unicdbdjdcd}((k1\_ordinal1~X0 \in X1){\unicdcdcdhd}(r1\_tarski~X0~X1)))\end{array}
\label{hyp:ehfdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_ordinal1~X0)~(k2\_ordinal1~\\
X0)){\unicdcdcdhd}((v2\_ordinal6~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_ordinal1~X0)~(k2\_ordinal1~X0))))))){\unicdbdjdcd}((k4\_ordinal1 \in X0){\unicdbdjdcd}\\
((v1\_funct\_1~(k3\_ordinal6~X1)){\unicdcdcdhd}((v1\_funct\_2~(k3\_ordinal6~X1)~\\
(k2\_ordinal1~X0)~(k2\_ordinal1~X0)){\unicdcdcdhd}(m1\_subset\_1~(k3\_ordinal6~\\
X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~X0)~(k2\_ordinal1~X0))))))))\end{array}
\label{hyp:ehededpfpgchegjgogbgmggd}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_ordinal6~\\
X0))){\unicdbdjdcd}((v1\_relat\_1~(k1\_funct\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_funct\_1~\\
X0~X1)))\end{array}
\label{hyp:ggdgcdbdpfpgchegjgogbgmggd}
\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~(k3\_ordinal6~\\
X0)){\unicdcdcdhd}((v1\_funct\_1~(k3\_ordinal6~X0)){\unicdcdcdhd}((v5\_ordinal1~(k3\_ordinal6~\\
X0)){\unicdcdcdhd}((v1\_ordinal2~(k3\_ordinal6~X0)){\unicdcdcdhd}(v3\_ordinal2~(k3\_ordinal6~\\
X0))))))\end{array}
\label{hyp:ggdgbdfdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k2\_ordinal6~X0)){\unicdcdcdhd}((v1\_funct\_1~(k2\_ordinal6~\\
X0)){\unicdcdcdhd}((v5\_ordinal1~(k2\_ordinal6~X0)){\unicdcdcdhd}((v1\_ordinal2~(k2\_ordinal6~\\
X0)){\unicdcdcdhd}(v2\_ordinal2~(k2\_ordinal6~X0)))))\end{array}
\label{hyp:ggdgbdbdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k11\_ordinal6~X0)){\unicdcdcdhd}((v1\_funct\_1~(k11\_ordinal6~X0)){\unicdcdcdhd}((v5\_ordinal1~\\
(k11\_ordinal6~X0)){\unicdcdcdhd}(v3\_ordinal6~(k11\_ordinal6~X0)))))\end{array}
\label{hyp:egehpflgbdbdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k2\_ordinal1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
((X2 \in X0){\unicdcdcdhd}(v3\_ordinal1~X2)))\end{array}
\label{hyp:egjdpfpgchegjgogbgmgbd}
\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}(k3\_ordinal6~X0=k2\_ordinal6~(ReplSep~\\
(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k9\_xtuple\_0~X0)))~({\uniddcgcg} X1 : \\
\iota .  r1\_abian~X1~X0)~({\uniddcgcg} X1 : \iota .  X1)))\end{array}
\label{hyp:eghdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  k2\_ordinal6~X0=k3\_wellord1~(k1\_wellord2~(k1\_ordinal6~\\
X0))~(k1\_wellord2~(k2\_ordinal1~X0))\end{array}
\label{hyp:eggdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_ordinal6}~{X0}}={{k2\_wellord2}~{({{k1\_wellord2}~{({{k2\_ordinal1}~{X0}})}})}}}}\label{hyp:egedpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k1\_ordinal1}~{X0}}={{{k2\_xboole\_0}~{X0}}~{({{k1\_tarski}~{X0}})}}}}\label{hyp:egbdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v3\_ordinal6~\\
X1)))){\unicdbdjdcd}((X1=k11\_ordinal6~X0){\unicdbdjded}((k9\_xtuple\_0~X1=k2\_ordinal1~\\
X0){\unicdcdcdhd}((k1\_funct\_1~X1~k6\_numbers=k6\_ordinal6~X0~k4\_ordinal1){\unicdcdcdhd}\\
(({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}((k1\_ordinal1~X2 \in k2\_ordinal1~\\
X0){\unicdbdjdcd}(k1\_funct\_1~X1~(k1\_ordinal1~X2)=k3\_ordinal6~(k1\_funct\_1~\\
X1~X2)))){\unicdcdcdhd}({\unicdcdadad} X2 .  ((v3\_ordinal1~X2){\unicdcdcdhd}((v4\_ordinal1~X2){\unicdcdcdhd}(\\
\preoh v1\_xboole\_0~X2))){\unicdbdjdcd}((X2 \in k2\_ordinal1~X0){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k7\_ordinal6~\\
(k5\_relat\_1~X1~X2)))))))))\end{array}
\label{hyp:egbdfdpfpgchegjgogbgmggd}
\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\_ordinal2~X0){\unicdcdcdhd}(v3\_ordinal2~X0)))))){\unicdbdjdcd}\\
((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_ordinal2~\\
X0){\unicdcdcdhd}(v2\_ordinal6~X0)))))\end{array}
\label{hyp:dgdgfdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_classes2}~{X0}})}{\unicdbdjdcd}{({{({{v1\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v2\_classes1}~{X0}})}})}}}\label{hyp:dgdgcdpfdgmgbgdhdhfgdhcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~X0)~(k2\_ordinal1~\\
X0)))){\unicdbdjdcd}(((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_funct\_2~X1~(k2\_ordinal1~X0)~(k2\_ordinal1~\\
X0))){\unicdbdjdcd}((v5\_ordinal1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_ordinal1~\\
X0)~(k2\_ordinal1~X0)){\unicdcdcdhd}(v1\_ordinal2~X1))))))\end{array}
\label{hyp:dgdgbdpfpgchegjgogbgmged}
\end{equation}
\begin{theorem}\label{thm:mghdjdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(v1\_classes2~X1)){\unicdbdjdcd}(((k4\_ordinal1 \in X1){\unicdcdcdhd}((X0 \in X1){\unicdcdcdhd}((v1\_funct\_1~\\
(k1\_funct\_1~(k11\_ordinal6~X1)~X0)){\unicdcdcdhd}((v1\_funct\_2~(k1\_funct\_1~\\
(k11\_ordinal6~X1)~X0)~(k2\_ordinal1~X1)~(k2\_ordinal1~X1)){\unicdcdcdhd}((v2\_ordinal6~\\
(k1\_funct\_1~(k11\_ordinal6~X1)~X0)){\unicdcdcdhd}(m1\_subset\_1~(k1\_funct\_1~\\
(k11\_ordinal6~X1)~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_ordinal1~\\
X1)~(k2\_ordinal1~X1))))))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_funct\_1~(k11\_ordinal6~\\
X1)~(k1\_ordinal1~X0))){\unicdcdcdhd}((v1\_funct\_2~(k1\_funct\_1~(k11\_ordinal6~\\
X1)~(k1\_ordinal1~X0))~(k2\_ordinal1~X1)~(k2\_ordinal1~X1)){\unicdcdcdhd}((v2\_ordinal6~\\
(k1\_funct\_1~(k11\_ordinal6~X1)~(k1\_ordinal1~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_funct\_1~(k11\_ordinal6~X1)~(k1\_ordinal1~X0))~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_ordinal1~X1)~(k2\_ordinal1~X1)))))))))\end{array}$$
\end{theorem}
\end{document}
