\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}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t21\_ordinal6 (TMTbVSTJoSroW7M5ynVsGWPSNdRJ7RM1j3v)}
\maketitle
Let $ r3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_wellord2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r4\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_wellord1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_wellord1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_wellord2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}((r4\_wellord1~\\
X0~X1){\unicdbdjdcd}(r4\_wellord1~X1~X0)))\end{array}
\label{hyp:ehedadpfhhfgmgmgpgchegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_ordinal6~X0){\unicdbdjdcd}((v1\_relat\_1~(k1\_wellord2~X0)){\unicdcdcdhd}\\
(v2\_wellord1~(k1\_wellord2~X0)))\end{array}
\label{hyp:ggdgidpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_ordinal6}~{({{k2\_ordinal1}~{X0}})}}}\label{hyp:ggdgbdpfpgchegjgogbgmggd}
\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))))\end{array}
\label{hyp:egehpflgcdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_relat\_1}~{({{k1\_wellord2}~{X0}})}}}\label{hyp:egehpflgbdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v3\_ordinal1}~{({{k1\_ordinal6}~{X0}})}}}\label{hyp:egehpflgbdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_relat\_1~X1){\unicdbdjdcd}(((v2\_wellord1~\\
X0){\unicdcdcdhd}(r4\_wellord1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((X2=k3\_wellord1~X0~X1){\unicdbdjded}(r3\_wellord1~X0~X1~X2)))))\end{array}
\label{hyp:egjdpfhhfgmgmgpgchegbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}((v2\_wellord1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~\\
X1){\unicdbdjdcd}((X1=k2\_wellord2~X0){\unicdbdjded}(r4\_wellord1~X0~(k1\_wellord2~X1)))))\end{array}
\label{hyp:egcdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v3\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_ordinal6}~{X0}})}}}\label{hyp:dgdgbdpfpgchegjgogbgmggd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  r3\_wellord1~(k1\_wellord2~(k1\_ordinal6~X0))~(k1\_wellord2~\\
(k2\_ordinal1~X0))~(k2\_ordinal6~X0)\end{array}$$
\end{theorem}
\end{document}
