\documentclass{article}
\newtheorem{axiom}{Axiom}
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\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}
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\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{t28\_ordinal2 (TMaTubw76kxBJ8EUGNJ7Z1WsVVEk82bmayR)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ 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 $ k1\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X2 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\\
\iota .  {\unicdcdadad} X3 .  ((v3\_ordinal1~X3){\unicdcdcdhd}(({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  v3\_ordinal1~\\
(X2~X4~X5)){\unicdcdcdhd}(({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  v3\_ordinal1~(X1~X4~X5)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
v3\_ordinal1~(X0~X4))))){\unicdbdjdcd}(({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(v3\_ordinal1~X5){\unicdbdjdcd}((X5=X0~X4){\unicdbdjded}({\unicdcdaddd} X6 .  ((v5\_ordinal1~X6){\unicdcdcdhd}\\
((v1\_relat\_1~X6){\unicdcdcdhd}((v1\_funct\_1~X6){\unicdcdcdhd}(v1\_ordinal2~X6)))){\unicdcdcdhd}((X5=\\
k1\_ordinal2~X6){\unicdcdcdhd}((k9\_xtuple\_0~X6=k1\_ordinal1~X4){\unicdcdcdhd}((k1\_funct\_1~\\
X6~k1\_xboole\_0=X3){\unicdcdcdhd}(({\unicdcdadad} X7 .  (v3\_ordinal1~X7){\unicdbdjdcd}((k1\_ordinal1~\\
X7 \in k1\_ordinal1~X4){\unicdbdjdcd}(k1\_funct\_1~X6~(k1\_ordinal1~X7)=X2~X7~(k1\_funct\_1~\\
X6~X7)))){\unicdcdcdhd}({\unicdcdadad} X7 .  (v3\_ordinal1~X7){\unicdbdjdcd}(((X7 \in k1\_ordinal1~X4){\unicdcdcdhd}\\
(v4\_ordinal1~X7)){\unicdbdjdcd}((X7=k1\_xboole\_0){\unicdcdcdid}(k1\_funct\_1~X6~X7=X1~X7~\\
(k5\_relat\_1~X6~X7))))))))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}\\
(X0~(k1\_ordinal1~X4)=X2~X4~(X0~X4))))\end{array}
\label{hyp:dhbdfdpfpgchegjgogbgmgcd}
\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}((X2=k10\_ordinal2~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v5\_ordinal1~\\
X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_ordinal2~X3)))){\unicdcdcdhd}\\
((X2=k1\_ordinal2~X3){\unicdcdcdhd}((k9\_xtuple\_0~X3=k1\_ordinal1~X1){\unicdcdcdhd}((k1\_funct\_1~\\
X3~k1\_xboole\_0=X0){\unicdcdcdhd}(({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}((k1\_ordinal1~\\
X4 \in k1\_ordinal1~X1){\unicdbdjdcd}(k1\_funct\_1~X3~(k1\_ordinal1~X4)=k1\_ordinal1~\\
(k1\_funct\_1~X3~X4)))){\unicdcdcdhd}({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}(((X4 \in k1\_ordinal1~\\
X1){\unicdcdcdhd}(v4\_ordinal1~X4)){\unicdbdjdcd}((X4=k1\_xboole\_0){\unicdcdcdid}(k1\_funct\_1~X3~X4=\\
k4\_ordinal2~(k5\_relat\_1~X3~X4)))))))))))))\end{array}
\label{hyp:egbdedpfpgchegjgogbgmgcd}
\end{equation}
\begin{theorem}\label{thm:ehcdidpfpgchegjgogbgmgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(k10\_ordinal2~\\
X0~(k1\_ordinal1~X1)=k1\_ordinal1~(k10\_ordinal2~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
