\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{t15\_ordinal5 (TMHS2qyB4rYDs3SwiuBTEvR7oKPfBf7bCps)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\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 $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_ordinal5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k12\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 : \iota{\unicdbdjdcd}\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X3 : \iota{\unicdbdjdcd}\\
\iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 : \iota{\unicdbdjdcd}\iota .  (({\unicdcdadad} X6 .  (v3\_ordinal1~\\
X6){\unicdbdjdcd}({\unicdcdadad} X7 .  (v3\_ordinal1~X7){\unicdbdjdcd}((X7=X5~X6){\unicdbdjded}({\unicdcdaddd} X8 .  ((\\
v5\_ordinal1~X8){\unicdcdcdhd}((v1\_relat\_1~X8){\unicdcdcdhd}((v1\_funct\_1~X8){\unicdcdcdhd}(v1\_ordinal2~\\
X8)))){\unicdcdcdhd}((X7=k1\_ordinal2~X8){\unicdcdcdhd}((k9\_xtuple\_0~X8=k1\_ordinal1~X6){\unicdcdcdhd}\\
((k1\_funct\_1~X8~k1\_xboole\_0=X4){\unicdcdcdhd}(({\unicdcdadad} X9 .  (v3\_ordinal1~X9){\unicdbdjdcd}\\
((k1\_ordinal1~X9 \in k1\_ordinal1~X6){\unicdbdjdcd}(k1\_funct\_1~X8~(k1\_ordinal1~\\
X9)=X3~X9~(k1\_funct\_1~X8~X9)))){\unicdcdcdhd}({\unicdcdadad} X9 .  (v3\_ordinal1~X9){\unicdbdjdcd}\\
(((X9 \in k1\_ordinal1~X6){\unicdcdcdhd}(v4\_ordinal1~X9)){\unicdbdjdcd}((X9=k1\_xboole\_0){\unicdcdcdid}\\
(k1\_funct\_1~X8~X9=X2~X9~(k5\_relat\_1~X8~X9))))))))))))){\unicdcdcdhd}(((X1{\unicdcdgdad}\\
k1\_xboole\_0){\unicdcdcdhd}(v4\_ordinal1~X1)){\unicdcdcdhd}((k9\_xtuple\_0~X0=X1){\unicdcdcdhd}({\unicdcdadad} X6 .  \\
(v3\_ordinal1~X6){\unicdbdjdcd}((X6 \in X1){\unicdbdjdcd}(k1\_funct\_1~X0~X6=X5~X6)))))){\unicdbdjdcd}(X5~\\
X1=X2~X1~X0)\end{array}
\label{hyp:dhbdgdpfpgchegjgogbgmgcd}
\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=k1\_ordinal5~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  ((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v5\_ordinal1~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=np\_\_1){\unicdcdcdhd}(({\unicdcdadad} X4 .  (v3\_ordinal1~X4){\unicdbdjdcd}((k1\_ordinal1~\\
X4 \in k1\_ordinal1~X1){\unicdbdjdcd}(k1\_funct\_1~X3~(k1\_ordinal1~X4)=k12\_ordinal2~\\
X0~(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=k8\_ordinal2~(k5\_relat\_1~X3~X4)))))))))))))\end{array}
\label{hyp:egedpfpgchegjgogbgmgfd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfpgchegjgogbgmgfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
v4\_ordinal1~X0){\unicdbdjdcd}((X0=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_ordinal2~X2)))){\unicdbdjdcd}\\
(((k9\_xtuple\_0~X2=X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}((X3 \in X0){\unicdbdjdcd}\\
(k1\_funct\_1~X2~X3=k1\_ordinal5~X1~X3)))){\unicdbdjdcd}(k1\_ordinal5~X1~X0=k8\_ordinal2~\\
X2))))))\end{array}$$
\end{theorem}
\end{document}
