\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{t26\_ordinal4 (TMHxX1dtVXLyKdAxscEG6fxBgS8rjxvrtDY)}
\maketitle
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ 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 $ v5\_ordinal1 : {{\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 $ k12\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_ordinal2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_ordinal2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}(((v4\_ordinal1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}(\\
v2\_ordinal2~X0)){\unicdbdjdcd}((k9\_xtuple\_0~X0=k1\_xboole\_0){\unicdcdcdid}((r1\_ordinal2~\\
(k4\_ordinal2~X0)~X0){\unicdcdcdhd}(k8\_ordinal2~X0=k4\_ordinal2~X0))))\end{array}
\label{hyp:ehidpfpgchegjgogbgmged}
\end{equation}
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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_ordinal2~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}(((np\_\_1 \in \\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (v3\_ordinal1~X2){\unicdbdjdcd}((X2 \in k9\_xtuple\_0~X0){\unicdbdjdcd}(k1\_funct\_1~\\
X0~X2=k12\_ordinal2~X1~X2)))){\unicdbdjdcd}(v2\_ordinal2~X0)))\end{array}
\label{hyp:ehcdfdpfpgchegjgogbgmged}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfpgchegjgogbgmged}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v3\_ordinal1~X1){\unicdbdjdcd}((\\
(np\_\_1 \in X0){\unicdcdcdhd}(v4\_ordinal1~X1)){\unicdbdjdcd}((X1=k1\_xboole\_0){\unicdcdcdid}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_ordinal2~\\
X2)))){\unicdbdjdcd}(((k9\_xtuple\_0~X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (v3\_ordinal1~X3){\unicdbdjdcd}\\
((X3 \in X1){\unicdbdjdcd}(k1\_funct\_1~X2~X3=k12\_ordinal2~X0~X3)))){\unicdbdjdcd}(k12\_ordinal2~\\
X0~X1=k4\_ordinal2~X2))))))\end{array}$$
\end{theorem}
\end{document}
