\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{t29\_ordinal6 (TMZLdHAT8U1HXyMuqCQniHom1VVJM1Y6EBd)}
\maketitle
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 $ k3\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
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}(k2\_ordinal1~(ReplSep~(toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~(k9\_xtuple\_0~X0)))~({\uniddcgcg} X1 : \iota .  r1\_abian~X1~\\
X0)~({\uniddcgcg} X1 : \iota .  X1))=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:ehcdidpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (k9\_xtuple\_0~(k2\_ordinal6~X0)=k1\_ordinal6~X0){\unicdcdcdhd}(k10\_xtuple\_0~\\
(k2\_ordinal6~X0)=k2\_ordinal1~X0)\end{array}
\label{hyp:ehbdidpfpgchegjgogbgmggd}
\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}
\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 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1=\\
k10\_xtuple\_0~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}({\unicdcdaddd} X3 .  (X3 \in k9\_xtuple\_0~\\
X0){\unicdcdcdhd}(X2=k1\_funct\_1~X0~X3))))\end{array}
\label{hyp:egddpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}(v1\_ordinal2~X1)))){\unicdbdjdcd}((X0 \in k9\_xtuple\_0~(k3\_ordinal6~X1)){\unicdbdjdcd}\\
(r1\_abian~(k1\_funct\_1~(k3\_ordinal6~X1)~X0)~X1))\end{array}$$
\end{theorem}
\end{document}
