\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{t46\_ordinal6 (TMEyCyhHvwstm8Q6g4e1eg8fYu3t3CFFvkf)}
\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 $ v3\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ordinal6 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k6\_numbers : {\iota}$ be given.
Let $ v1\_ordinal2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_abian : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_ordinal6}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {{({{X1} \in {X0}})}{\unicdbdjdcd}{({{v3\_ordinal1}~{X1}})}}})}}}\label{hyp:ehbdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_ordinal6~\\
X0))){\unicdbdjdcd}((v5\_ordinal1~(k1\_funct\_1~X0~X1)){\unicdcdcdhd}(v1\_ordinal2~(k1\_funct\_1~\\
X0~X1)))\end{array}
\label{hyp:ggdgcdcdpfpgchegjgogbgmggd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v5\_ordinal1}~{X0}})}{\unicdbdjded}{({{v3\_ordinal1}~{({{k9\_xtuple\_0}~{X0}})}})}}}\label{hyp:eghdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v3\_ordinal1~X1))\end{array}
\label{hyp:dgdgcdpfpgchegjgogbgmgcd}
\end{equation}
\begin{theorem}\label{thm:ehedgdpfpgchegjgogbgmggd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_ordinal1~\\
X0){\unicdcdcdhd}(v3\_ordinal6~X0)))){\unicdbdjdcd}(v1\_ordinal6~(ReplSep~(toset~({\uniddcgcg} X1 : \\
\iota .  m1\_subset\_1~X1~(k9\_xtuple\_0~(k1\_funct\_1~X0~k6\_numbers))))~\\
({\uniddcgcg} X1 : \iota .  (X1 \in k9\_xtuple\_0~(k1\_funct\_1~X0~k6\_numbers)){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}(v1\_ordinal2~\\
X2)))){\unicdbdjdcd}((X2 \in k10\_xtuple\_0~X0){\unicdbdjdcd}(r1\_abian~X1~X2))))~({\uniddcgcg} X1 : \iota .  \\
X1)))\end{array}$$
\end{theorem}
\end{document}
