\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{t3\_algseq\_1 (TMNarw57t7wXD6UPd67oUxFw21bTK1Vtoti)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k7\_nat\_d : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
\preoh (r1\_xxreal\_0~X1~X0){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k1\_nat\_1~X0~np\_\_1)~X1)){\unicdbdjdcd}(\\
r1\_xxreal\_0~X0~(k7\_nat\_d~X1~np\_\_1))))\end{array}
\label{hyp:ehedjdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
r1\_xxreal\_0~(k1\_nat\_1~X0~np\_\_1)~X1){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X1~(k7\_nat\_d~\\
X0~np\_\_1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X1~(k7\_nat\_d~X0~np\_\_2)){\unicdcdcdhd}(r1\_xxreal\_0~\\
X0~X1)))))\end{array}
\label{hyp:ehedgdpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
X0 \in k7\_card\_1~X1){\unicdbdjded}(\preoh r1\_xxreal\_0~X1~X0)))\end{array}
\label{hyp:ehbdpfbgmghgdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v3\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X0)){\unicdbdjdcd}(v7\_ordinal1~\\
(k1\_ordinal1~X0))\end{array}
\label{hyp:ggdghdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k1\_ordinal1}~{X0}}={{{k1\_nat\_1}~{X0}}~{np\_\_1}}})}}}\label{hyp:egcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{({{v3\_ordinal1}~{X0}})}{\unicdcdcdhd}{({{v7\_ordinal1}~{X0}})}})}}}\label{hyp:dgdgbdpfogbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddpfbgmghgdhfgbhpfbd}
${{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{X0} \in {{k7\_card\_1}~{({{{k1\_nat\_1}~{X0}}~{np\_\_1}})}}})}}}$.
\end{theorem}
\end{document}
