\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{t8\_finseq\_3 (TMMHMbE7aJZuT95ui2kihGi2i39ptc9fNhn)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\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 $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k4\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_ordinal1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X0~(k7\_nat\_d~X1~np\_\_1))){\unicdbdjdcd}((\preoh \\
r1\_xxreal\_0~(k1\_nat\_1~X1~np\_\_1)~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k1\_nat\_1~\\
X1~np\_\_1)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k2\_nat\_1~(k1\_nat\_1~X1~np\_\_1)~np\_\_1)~\\
X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k2\_nat\_1~(k1\_nat\_1~X1~np\_\_1)~np\_\_1)){\unicdcdcdhd}((\\
\preoh r1\_xxreal\_0~(k1\_nat\_1~X1~np\_\_2)~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k1\_nat\_1~\\
X1~np\_\_2)))))))))\end{array}
\label{hyp:ehedidpfogbgehpfeg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k4\_card\_1}~{X0}}={{{k1\_nat\_1}~{X0}}~{np\_\_1}}})}}}\label{hyp:ehddidpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{{k2\_finseq\_1}~{X0}}={{k1\_finseq\_1}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggjgogdhfgbhpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(k1\_finseq\_1~X0=ReplSep~(toset~(\\
{\uniddcgcg} X1 : \iota .  m2\_subset\_1~X1~k1\_numbers~k5\_numbers))~({\uniddcgcg} X1 : \iota .  \\
(r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0))~({\uniddcgcg} X1 : \iota .  X1))\end{array}
\label{hyp:egbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehidpfggjgogdhfgbhpfdd}
${{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({\preoh{{{{{k1\_nat\_1}~{X0}}~{np\_\_1}} \in {{k2\_finseq\_1}~{X0}}}}})}}}$.
\end{theorem}
\end{document}
