\documentclass{article}
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\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t41\_finseq\_3 (TMKvPmeQEaRY93Ccw3J6ABxcGDz336tXWRm)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m2\_finseq\_1}~{({{k14\_finseq\_1}~{X0}})}}~{k5\_numbers}}}\label{hyp:egehpflgbdedpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ({\unicdcdaddd} X1 .  (v7\_ordinal1~X1){\unicdcdcdhd}(r1\_tarski~X0~(k2\_finseq\_1~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~k5\_numbers){\unicdbdjdcd}((X1=k14\_finseq\_1~\\
X0){\unicdbdjded}((k10\_xtuple\_0~X1=X0){\unicdcdcdhd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}({\unicdcdadad} X5 .  (\\
v7\_ordinal1~X5){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X3~X2){\unicdcdcdhd}\\
((r1\_xxreal\_0~X3~(k3\_finseq\_1~X1)){\unicdcdcdhd}((X4=k1\_funct\_1~X1~X2){\unicdcdcdhd}((\\
X5=k1\_funct\_1~X1~X3){\unicdcdcdhd}(r1\_xxreal\_0~X5~X4)))))))))))))\end{array}
\label{hyp:egbdddpfggjgogdhfgbhpfbd}
\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:ehedbdpfggjgogdhfgbhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (v7\_ordinal1~X5){\unicdbdjdcd}(\preoh (r1\_tarski~X0~(k2\_finseq\_1~X1)){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~X3~X2){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X4){\unicdcdcdhd}((r1\_xxreal\_0~\\
X5~(k3\_finseq\_1~(k14\_finseq\_1~X0))){\unicdcdcdhd}((k1\_funct\_1~(k14\_finseq\_1~\\
X0)~X5=X2){\unicdcdcdhd}((k1\_funct\_1~(k14\_finseq\_1~X0)~X4=X3){\unicdcdcdhd}(r1\_xxreal\_0~\\
X4~X5)))))))))))\end{array}$$
\end{theorem}
\end{document}
