\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=}
\newcommand\unicdcdcdbg{\cup}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t52\_finseq\_3 (TMMVmfMGFUq5gCj3njMzDa96t921h6uPyrH)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((k5\_relat\_1~X0~(k2\_finseq\_1~X1)=\\
X0){\unicdbdjded}(r1\_xxreal\_0~(k3\_finseq\_1~X0)~X1)))\end{array}
\label{hyp:ehedjdpfggjgogdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(k14\_finseq\_1~(k2\_finseq\_1~X0)=\\
k1\_finseq\_2~X0)\end{array}
\label{hyp:ehedidpfggjgogdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}(k3\_finseq\_1~(k14\_finseq\_1~(k2\_finseq\_1~\\
X0))=X0)\end{array}
\label{hyp:ehedgdpfggjgogdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_relat\_1~(k1\_finseq\_2~X0)){\unicdcdcdhd}\\
((v1\_funct\_1~(k1\_finseq\_2~X0)){\unicdcdcdhd}((v3\_card\_1~(k1\_finseq\_2~X0)~\\
X0){\unicdcdcdhd}(v1\_finseq\_1~(k1\_finseq\_2~X0)))))\end{array}
\label{hyp:ggdgbdpfggjgogdhfgbhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehfdcdpfggjgogdhfgbhpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((\\
k5\_relat\_1~(k1\_finseq\_2~X0)~(k2\_finseq\_1~X1)=k1\_finseq\_2~X0){\unicdbdjded}\\
(r1\_xxreal\_0~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
