\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\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t4\_int\_6 (TMFfEhgMYbpCUfjxRywGH9Eqi2fRrfayLdr)}
\maketitle
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 $ v1\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k16\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_valued\_0~\\
X2))){\unicdbdjdcd}((k5\_relat\_1~(k18\_valued\_1~X1~X2)~X0=k18\_valued\_1~(k5\_relat\_1~\\
X1~X0)~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}((k5\_relat\_1~(k18\_valued\_1~X1~X2)~X0=\\
k18\_valued\_1~(k5\_relat\_1~X1~X0)~X2){\unicdcdcdhd}(k5\_relat\_1~(k18\_valued\_1~\\
X1~X2)~X0=k18\_valued\_1~X1~(k5\_relat\_1~X2~X0)))))\end{array}
\label{hyp:ehedfdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v1\_valued\_0~X0){\unicdcdcdhd}(v1\_finseq\_1~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_valued\_0~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))))){\unicdbdjdcd}((v1\_relat\_1~(k18\_valued\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k18\_valued\_1~X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~(k18\_valued\_1~\\
X0~X1))))\end{array}
\label{hyp:ggdgedddpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~X1)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k18\_valued\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k18\_valued\_1~\\
X0~X1)))\end{array}
\label{hyp:egehpflgbdidpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((\\
v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1))){\unicdbdjdcd}(k16\_finseq\_1~X0~X1=k5\_relat\_1~\\
X1~(k2\_finseq\_1~X0)))\end{array}
\label{hyp:egbdfdpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedpfjgogehpfgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_finseq\_1~\\
X0){\unicdcdcdhd}(v1\_valued\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_finseq\_1~X1){\unicdcdcdhd}(v1\_valued\_0~X1)))){\unicdbdjdcd}((k3\_finseq\_1~X0=\\
k3\_finseq\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~\\
X2~(k3\_finseq\_1~X0)){\unicdbdjdcd}(k16\_finseq\_1~X2~(k18\_valued\_1~X0~X1)=k18\_valued\_1~\\
(k16\_finseq\_1~X2~X0)~(k16\_finseq\_1~X2~X1))))))\end{array}$$
\end{theorem}
\end{document}
