\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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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{t1\_catalan2 (TMNaKUKwB4HEjkq79tG2u8rQirDtRB3jHaD)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_afinsq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1)))){\unicdbdjdcd}(k1\_ordinal4~\\
(k5\_relat\_1~X1~X0)~(k2\_afinsq\_2~X1~X0)=X1))\end{array}
\label{hyp:ehbdddpfbgggjgogdhbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdcdcdhd}\\
(v7\_ordinal1~X2)){\unicdbdjdcd}((v1\_relat\_1~(k2\_afinsq\_2~X1~X2)){\unicdcdcdhd}((v5\_relat\_1~\\
(k2\_afinsq\_2~X1~X2)~X0){\unicdcdcdhd}((v1\_funct\_1~(k2\_afinsq\_2~X1~X2)){\unicdcdcdhd}((v5\_ordinal1~\\
(k2\_afinsq\_2~X1~X2)){\unicdcdcdhd}(v1\_finset\_1~(k2\_afinsq\_2~X1~X2))))))\end{array}
\label{hyp:ggdgcdgdpfbgggjgogdhbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v5\_ordinal1~X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}((v1\_relat\_1~\\
(k2\_afinsq\_2~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k2\_afinsq\_2~X0~X1)){\unicdcdcdhd}((v5\_ordinal1~\\
(k2\_afinsq\_2~X0~X1)){\unicdcdcdhd}(v1\_finset\_1~(k2\_afinsq\_2~X0~X1)))))\end{array}
\label{hyp:egehpflgcdpfbgggjgogdhbhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdpfdgbgehbgmgbgogcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v5\_ordinal1~\\
X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(\\
v1\_finset\_1~X2))))){\unicdbdjdcd}({\unicdcdaddd} X3 .  ((v5\_ordinal1~X3){\unicdcdcdhd}((v1\_relat\_1~\\
X3){\unicdcdcdhd}((v5\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finset\_1~X3))))){\unicdcdcdhd}\\
(X2=k1\_ordinal4~(k5\_relat\_1~X2~X1)~X3)))\end{array}$$
\end{theorem}
\end{document}
