\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{t20\_catalan2 (TMFzUsBv2FR8423jssx4mFfdipSkN2J9ao9)}
\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 $ k5\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_catalan2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_catalan2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_afinsq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_catalan2~X0~X1)~(k1\_zfmisc\_1~(k8\_afinsq\_1~(k7\_domain\_1~\\
k5\_numbers~k6\_numbers~np\_\_1))))\end{array}
\label{hyp:egehpflgcdpfdgbgehbgmgbgogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k8\_afinsq\_1~(k7\_domain\_1~k5\_numbers~\\
k6\_numbers~np\_\_1)))){\unicdbdjdcd}((X2=k2\_catalan2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in \\
X2){\unicdbdjded}({\unicdcdaddd} X4 .  ((v5\_ordinal1~X4){\unicdcdcdhd}((v1\_relat\_1~X4){\unicdcdcdhd}((v5\_relat\_1~\\
X4~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finset\_1~X4))))){\unicdcdcdhd}((X4=\\
X3){\unicdcdcdhd}((v1\_catalan2~X4){\unicdcdcdhd}((k1\_relset\_1~k5\_numbers~X4=X0){\unicdcdcdhd}(k7\_afinsq\_2~\\
X4=X1)))))))))\end{array}
\label{hyp:egcdpfdgbgehbgmgbgogcd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfdgbgehbgmgbgogcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v5\_ordinal1~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~k5\_numbers){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finset\_1~X2))))){\unicdbdjdcd}((X2 \in k2\_catalan2~X0~X1){\unicdbdjded}\\
((v1\_catalan2~X2){\unicdcdcdhd}((k1\_relset\_1~k5\_numbers~X2=X0){\unicdcdcdhd}(k7\_afinsq\_2~\\
X2=X1))))))\end{array}$$
\end{theorem}
\end{document}
