\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{t21\_catalan2 (TMR2kkBne7WtzGvvKfqSt3XLyGsve3zbiqv)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_catalan2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_card\_fin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ 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 $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_catalan2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k24\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~\\
X2){\unicdbdjdcd}((X0 \in k1\_card\_fin~X1~X2~np\_\_1~k6\_numbers){\unicdbdjded}({\unicdcdaddd} X3 .  ((v5\_ordinal1~\\
X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finset\_1~X3))))){\unicdcdcdhd}((X3=X0){\unicdcdcdhd}((k1\_relset\_1~k5\_numbers~\\
X3=X1){\unicdcdcdhd}((r1\_tarski~(k2\_relset\_1~k5\_numbers~X3)~(k7\_domain\_1~\\
k5\_numbers~k6\_numbers~np\_\_1)){\unicdcdcdhd}(k7\_afinsq\_2~X3=X2)))))))\end{array}
\label{hyp:ehedadpfdgbgchegpfggjgog}
\end{equation}
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 .  {\unicdcdadad} X1 .  (r1\_tarski~X0~X1){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X0){\unicdbdjdcd}\\
(X2 \in X1))\end{array}
\label{hyp:egddpfehbgchdhlgjg}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_relat\_1~\\
X0~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0))))){\unicdbdjdcd}((v1\_catalan2~\\
X0){\unicdbdjded}((r1\_tarski~(k2\_relset\_1~k5\_numbers~X0)~(k7\_domain\_1~k5\_numbers~\\
k6\_numbers~np\_\_1)){\unicdcdcdhd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}((r1\_xxreal\_0~\\
X1~(k1\_relset\_1~k5\_numbers~X0)){\unicdbdjdcd}(r1\_xxreal\_0~(k24\_binop\_2~np\_\_2~\\
(k7\_afinsq\_2~(k5\_relat\_1~X0~X1)))~X1)))))\end{array}
\label{hyp:egbdpfdgbgehbgmgbgogcd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfdgbgehbgmgbgogcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(r1\_tarski~\\
(k2\_catalan2~X0~X1)~(k1\_card\_fin~X0~X1~np\_\_1~k6\_numbers)))\end{array}$$
\end{theorem}
\end{document}
