\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{t5\_flang\_1 (TMSM79LeC8JenjHuifmpgsrFS8naVxvFYhM)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_catalan2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_ordinal1 : {{\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\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_ordinal4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
(k1\_ordinal4~X0~X1)){\unicdcdcdhd}((v5\_relat\_1~(k1\_ordinal4~X0~X1)~X2){\unicdcdcdhd}((v5\_ordinal1~\\
(k1\_ordinal4~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k1\_ordinal4~X0~X1)){\unicdcdcdhd}(v1\_finset\_1~\\
(k1\_ordinal4~X0~X1)))))){\unicdbdjdcd}(((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_relat\_1~X0~X2){\unicdcdcdhd}\\
((v5\_ordinal1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0))))){\unicdcdcdhd}((\\
v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~X2){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_finset\_1~X1))))))))\end{array}
\label{hyp:ehddbdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_catalan2}~{X0}}={{k8\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdgbgehbgmgbgogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finset\_1~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_ordinal1~\\
X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdbdjdcd}((v1\_relat\_1~(k1\_ordinal4~\\
X0~X1)){\unicdcdcdhd}((v5\_ordinal1~(k1\_ordinal4~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k1\_ordinal4~\\
X0~X1)){\unicdcdcdhd}(v1\_finset\_1~(k1\_ordinal4~X0~X1)))))\end{array}
\label{hyp:ggdgfdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k8\_afinsq\_1}~{X0}})}}}}}\label{hyp:ggdgcdadpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v5\_ordinal1~X0){\unicdcdcdhd}(\\
v1\_funct\_1~X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_ordinal1~X1){\unicdcdcdhd}(v1\_funct\_1~\\
X1)))){\unicdbdjdcd}((v1\_relat\_1~(k1\_ordinal4~X0~X1)){\unicdcdcdhd}((v5\_ordinal1~(k1\_ordinal4~\\
X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k1\_ordinal4~X0~X1))))\end{array}
\label{hyp:egehpflgbdpfpgchegjgogbgmged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1=k8\_afinsq\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}((v5\_ordinal1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v1\_finset\_1~X2))))))\end{array}
\label{hyp:eghdpfbgggjgogdhbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}\\
(X1 \in X0))){\unicdcdcdhd}((v1\_xboole\_0~X0){\unicdbdjdcd}((m1\_subset\_1~X1~X0){\unicdbdjded}(v1\_xboole\_0~\\
X1)))\end{array}
\label{hyp:egbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfggmgbgoghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_catalan2~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v5\_ordinal1~X2){\unicdcdcdhd}((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finset\_1~\\
X2)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v5\_ordinal1~X3){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finset\_1~X3)))){\unicdbdjdcd}((X1=k1\_ordinal4~X2~X3){\unicdbdjdcd}((m1\_subset\_1~\\
X2~(k3\_catalan2~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k3\_catalan2~X0))))))\end{array}$$
\end{theorem}
\end{document}
