\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{t57\_flang\_1 (TMQjqzwvQXhBgq9EZSJtNLfLnpFG36pN6N1)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_catalan2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}((k8\_flang\_1~X0~X1=k4\_subset\_1~(k3\_catalan2~X0)~(k4\_flang\_1~\\
X0~(k2\_flang\_1~X0))~(k6\_flang\_1~X0~X1~(k8\_flang\_1~X0~X1))){\unicdcdcdhd}(k8\_flang\_1~\\
X0~X1=k4\_subset\_1~(k3\_catalan2~X0)~(k4\_flang\_1~X0~(k2\_flang\_1~\\
X0))~(k6\_flang\_1~X0~(k8\_flang\_1~X0~X1)~X1)))\end{array}
\label{hyp:ehfdgdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}(k7\_flang\_1~X0~X1~k6\_numbers=k4\_flang\_1~X0~(k2\_flang\_1~\\
X0))\end{array}
\label{hyp:ehcdedpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}((k4\_subset\_1~(k3\_catalan2~X0)~(k6\_flang\_1~X0~X1~X2)~(k6\_flang\_1~\\
X0~X1~X3)=k6\_flang\_1~X0~X1~(k4\_subset\_1~(k3\_catalan2~X0)~X2~X3)){\unicdcdcdhd}\\
(k4\_subset\_1~(k3\_catalan2~X0)~(k6\_flang\_1~X0~X2~X1)~(k6\_flang\_1~\\
X0~X3~X1)=k6\_flang\_1~X0~(k4\_subset\_1~(k3\_catalan2~X0)~X2~X3)~X1))))\end{array}
\label{hyp:ehcdadpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}(k6\_flang\_1~X0~(k6\_flang\_1~X0~X1~X2)~X3=k6\_flang\_1~X0~X1~(\\
k6\_flang\_1~X0~X2~X3))))\end{array}
\label{hyp:ehbdidpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}((k6\_flang\_1~X0~X1~(k4\_flang\_1~X0~(k2\_flang\_1~X0))=X1){\unicdcdcdhd}\\
(k6\_flang\_1~X0~(k4\_flang\_1~X0~(k2\_flang\_1~X0))~X1=X1))\end{array}
\label{hyp:ehbdddpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}(m1\_subset\_1~(k8\_flang\_1~X0~X1)~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0)))\end{array}
\label{hyp:egehpflgidpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k3\_catalan2~X0))){\unicdcdcdhd}(v7\_ordinal1~X2)){\unicdbdjdcd}(m1\_subset\_1~(k7\_flang\_1~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k3\_catalan2~X0)))\end{array}
\label{hyp:egehpflghdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k3\_catalan2~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k6\_flang\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0)))\end{array}
\label{hyp:egehpflggdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}(k8\_flang\_1~X0~X1=k3\_tarski~(ReplSep~(toset~({\uniddcgcg} X2 : \iota .  \\
m1\_subset\_1~X2~(k1\_zfmisc\_1~(k3\_catalan2~X0))))~({\uniddcgcg} X2 : \iota .  \\
{\unicdcdaddd} X3 .  (v7\_ordinal1~X3){\unicdcdcdhd}(X2=k7\_flang\_1~X0~X1~X3))~({\uniddcgcg} X2 : \\
\iota .  X2)))\end{array}
\label{hyp:egddpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdhdpfggmgbgoghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k3\_catalan2~\\
X0))){\unicdbdjdcd}(k6\_flang\_1~X0~X1~(k8\_flang\_1~X0~X1)=k6\_flang\_1~X0~(k8\_flang\_1~\\
X0~X1)~X1)\end{array}$$
\end{theorem}
\end{document}
