\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{t14\_flang\_3 (TMaNbHwfdVBZbKeaGrX1k6hrytNzp5PFCMh)}
\maketitle
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 $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_flang\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_flang\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_catalan2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_numbers : {\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}(k2\_flang\_1~X0 \in k8\_flang\_1~X0~X1)\end{array}
\label{hyp:ehedidpfggmgbgoghgpfbd}
\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=k4\_flang\_1~X0~(k2\_flang\_1~X0)){\unicdbdjded}((X1=\\
k1\_xboole\_0){\unicdcdcdid}(X1=k4\_flang\_1~X0~(k2\_flang\_1~X0))))\end{array}
\label{hyp:ehedhdpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k8\_afinsq\_1~X1))){\unicdbdjdcd}(\preoh (X0 \in X2){\unicdcdcdhd}((X0{\unicdcdgdad}k2\_flang\_1~X1){\unicdcdcdhd}(k8\_flang\_1~\\
X1~X2=k4\_flang\_1~X1~(k2\_flang\_1~X1))))\end{array}
\label{hyp:ehbdfdpfggmgbgoghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((k1\_flang\_3~X0~X1~X2=k8\_flang\_1~\\
X0~X1){\unicdbdjded}((k2\_flang\_1~X0 \in X1){\unicdcdcdid}(X2=k6\_numbers))))\end{array}
\label{hyp:ehbdbdpfggmgbgoghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((k2\_flang\_1~X0 \in k1\_flang\_3~\\
X0~X1~X2){\unicdbdjded}((X2=k6\_numbers){\unicdcdcdid}(k2\_flang\_1~X0 \in X1))))\end{array}
\label{hyp:ehbdadpfggmgbgoghgpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k3\_catalan2~X0)){\unicdbdjdcd}(m1\_subset\_1~\\
(k4\_flang\_1~X0~X1)~(k1\_zfmisc\_1~(k3\_catalan2~X0)))\end{array}
\label{hyp:egehpflgedpfggmgbgoghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k2\_flang\_1}~{X0}})}}~{({{k3\_catalan2}~{X0}})}}}\label{hyp:egehpflgcdpfggmgbgoghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdedpfggmgbgoghgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k8\_afinsq\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\preoh (X0 \in X2){\unicdcdcdhd}\\
((X0{\unicdcdgdad}k2\_flang\_1~X1){\unicdcdcdhd}(k1\_flang\_3~X1~X2~X3=k4\_flang\_1~X1~(k2\_flang\_1~\\
X1)))))\end{array}$$
\end{theorem}
\end{document}
