\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{t112\_flang\_2 (TMUBqrx8fgob985McC2V8Ht4AeQ1ncVq2hH)}
\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 $ k6\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_flang\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_flang\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_flang\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\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 $ k3\_catalan2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~\\
X0))){\unicdbdjdcd}(k2\_flang\_2~X0~X1=k4\_subset\_1~(k8\_afinsq\_1~X0)~(k4\_flang\_1~\\
X0~(k2\_flang\_1~X0))~X1)\end{array}
\label{hyp:ehhdgdpfggmgbgoghgpfcd}
\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 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k6\_flang\_1~X0~(k7\_flang\_1~\\
X0~X1~X2)~X1=k6\_flang\_1~X0~X1~(k7\_flang\_1~X0~X1~X2)))\end{array}
\label{hyp:ehddcdpfggmgbgoghgpfbd}
\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\_2~X0~X1~X2~(k2\_xcmplx\_0~\\
X2~np\_\_1)=k4\_subset\_1~(k3\_catalan2~X0)~(k7\_flang\_1~X0~X1~X2)~(k7\_flang\_1~\\
X0~X1~(k2\_xcmplx\_0~X2~np\_\_1))))\end{array}
\label{hyp:ehcdidpfggmgbgoghgpfcd}
\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 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k7\_flang\_1~X0~X1~(k2\_xcmplx\_0~\\
X2~np\_\_1)=k6\_flang\_1~X0~(k7\_flang\_1~X0~X1~X2)~X1))\end{array}
\label{hyp:ehcdddpfggmgbgoghgpfbd}
\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}
\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}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\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}
{{\unicdcdadad} X0 .  {{{k2\_flang\_1}~{X0}}={{k4\_afinsq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfggmgbgoghgpfbd}
\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 .  (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:ehbdbdcdpfggmgbgoghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k8\_afinsq\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}(k6\_flang\_1~X0~(k2\_flang\_2~\\
X0~X1)~(k7\_flang\_1~X0~X1~X2)=k1\_flang\_2~X0~X1~X2~(k2\_xcmplx\_0~X2~np\_\_1)))\end{array}$$
\end{theorem}
\end{document}
