\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{t38\_armstrng (TMMJZwF3bTrfBYNogRDkQnU2bKQWp9qeWbx)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k12\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k11\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ v6\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~\\
X0)))){\unicdbdjdcd}((r1\_relset\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)~X1~(k10\_armstrng~\\
X0~(k11\_armstrng~X0~X1))){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)))){\unicdbdjdcd}(((r1\_relset\_1~\\
(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)~X1~X2){\unicdcdcdhd}(v6\_armstrng~X2~X0)){\unicdbdjdcd}\\
(r1\_relset\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)~(k10\_armstrng~\\
X0~(k11\_armstrng~X0~X1))~X2)))))\end{array}
\label{hyp:ehddhdpfbgchngdhehchoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)))){\unicdbdjdcd}(v6\_armstrng~(k10\_armstrng~\\
X0~X1)~X0))\end{array}
\label{hyp:ehddddpfbgchngdhehchoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(r2\_relset\_1~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k11\_armstrng~\\
X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0)))\end{array}
\label{hyp:egehpflgbdbdpfbgchngdhehchoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  m1\_subset\_1~(k10\_armstrng~X0~X1)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)))\end{array}
\label{hyp:egehpflgbdadpfbgchngdhehchoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v6\_armstrng~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0))))){\unicdbdjdcd}((X2=k12\_armstrng~\\
X0~X1){\unicdbdjded}((r1\_relset\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)~X1~X2){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_setfam\_1~\\
X0)~(k9\_setfam\_1~X0)))){\unicdbdjdcd}(((r1\_relset\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~\\
X0)~X1~X3){\unicdcdcdhd}(v6\_armstrng~X3~X0)){\unicdbdjdcd}(r1\_relset\_1~(k9\_setfam\_1~X0)~\\
(k9\_setfam\_1~X0)~X2~X3)))))))\end{array}
\label{hyp:egcdedpfbgchngdhehchoghg}
\end{equation}
\begin{theorem}\label{thm:ehddidpfbgchngdhehchoghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~\\
X0)))){\unicdbdjdcd}(r2\_relset\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)~(k12\_armstrng~\\
X0~X1)~(k10\_armstrng~X0~(k11\_armstrng~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
