\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{t43\_armstrng (TMLMQmGsYBqAxUP9AQwWKBNLqmVcd4C3jqz)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_armstrng : {{\iota}{\unicdbdjdcd}{{\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 $ r5\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k10\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r4\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(r5\_armstrng~\\
X0~X1~(k9\_armstrng~X0~(k10\_armstrng~X0~X1))))\end{array}
\label{hyp:ehedcdpfbgchngdhehchoghg}
\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~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(((v1\_armstrng~\\
X1~X0){\unicdcdcdhd}(v2\_finsub\_1~X1)){\unicdbdjdcd}((X1=k9\_armstrng~X0~(k10\_armstrng~X0~\\
X1)){\unicdcdcdhd}({\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}((X1=k9\_armstrng~\\
X0~X2){\unicdbdjdcd}(r2\_relset\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)~X2~(k10\_armstrng~\\
X0~X1)))))))\end{array}
\label{hyp:ehddfdpfbgchngdhehchoghg}
\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 .  \\
((v6\_armstrng~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0))))){\unicdbdjdcd}((v1\_armstrng~(k9\_armstrng~\\
X0~X1)~X0){\unicdcdcdhd}(v2\_finsub\_1~(k9\_armstrng~X0~X1))))\end{array}
\label{hyp:ehddcdpfbgchngdhehchoghg}
\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~(k9\_armstrng~\\
X0~X1)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0)))\end{array}
\label{hyp:egehpflgjdpfbgchngdhehchoghg}
\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}(k9\_armstrng~X0~X1=ReplSep~\\
(toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(k1\_zfmisc\_1~X0)))~({\uniddcgcg} X2 : \\
\iota .  {\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}(r4\_armstrng~\\
X0~X1~X3~X2))~({\uniddcgcg} X2 : \iota .  X2))\end{array}
\label{hyp:egcdbdpfbgchngdhehchoghg}
\end{equation}
\begin{theorem}\label{thm:ehedddpfbgchngdhehchoghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v6\_armstrng~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0))))){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))){\unicdcdcdhd}((r5\_armstrng~X0~X2~(k9\_armstrng~\\
X0~X1)){\unicdcdcdhd}(r2\_relset\_1~(k9\_setfam\_1~X0)~(k9\_setfam\_1~X0)~X1~(k10\_armstrng~\\
X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
