\documentclass{article}
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\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t51\_armstrng (TMZ62fJVAyvG4XkkoMfuP9vPXu3fWuvj8yq)}
\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 $ v11\_armstrng : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_armstrng : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_armstrng : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_armstrng : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_armstrng : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_finset\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(\preoh (\preoh v1\_xboole\_0~X1){\unicdcdcdhd}((v11\_armstrng~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{\unicdcdgdad}k13\_armstrng~\\
X0~X2)))))\end{array}
\label{hyp:ehedjdpfbgchngdhehchoghg}
\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}({\unicdcdaddd} X2 .  (l1\_armstrng~\\
X2){\unicdcdcdhd}((u1\_armstrng~X2=X0){\unicdcdcdhd}(({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}(\\
k1\_funct\_1~(u2\_armstrng~X2)~X3=k4\_numbers)){\unicdcdcdhd}(X1=k5\_armstrng~\\
X2)))))\end{array}
\label{hyp:ehedgdpfbgchngdhehchoghg}
\end{equation}
\begin{theorem}\label{thm:ehfdbdpfbgchngdhehchoghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_finset\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(\preoh (\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}((v11\_armstrng~X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (l1\_armstrng~X2){\unicdbdjdcd}(\preoh (u1\_armstrng~\\
X2=X0){\unicdcdcdhd}(X1=k13\_armstrng~(u1\_armstrng~X2)~(k5\_armstrng~X2)))))))\end{array}$$
\end{theorem}
\end{document}
