\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{t10\_armstrng (TMNHWaSfGLezs5dMopCoP7dN31bfNCsDLzq)}
\maketitle
Let $ l1\_armstrng : {{\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 $ u1\_armstrng : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_armstrng : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(k4\_tarski~(k4\_tarski~X0~X2)~X4=k4\_tarski~(k4\_tarski~X1~X3)~X5){\unicdbdjdcd}\\
((X0=X1){\unicdcdcdhd}(X2=X3))\end{array}
\label{hyp:mgbdadpffgogdhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_armstrng~X0){\unicdbdjdcd}(k5\_armstrng~X0=ReplSep2~(toset~\\
({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_armstrng~X0))))~\\
({\uniddcgcg} X1 : \iota .  toset~({\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(k1\_zfmisc\_1~(\\
u1\_armstrng~X0))))~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  r2\_armstrng~X0~X1~\\
X2)~({\uniddcgcg} X1 : \iota .  {\uniddcgcg} X2 : \iota .  k4\_tarski~X1~X2))\end{array}
\label{hyp:egidpfbgchngdhehchoghg}
\end{equation}
\begin{theorem}\label{thm:ehbdadpfbgchngdhehchoghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_armstrng~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_armstrng~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(u1\_armstrng~X0))){\unicdbdjdcd}((k4\_tarski~X1~X2 \in k5\_armstrng~X0){\unicdbdjded}(r2\_armstrng~\\
X0~X1~X2))))\end{array}$$
\end{theorem}
\end{document}
