\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{l74\_armstrng (TMJ7yxJJ9jh7czh383rM7gyYXVnkWcjKq6K)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (k4\_tarski~X0~X1=\\
k4\_tarski~X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3))\end{array}
\label{hyp:ehbdpfihehfhahmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k6\_armstrng~X0~X1~X2=\\
k4\_tarski~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfbgchngdhehchoghg}
\end{equation}
\begin{theorem}\label{thm:mghdedpfbgchngdhehchoghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X1=ReplSep2~(toset~({\uniddcgcg} X3 : \\
\iota .  m1\_subset\_1~X3~(k1\_zfmisc\_1~X0)))~({\uniddcgcg} X3 : \iota .  toset~({\uniddcgcg} X4 : \\
\iota .  m1\_subset\_1~X4~(k1\_zfmisc\_1~X0)))~({\uniddcgcg} X3 : \iota .  {\uniddcgcg} X4 : \iota .  \\
{\unicdcdadad} X5 .  ((X5 \in X2){\unicdcdcdhd}(r1\_tarski~X3~X5)){\unicdbdjdcd}(r1\_tarski~X4~X5))~({\uniddcgcg} X3 : \\
\iota .  {\uniddcgcg} X4 : \iota .  k6\_armstrng~X0~X3~X4)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}((k6\_armstrng~X0~X3~X4 \in X1){\unicdbdjded}({\unicdcdadad} X5 .  ((X5 \in X2){\unicdcdcdhd}(r1\_tarski~\\
X3~X5)){\unicdbdjdcd}(r1\_tarski~X4~X5)))))\end{array}$$
\end{theorem}
\end{document}
