\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{t11\_armstrng (TMRvZ3cJ6rwoSYV1HMYZZ2WRnbd5j1Hw2XM)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_armstrng : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_armstrng : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_relat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}(((k1\_xtuple\_0~\\
X1=k1\_xtuple\_0~X2){\unicdcdcdhd}(k2\_xtuple\_0~X1=k2\_xtuple\_0~X2)){\unicdbdjdcd}(X1=X2))))\end{array}
\label{hyp:ehjdadpfngdgbgchehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (X1 \in k4\_armstrng~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(X1=k4\_tarski~X2~X3)))\end{array}
\label{hyp:ehidpfbgchngdhehchoghg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {\preoh{{{v1\_xboole\_0}~{({{k4\_armstrng}~{X0}})}}}}}\label{hyp:ggdgcdpfbgchngdhehchoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k4\_armstrng~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k4\_armstrng~X0)){\unicdbdjdcd}((r3\_armstrng~X0~X1~X2){\unicdbdjded}((r1\_tarski~\\
(k1\_xtuple\_0~X1)~(k1\_xtuple\_0~X2)){\unicdcdcdhd}(r1\_tarski~(k2\_xtuple\_0~X2)~\\
(k2\_xtuple\_0~X1)))))\end{array}
\label{hyp:egjdpfbgchngdhehchoghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  \preoh (X1 \in X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  X1{\unicdcdgdad}k4\_tarski~X2~X3))\end{array}
\label{hyp:egbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfbgchngdhehchoghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k4\_armstrng~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k4\_armstrng~X0)){\unicdbdjdcd}(((r3\_armstrng~X0~X2~X1){\unicdcdcdhd}(r3\_armstrng~\\
X0~X1~X2)){\unicdbdjdcd}(X1=X2)))\end{array}$$
\end{theorem}
\end{document}
