\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{t9\_combgras (TMcxsv9L2bicn922msGpQo7ShyfyUknSN5W)}
\maketitle
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r4\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_incsp\_1~X1){\unicdbdjdcd}((g1\_incsp\_1~\\
(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0)~(u3\_incsp\_1~X0)=g1\_incsp\_1~(u1\_incsp\_1~\\
X1)~(u2\_incsp\_1~X1)~(u3\_incsp\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X1)){\unicdbdjdcd}\\
((X2=X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u2\_incsp\_1~X1)){\unicdbdjdcd}(((X4=X5){\unicdcdcdhd}(r1\_incsp\_1~X0~X2~\\
X4)){\unicdbdjdcd}(r1\_incsp\_1~X1~X3~X5)))))))))\end{array}
\label{hyp:ehidpfdgpgngcghgchbgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_incsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
((r4\_incsp\_1~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(r1\_incsp\_1~X0~X3~X2))))))\end{array}
\label{hyp:egedpfjgogdgdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehjdpfdgpgngcghgchbgdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_incsp\_1~X1){\unicdbdjdcd}((g1\_incsp\_1~\\
(u1\_incsp\_1~X0)~(u2\_incsp\_1~X0)~(u3\_incsp\_1~X0)=g1\_incsp\_1~(u1\_incsp\_1~\\
X1)~(u2\_incsp\_1~X1)~(u3\_incsp\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_incsp\_1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(k1\_zfmisc\_1~(u1\_incsp\_1~X1))){\unicdbdjdcd}((X2=X3){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u2\_incsp\_1~X1)){\unicdbdjdcd}\\
(((X4=X5){\unicdcdcdhd}(r4\_incsp\_1~X0~X2~X4)){\unicdbdjdcd}(r4\_incsp\_1~X1~X3~X5)))))))))\end{array}$$
\end{theorem}
\end{document}
