\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{t13\_projred1 (TMJHVuAaXxei6ZBDpLHqQEFWdmmegLoeQ8F)}
\maketitle
Let $ v6\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_incproj : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}(r1\_incsp\_1~X0~X2~X1)))\end{array}
\label{hyp:ehhdpfahchpgkgchfgegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
(\preoh ({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(u1\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X7~X5){\unicdcdcdhd}(r1\_incsp\_1~X0~X7~X6))){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X5){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X2~X5){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X5){\unicdcdcdhd}((r1\_incsp\_1~X0~X4~X5){\unicdcdcdhd}((r2\_zfmisc\_1~\\
X1~X2~X3~X4){\unicdcdcdhd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~\\
(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
(\preoh (r1\_incsp\_1~X0~X7~X6){\unicdcdcdhd}((r1\_incsp\_1~X0~X8~X6){\unicdcdcdhd}((r1\_incsp\_1~X0~\\
X9~X6){\unicdcdcdhd}((r1\_incsp\_1~X0~X10~X6){\unicdcdcdhd}(r2\_zfmisc\_1~X7~X8~X9~X10)))))))))))))))))))))\end{array}
\label{hyp:mgbdddpfahchpgkgchfgegbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}((v6\_incsp\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~\\
X1~X3){\unicdcdcdhd}(r1\_incsp\_1~X0~X2~X3))))))\end{array}
\label{hyp:egfdpfjgogdgahchpgkg}
\end{equation}
\begin{theorem}\label{thm:ehbdddpfahchpgkgchfgegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~X0)))))){\unicdbdjdcd}(({\unicdcdaddd} X1 .  \\
(m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~(u1\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}\\
((r1\_incsp\_1~X0~X4~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X5~X1){\unicdcdcdhd}(r2\_zfmisc\_1~X2~X3~\\
X4~X5)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~\\
X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~\\
X2~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X4~X1){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X5~X1){\unicdcdcdhd}(r2\_zfmisc\_1~X2~X3~X4~X5)))))))))))\end{array}$$
\end{theorem}
\end{document}
