\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{t37\_projpl\_1 (TMXewneosxJrM5AcFgc9zDbpQbJ5gxa1Ya9)}
\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 $ v5\_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 $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
((X1{\unicdcdgdad}X2){\unicdbdjdcd}((r1\_incsp\_1~X0~X1~(k1\_projpl\_1~X0~X1~X2)){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X2~(k1\_projpl\_1~X0~X1~X2)){\unicdcdcdhd}((k1\_projpl\_1~X0~X1~X2=k1\_projpl\_1~\\
X0~X2~X1){\unicdcdcdhd}(((r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}(r1\_incsp\_1~X0~X2~X3)){\unicdbdjdcd}(X3=k1\_projpl\_1~\\
X0~X1~X2)))))))))\end{array}
\label{hyp:ehbdgdpfahchpgkgahmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((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)))))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)))){\unicdbdjdcd}(m1\_subset\_1~(k1\_projpl\_1~X0~X1~X2)~(u2\_incsp\_1~\\
X0))\end{array}
\label{hyp:egehpflgbdpfahchpgkgahmgpfbd}
\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}((v5\_incproj~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}(r1\_incsp\_1~X0~X3~X2))))))\end{array}
\label{hyp:egjdpfjgogdgahchpgkg}
\end{equation}
\begin{theorem}\label{thm:ehddhdpfahchpgkgahmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}((v5\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
(\preoh (r1\_incsp\_1~X0~X2~X7){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X7){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~\\
X1~X7){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}((X4{\unicdcdgdad}X1){\unicdcdcdhd}((X5{\unicdcdgdad}X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X4~(k1\_projpl\_1~\\
X0~X1~X2)){\unicdcdcdhd}((r1\_incsp\_1~X0~X5~(k1\_projpl\_1~X0~X1~X3)){\unicdcdcdhd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (r1\_incsp\_1~X0~X8~(k1\_projpl\_1~\\
X0~X4~X5)){\unicdcdcdhd}((r1\_incsp\_1~X0~X8~X6){\unicdcdcdhd}(X8{\unicdcdgdad}X1)))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
