\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{t23\_projpl\_1 (TMMavLDTAPc4PNtPrA4sYoxdeATLZrAQT5g)}
\maketitle
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ v1\_projpl\_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 $ r4\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r5\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r4\_projpl\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(((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)))))){\unicdbdjded}((v1\_projpl\_1~X0){\unicdcdcdhd}(({\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}(r4\_incsp\_1~X0~(k7\_domain\_1~\\
(u1\_incsp\_1~X0)~X1~X2)~X3)))){\unicdcdcdhd}((\preoh {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u2\_incsp\_1~X0)){\unicdbdjdcd}(r1\_incsp\_1~\\
X0~X1~X2))){\unicdcdcdhd}(({\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}\\
((r1\_zfmisc\_1~X2~X3~X4){\unicdcdcdhd}(r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~\\
X0)~X2~X3~X4)~X1)))))){\unicdcdcdhd}({\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}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (r4\_incsp\_1~X0~\\
(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~X5)~X6){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~\\
(u1\_incsp\_1~X0)~X3~X4~X5)~X7){\unicdcdcdhd}((r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~\\
X0)~X1~X3)~X8){\unicdcdcdhd}((r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~X0)~X2~X4)~\\
X9){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X5~X8){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X5~X9){\unicdcdcdhd}((X6{\unicdcdgdad}X7){\unicdcdcdhd}\\
({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_incsp\_1~X0)){\unicdbdjdcd}(\preoh r2\_projpl\_1~\\
X0~X10~X8~X9)))))))))))))))))))))))\end{array}
\label{hyp:ehedpfahchpgkgahmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(((v1\_projpl\_1~X0){\unicdcdcdhd}(({\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}\\
(r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~X0)~X1~X2)~X3)))){\unicdcdcdhd}({\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}\\
(r2\_projpl\_1~X0~X3~X1~X2)))))){\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}(\preoh r5\_projpl\_1~X0~X1~X2~X3~X4))))){\unicdcdcdid}({\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}((r1\_zfmisc\_1~X2~\\
X3~X4){\unicdcdcdhd}(r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X2~X3~X4)~X1))))))))\end{array}
\label{hyp:ehcdcdpfahchpgkgahmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(\preoh ({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_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}(r5\_projpl\_1~X0~X1~X2~X3~X4))))){\unicdcdcdhd}({\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}\\
(r4\_projpl\_1~X0~X1~X2~X3)))))\end{array}
\label{hyp:ehbdidpfahchpgkgahmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(\preoh (\preoh {\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}(r4\_projpl\_1~X0~X1~X2~X3)))){\unicdcdcdhd}\\
(({\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}\\
(r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~X0)~X1~X2)~X3)))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u2\_incsp\_1~X0)){\unicdbdjdcd}(r1\_incsp\_1~X0~X1~X2)))))\end{array}
\label{hyp:ehbdhdpfahchpgkgahmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(\preoh ((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}({\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}\\
(\preoh r5\_projpl\_1~X0~X1~X2~X3~X4))))))\end{array}
\label{hyp:ehbdfdpfahchpgkgahmgpfbd}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}((r2\_projpl\_1~X0~X1~X2~X3){\unicdbdjded}((\\
r1\_incsp\_1~X0~X1~X2){\unicdcdcdhd}(r1\_incsp\_1~X0~X1~X3))))))\end{array}
\label{hyp:egcdpfahchpgkgahmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfahchpgkgahmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}(((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}\\
((v2\_incproj~X0){\unicdcdcdhd}((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}((v5\_incproj~\\
X0){\unicdcdcdhd}(l1\_incsp\_1~X0))))))){\unicdbdjded}((v1\_projpl\_1~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdcdcdhd}\\
(r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~X0)~X1~X2)~X3)))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
(r2\_projpl\_1~X0~X3~X1~X2)))){\unicdcdcdhd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~\\
(u1\_incsp\_1~X0)){\unicdcdcdhd}(r5\_projpl\_1~X0~X1~X2~X3~X4)))))))))\end{array}$$
\end{theorem}
\end{document}
