\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{t15\_projred1 (TMaFMt6jyB5cWr9Q2Rt935wmoFXVQADMYiM)}
\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 $ v8\_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 $ r2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ r4\_incsp\_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 $ k7\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u2\_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}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~\\
X2~X3~X4)~X1){\unicdbdjded}((r1\_incsp\_1~X0~X2~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}(r1\_incsp\_1~\\
X0~X4~X1))))))))\end{array}
\label{hyp:ehcdpfjgogdgdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u2\_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\_incsp\_1~X0~(k7\_domain\_1~\\
(u1\_incsp\_1~X0)~X2~X3)~X1){\unicdbdjded}((r1\_incsp\_1~X0~X2~X1){\unicdcdcdhd}(r1\_incsp\_1~X0~\\
X3~X1))))))\end{array}
\label{hyp:ehbdpfjgogdgdhahpfbd}
\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}((v8\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~\\
X0))))))){\unicdbdjdcd}({\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}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~\\
X6~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(u1\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X8 .  (m1\_subset\_1~X8~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~\\
X9~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X10 .  (m1\_subset\_1~X10~(u2\_incsp\_1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X11 .  (m1\_subset\_1~X11~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X12 .  \\
(m1\_subset\_1~X12~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X13 .  (m1\_subset\_1~\\
X13~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X14 .  (m1\_subset\_1~X14~(u2\_incsp\_1~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X15 .  (m1\_subset\_1~X15~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X16 .  \\
(m1\_subset\_1~X16~(u1\_incsp\_1~X0)){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X2~X12){\unicdcdcdhd}((\\
\preoh r1\_incsp\_1~X0~X3~X12){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X1~X11){\unicdcdcdhd}((\preoh r1\_incsp\_1~\\
X0~X4~X11){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X1~X13){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X3~X13){\unicdcdcdhd}((\\
\preoh r1\_incsp\_1~X0~X2~X14){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X4~X14){\unicdcdcdhd}((r4\_incsp\_1~X0~\\
(k8\_domain\_1~(u1\_incsp\_1~X0)~X5~X1~X4)~X12){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~\\
(u1\_incsp\_1~X0)~X5~X2~X3)~X11){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~\\
X0)~X6~X2~X4)~X13){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~\\
X6~X1~X3)~X14){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X7~X1~\\
X2)~X8){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X7~X3~X4)~X9){\unicdcdcdhd}\\
((r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~X0)~X5~X6)~X10){\unicdcdcdhd}((\preoh r1\_incsp\_1~\\
X0~X7~X10){\unicdcdcdhd}((r1\_incsp\_1~X0~X6~X15){\unicdcdcdhd}((r1\_incsp\_1~X0~X7~X15){\unicdcdcdhd}((r2\_zfmisc\_1~\\
X10~X15~X13~X14){\unicdcdcdhd}((r1\_incsp\_1~X0~X16~X8){\unicdcdcdhd}(r2\_zfmisc\_1~X7~X16~X1~X2)))))))))))))))))))))))))))))))))))))\end{array}
\label{hyp:mgbdfdpfahchpgkgchfgegbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpfahchpgkgchfgegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}((v8\_incproj~X0){\unicdcdcdhd}(l1\_incsp\_1~\\
X0))))))){\unicdbdjdcd}({\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  \\
(m1\_subset\_1~X2~(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~\\
(u2\_incsp\_1~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u2\_incsp\_1~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u2\_incsp\_1~X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~\\
X1~X2){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X4){\unicdcdcdhd}((r1\_incsp\_1~\\
X0~X1~X5){\unicdcdcdhd}(r2\_zfmisc\_1~X2~X3~X4~X5))))))))))\end{array}$$
\end{theorem}
\end{document}
