\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{t19\_projred2 (TMQCZ8sPTiropTP3ze8HyaCB9oy6YDEkPEF)}
\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 $ v9\_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 $ 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 $ k8\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_projred2 : {{\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}({\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 .  (l1\_incsp\_1~X0){\unicdbdjdcd}((v1\_incproj~X0){\unicdbdjded}({\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}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~\\
X3){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X4){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~X4){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}(X3{\unicdcdgdad}\\
X4)))))))))))\end{array}
\label{hyp:egedpfjgogdgahchpgkg}
\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~(u2\_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}\\
((r1\_projred2~X0~X1~X2~X3){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_incsp\_1~\\
X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~X4~X1){\unicdcdcdhd}((r1\_incsp\_1~X0~X4~X2){\unicdcdcdhd}(r1\_incsp\_1~\\
X0~X4~X3))))))))\end{array}
\label{hyp:egbdpfahchpgkgchfgegcd}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfahchpgkgchfgegcd}
$$\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}((v9\_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~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\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~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~X11~(u2\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X12 .  (m1\_subset\_1~X12~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X13 .  \\
(m1\_subset\_1~X13~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X14 .  (m1\_subset\_1~\\
X14~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X15 .  (m1\_subset\_1~X15~(u2\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X16 .  (m1\_subset\_1~X16~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X17 .  \\
(m1\_subset\_1~X17~(u2\_incsp\_1~X0)){\unicdbdjdcd}(((r4\_incsp\_1~X0~(k7\_domain\_1~\\
(u1\_incsp\_1~X0)~X4~X5)~X10){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~\\
X0)~X5~X6~X7)~X12){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~\\
X4~X7~X8)~X11){\unicdcdcdhd}((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X2~\\
X7)~X13){\unicdcdcdhd}((r4\_incsp\_1~X0~(k7\_domain\_1~(u1\_incsp\_1~X0)~X4~X9)~X14){\unicdcdcdhd}\\
((r4\_incsp\_1~X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X1~X5~X8)~X15){\unicdcdcdhd}((r4\_incsp\_1~\\
X0~(k8\_domain\_1~(u1\_incsp\_1~X0)~X2~X8~X9)~X16){\unicdcdcdhd}((r4\_incsp\_1~X0~(\\
k8\_domain\_1~(u1\_incsp\_1~X0)~X5~X9~X3)~X17){\unicdcdcdhd}(r1\_incsp\_1~X0~X3~X13))))))))){\unicdbdjdcd}\\
((r1\_incsp\_1~X0~X1~X10){\unicdcdcdid}((r1\_incsp\_1~X0~X1~X11){\unicdcdcdid}((r1\_incsp\_1~X0~\\
X2~X12){\unicdcdcdid}((r1\_incsp\_1~X0~X2~X11){\unicdcdcdid}((r1\_incsp\_1~X0~X3~X10){\unicdcdcdid}((r1\_projred2~\\
X0~X10~X12~X11){\unicdcdcdid}((X1=X2){\unicdcdcdid}((X2=X3){\unicdcdcdid}((\preoh r1\_incsp\_1~X0~X2~X14){\unicdcdcdhd}((\\
\preoh r1\_incsp\_1~X0~X3~X14){\unicdcdcdhd}(X10{\unicdcdgdad}X14)))))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
