\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{t21\_projred2 (TMP1TsRN5g2KjgmQKf8tQe4WB28GjasjgK4)}
\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 $ 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.
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_projred1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\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}((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~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_incsp\_1~X0~X1~X2){\unicdcdcdhd}((\preoh \\
r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}(k2\_funct\_1~(k1\_projred1~X0~X2~X3~X1){\unicdcdgdad}k1\_projred1~\\
X0~X3~X2~X1))))))\end{array}
\label{hyp:ehidpfahchpgkgchfgegcd}
\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}((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~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_incsp\_1~X0~X1~X2){\unicdcdcdhd}((\preoh \\
r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}(\preoh v2\_funct\_1~(k1\_projred1~X0~X2~X3~X1)))))))\end{array}
\label{hyp:ehhdpfahchpgkgchfgegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\\
v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((v2\_funct\_1~X0){\unicdcdcdhd}(v2\_funct\_1~\\
X1)){\unicdbdjdcd}(k2\_funct\_1~(k3\_relat\_1~X0~X1)=k3\_relat\_1~(k2\_funct\_1~X1)~\\
(k2\_funct\_1~X0))))\end{array}
\label{hyp:ehededpfggfhogdgehpfbd}
\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}((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~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u2\_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}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~\\
X2~X4){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X1~X5){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X2~X5){\unicdcdcdhd}((\preoh r1\_projred2~\\
X0~X3~X4~X5){\unicdcdcdhd}((r1\_projred2~X0~X3~X5~X6){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X2~X6){\unicdcdcdhd}(\\
(X3{\unicdcdgdad}X6){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X7){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~X7){\unicdcdcdhd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (r1\_incsp\_1~X0~\\
X8~X7){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X8~X3){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X8~X6){\unicdcdcdhd}(k3\_relat\_1~\\
(k1\_projred1~X0~X3~X5~X1)~(k1\_projred1~X0~X5~X4~X2)=k3\_relat\_1~(k1\_projred1~\\
X0~X3~X6~X8)~(k1\_projred1~X0~X6~X4~X2))))))))))))))))))))))))\end{array}
\label{hyp:ehcdadpfahchpgkgchfgegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((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)))))))){\unicdcdcdhd}\\
((m1\_subset\_1~X1~(u2\_incsp\_1~X0)){\unicdcdcdhd}((m1\_subset\_1~X2~(u2\_incsp\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(u1\_incsp\_1~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k1\_projred1~\\
X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k1\_projred1~X0~X1~X2~X3)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_incsp\_1~X0)~(u1\_incsp\_1~X0)))))\end{array}
\label{hyp:egehpflgbdpfahchpgkgchfgegbd}
\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}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfahchpgkgchfgegcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}((v5\_incproj~X0){\unicdcdcdhd}((v9\_incproj~\\
X0){\unicdcdcdhd}(l1\_incsp\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~\\
X7~(u2\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_incsp\_1~X0~X1~X3){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~\\
X2~X4){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X1~X5){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X2~X5){\unicdcdcdhd}((\preoh r1\_projred2~\\
X0~X3~X4~X5){\unicdcdcdhd}((r1\_projred2~X0~X4~X5~X6){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X1~X6){\unicdcdcdhd}(\\
(X4{\unicdcdgdad}X6){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((r1\_incsp\_1~X0~X1~X7){\unicdcdcdhd}((r1\_incsp\_1~X0~X2~X7){\unicdcdcdhd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~(u1\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (r1\_incsp\_1~X0~\\
X8~X7){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X8~X4){\unicdcdcdhd}((\preoh r1\_incsp\_1~X0~X8~X6){\unicdcdcdhd}(k3\_relat\_1~\\
(k1\_projred1~X0~X3~X5~X1)~(k1\_projred1~X0~X5~X4~X2)=k3\_relat\_1~(k1\_projred1~\\
X0~X3~X6~X1)~(k1\_projred1~X0~X6~X4~X8))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
