\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\_projred1 (TMUWXJ4UD4bHDhui4Tpxq7ZfCtAA3QZNf92)}
\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 $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_projred1 : {{\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 $ 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.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(\preoh (X2 \in k10\_xtuple\_0~\\
X3){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}(\preoh (X4 \in k1\_relset\_1~X0~X3){\unicdcdcdhd}\\
(X2=k1\_funct\_1~X3~X4))))\end{array}
\label{hyp:ehddpfahbgchehggfhogbd}
\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~(u1\_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}\\
(((r1\_incsp\_1~X0~X2~X4){\unicdcdcdhd}(X3=k1\_funct\_1~(k1\_projred1~X0~X4~X5~X1)~\\
X2)){\unicdbdjdcd}((r1\_incsp\_1~X0~X1~X4){\unicdcdcdid}((r1\_incsp\_1~X0~X1~X5){\unicdcdcdid}(r1\_incsp\_1~\\
X0~X3~X5)))))))))\end{array}
\label{hyp:ehcdadpfahchpgkgchfgegbd}
\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}((v5\_incproj~X0){\unicdcdcdhd}((v9\_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~(u1\_incsp\_1~X0)){\unicdbdjdcd}(\preoh (\preoh r1\_incsp\_1~X0~X3~X1){\unicdcdcdhd}((\preoh \\
r1\_incsp\_1~X0~X3~X2){\unicdcdcdhd}(\preoh {\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}(m1\_subset\_1~\\
X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_incsp\_1~X0)~(u1\_incsp\_1~X0))))){\unicdbdjdcd}\\
((X4=k1\_projred1~X0~X1~X2~X3){\unicdbdjded}((r1\_tarski~(k1\_relset\_1~(u1\_incsp\_1~\\
X0)~X4)~(u1\_incsp\_1~X0)){\unicdcdcdhd}(({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}((X5 \in k1\_relset\_1~(u1\_incsp\_1~X0)~X4){\unicdbdjded}(r1\_incsp\_1~X0~X5~X1))){\unicdcdcdhd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_incsp\_1~X0)){\unicdbdjdcd}(((r1\_incsp\_1~X0~X5~X1){\unicdcdcdhd}(r1\_incsp\_1~X0~X6~X2)){\unicdbdjdcd}\\
((k1\_funct\_1~X4~X5=X6){\unicdbdjded}({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~(u2\_incsp\_1~\\
X0)){\unicdcdcdhd}((r1\_incsp\_1~X0~X3~X7){\unicdcdcdhd}((r1\_incsp\_1~X0~X5~X7){\unicdcdcdhd}(r1\_incsp\_1~\\
X0~X6~X7)))))))))))))))))\end{array}
\label{hyp:egbdpfahchpgkgchfgegbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfahchpgkgchfgegbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v6\_incsp\_1~X0){\unicdcdcdhd}((v1\_incproj~X0){\unicdcdcdhd}((v2\_incproj~X0){\unicdcdcdhd}\\
((v3\_incproj~X0){\unicdcdcdhd}((v4\_incproj~X0){\unicdcdcdhd}((v5\_incproj~X0){\unicdcdcdhd}((v9\_incproj~\\
X0){\unicdcdcdhd}(l1\_incsp\_1~X0)))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u2\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u2\_incsp\_1~X0)){\unicdbdjdcd}((X2 \in k10\_xtuple\_0~(k1\_projred1~X0~X3~X4~X1)){\unicdbdjdcd}\\
((r1\_incsp\_1~X0~X1~X3){\unicdcdcdid}((r1\_incsp\_1~X0~X1~X4){\unicdcdcdid}(r1\_incsp\_1~X0~X2~\\
X4))))))))\end{array}$$
\end{theorem}
\end{document}
