\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{t17\_hessenbe (TMSS4sMVF8murUN1LYnUhCcsXpQBQDfdy7q)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_collsp : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}((v2\_anproj\_2~X0){\unicdcdcdhd}((v3\_anproj\_2~X0){\unicdcdcdhd}(l1\_collsp~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(\preoh (\preoh r1\_collsp~X0~X1~X2~X3){\unicdcdcdhd}((r1\_collsp~X0~X1~X2~X4){\unicdcdcdhd}((X1{\unicdcdgdad}X4){\unicdcdcdhd}(r1\_collsp~\\
X0~X1~X4~X3))))))))\end{array}
\label{hyp:ehgdpfigfgdhdhfgogcgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}((v2\_anproj\_2~X0){\unicdcdcdhd}((v3\_anproj\_2~X0){\unicdcdcdhd}(l1\_collsp~\\
X0))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((r1\_collsp~X0~X1~X2~X3){\unicdbdjdcd}((r1\_collsp~X0~X2~X3~\\
X1){\unicdcdcdhd}((r1\_collsp~X0~X3~X1~X2){\unicdcdcdhd}((r1\_collsp~X0~X2~X1~X3){\unicdcdcdhd}((r1\_collsp~\\
X0~X1~X3~X2){\unicdcdcdhd}(r1\_collsp~X0~X3~X2~X1)))))))))\end{array}
\label{hyp:ehbdpfigfgdhdhfgogcgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}((v2\_anproj\_2~X0){\unicdcdcdhd}((v3\_anproj\_2~X0){\unicdcdcdhd}((v6\_anproj\_2~\\
X0){\unicdcdcdhd}((v7\_anproj\_2~X0){\unicdcdcdhd}(l1\_collsp~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(((r1\_collsp~X0~X3~X5~X9){\unicdcdcdhd}((r1\_collsp~X0~X2~X4~X9){\unicdcdcdhd}((r1\_collsp~\\
X0~X5~X7~X8){\unicdcdcdhd}((r1\_collsp~X0~X4~X6~X8){\unicdcdcdhd}((r1\_collsp~X0~X3~X7~X10){\unicdcdcdhd}((\\
r1\_collsp~X0~X2~X6~X10){\unicdcdcdhd}((r1\_collsp~X0~X1~X3~X2){\unicdcdcdhd}((r1\_collsp~X0~X1~\\
X5~X4){\unicdcdcdhd}(r1\_collsp~X0~X1~X7~X6))))))))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}((X3=X2){\unicdcdcdid}((X1=\\
X4){\unicdcdcdid}((X5=X4){\unicdcdcdid}((X1=X6){\unicdcdcdid}((X7=X6){\unicdcdcdid}((r1\_collsp~X0~X1~X3~X5){\unicdcdcdid}((r1\_collsp~\\
X0~X1~X3~X7){\unicdcdcdid}((r1\_collsp~X0~X1~X5~X7){\unicdcdcdid}((r1\_collsp~X0~X1~X8~X9){\unicdcdcdid}(r1\_collsp~\\
X0~X8~X10~X9))))))))))))))))))))))\end{array}
\label{hyp:mgbdjdpfigfgdhdhfgogcgfg}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfigfgdhdhfgogcgfg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_collsp~X0){\unicdcdcdhd}((v3\_collsp~X0){\unicdcdcdhd}\\
((v4\_collsp~X0){\unicdcdcdhd}((v2\_anproj\_2~X0){\unicdcdcdhd}((v3\_anproj\_2~X0){\unicdcdcdhd}((v6\_anproj\_2~\\
X0){\unicdcdcdhd}((v7\_anproj\_2~X0){\unicdcdcdhd}(l1\_collsp~X0))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(((r1\_collsp~X0~X3~X5~X8){\unicdcdcdhd}((r1\_collsp~X0~X2~X4~X8){\unicdcdcdhd}((r1\_collsp~\\
X0~X5~X7~X9){\unicdcdcdhd}((r1\_collsp~X0~X4~X6~X9){\unicdcdcdhd}((r1\_collsp~X0~X3~X7~X10){\unicdcdcdhd}((\\
r1\_collsp~X0~X2~X6~X10){\unicdcdcdhd}((r1\_collsp~X0~X1~X3~X2){\unicdcdcdhd}((r1\_collsp~X0~X1~\\
X5~X4){\unicdcdcdhd}(r1\_collsp~X0~X1~X7~X6))))))))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}((X3=X2){\unicdcdcdid}((X1=\\
X4){\unicdcdcdid}((X5=X4){\unicdcdcdid}((X1=X6){\unicdcdcdid}((X7=X6){\unicdcdcdid}((r1\_collsp~X0~X1~X3~X5){\unicdcdcdid}((r1\_collsp~\\
X0~X1~X3~X7){\unicdcdcdid}((r1\_collsp~X0~X1~X5~X7){\unicdcdcdid}(r1\_collsp~X0~X9~X10~X8)))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
