\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t17\_combgras (TMWN4ZUmkqWfqsiGAcFaVpijf2LVzpdvxJY)}
\maketitle
Let $ l1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ g1\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v6\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ u2\_incsp\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_incsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_combgras : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((l1\_incsp\_1~X0){\unicdcdcdhd}\\
((l1\_incsp\_1~X1){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_incsp\_1~\\
X0)~(u1\_incsp\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_incsp\_1~X0)~(u1\_incsp\_1~X1)))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~\\
X3~(u2\_incsp\_1~X0)~(u2\_incsp\_1~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u2\_incsp\_1~X0)~(u2\_incsp\_1~X1))))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
{\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  (g1\_combgras~X0~X1~X2~X3=g1\_combgras~\\
X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgpgngcghgchbgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_incsp\_1~X0){\unicdcdcdhd}((l1\_incsp\_1~\\
X1){\unicdcdcdhd}(l1\_combgras~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~(u2\_combgras~X0~X1~X2)){\unicdcdcdhd}\\
((v1\_funct\_2~(u2\_combgras~X0~X1~X2)~(u2\_incsp\_1~X0)~(u2\_incsp\_1~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~(u2\_combgras~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u2\_incsp\_1~X0)~(u2\_incsp\_1~X1))))))\end{array}
\label{hyp:egehpffhcdpfdgpgngcghgchbgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((l1\_incsp\_1~X0){\unicdcdcdhd}((l1\_incsp\_1~\\
X1){\unicdcdcdhd}(l1\_combgras~X2~X0~X1))){\unicdbdjdcd}((v1\_funct\_1~(u1\_combgras~X0~X1~X2)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_combgras~X0~X1~X2)~(u1\_incsp\_1~X0)~(u1\_incsp\_1~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~(u1\_combgras~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_incsp\_1~X0)~(u1\_incsp\_1~X1))))))\end{array}
\label{hyp:egehpffhbdpfdgpgngcghgchbgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_incsp\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_combgras~X2~X0~X1){\unicdbdjdcd}((v6\_combgras~X2~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~(u1\_incsp\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u2\_incsp\_1~X0)){\unicdbdjdcd}\\
((r1\_incsp\_1~X0~X3~X4){\unicdbdjded}(r1\_incsp\_1~X1~(k2\_combgras~X0~X1~X2~X3)~(\\
k3\_combgras~X0~X1~X2~X4))))))))\end{array}
\label{hyp:egidpfdgpgngcghgchbgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_incsp\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_combgras~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u2\_incsp\_1~\\
X0)){\unicdbdjdcd}(k3\_combgras~X0~X1~X2~X3=k3\_funct\_2~(u2\_incsp\_1~X0)~(u2\_incsp\_1~\\
X1)~(u2\_combgras~X0~X1~X2)~X3))))\end{array}
\label{hyp:eghdpfdgpgngcghgchbgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_incsp\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_combgras~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_incsp\_1~\\
X0)){\unicdbdjdcd}(k2\_combgras~X0~X1~X2~X3=k3\_funct\_2~(u1\_incsp\_1~X0)~(u1\_incsp\_1~\\
X1)~(u1\_combgras~X0~X1~X2)~X3))))\end{array}
\label{hyp:eggdpfdgpgngcghgchbgdh}
\end{equation}
\begin{theorem}\label{thm:ehbdhdpfdgpgngcghgchbgdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (l1\_incsp\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (l1\_incsp\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(l1\_combgras~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  (l1\_combgras~X3~X0~X1){\unicdbdjdcd}(((g1\_combgras~\\
X0~X1~(u1\_combgras~X0~X1~X2)~(u2\_combgras~X0~X1~X2)=g1\_combgras~X0~\\
X1~(u1\_combgras~X0~X1~X3)~(u2\_combgras~X0~X1~X3)){\unicdcdcdhd}(v6\_combgras~X2~\\
X0~X1)){\unicdbdjdcd}(v6\_combgras~X3~X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
