\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\_pencil\_4 (TMZiXtDwho2xupfLF6rKgGE83CHUmMGXhEk)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_matrlin : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k1\_vectsp\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_pencil\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v3\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_pencil\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_vectsp\_9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ g1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_pencil\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_pre\_topc : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v8\_vectsp\_1~X2~X0){\unicdcdcdhd}((v9\_vectsp\_1~X2~X0){\unicdcdcdhd}((v10\_vectsp\_1~\\
X2~X0){\unicdcdcdhd}((v11\_vectsp\_1~X2~X0){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~\\
X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}((v1\_matrlin~X2~X0){\unicdcdcdhd}(l1\_vectsp\_1~X2~X0))))))))))){\unicdbdjdcd}\\
(\preoh (r1\_xxreal\_0~X1~(k1\_vectsp\_9~X0~X2)){\unicdcdcdhd}(v1\_xboole\_0~(k2\_vectsp\_9~\\
X0~X2~X1)))))\end{array}
\label{hyp:ehddgdpfghfgdgehdhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_vectsp\_9~\\
X0~X1)~X2){\unicdcdcdid}(v6\_pencil\_1~(k5\_pencil\_4~X0~X1~X2))))))\end{array}
\label{hyp:ehcdadpfahfgogdgjgmgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_vectsp\_9~\\
X0~X1)~X2){\unicdcdcdid}(v5\_pencil\_1~(k5\_pencil\_4~X0~X1~X2))))))\end{array}
\label{hyp:ehbdjdpfahfgogdgjgmgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_vectsp\_9~\\
X0~X1)~X2){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_3~(k1\_vectsp\_9~X0~X1)){\unicdcdcdhd}(v4\_pencil\_1~\\
(k5\_pencil\_4~X0~X1~X2)))))))\end{array}
\label{hyp:ehbdidpfahfgogdgjgmgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k1\_vectsp\_9~\\
X0~X1)~X2){\unicdcdcdhd}(v3\_pencil\_1~(k5\_pencil\_4~X0~X1~X2))))))\end{array}
\label{hyp:ehbdhdpfahfgogdgjgmgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_pre\_topc~X0~X1=g1\_pre\_topc~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v2\_struct\_0~X0){\unicdcdcdhd}(l1\_struct\_0~X0)){\unicdbdjdcd}(v1\_xboole\_0~\\
(u1\_struct\_0~X0))\end{array}
\label{hyp:ggdgbdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}\\
((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdcdcdhd}(v7\_ordinal1~\\
X2))){\unicdbdjdcd}((v1\_pre\_topc~(k5\_pencil\_4~X0~X1~X2)){\unicdcdcdhd}(l1\_pre\_topc~(k5\_pencil\_4~\\
X0~X1~X2)))\end{array}
\label{hyp:egehpflgfdpfahfgogdgjgmgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~\\
X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}\\
((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdcdcdhd}(v7\_ordinal1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~(k4\_pencil\_4~X0~X1~X2)~(k1\_zfmisc\_1~(k1\_zfmisc\_1~\\
(k2\_vectsp\_9~X0~X1~X2))))\end{array}
\label{hyp:egehpflgedpfahfgogdgjgmgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}\\
((v13\_algstr\_0~X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~\\
X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdcdcdhd}\\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}(v7\_ordinal1~(k1\_vectsp\_9~X0~X1))\end{array}
\label{hyp:egehpflgbdpfghfgdgehdhahpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(k5\_pencil\_4~X0~X1~X2=g1\_pre\_topc~(k2\_vectsp\_9~\\
X0~X1~X2)~(k4\_pencil\_4~X0~X1~X2))))\end{array}
\label{hyp:egfdpfahfgogdgjgmgpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgcdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_pre\_topc~X0){\unicdbdjdcd}((v1\_pre\_topc~X0){\unicdbdjdcd}(X0=g1\_pre\_topc~\\
(u1\_struct\_0~X0)~(u1\_pre\_topc~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfahchfgpfehpgahdg}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfahfgogdgjgmgpfed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v8\_vectsp\_1~X1~X0){\unicdcdcdhd}\\
((v9\_vectsp\_1~X1~X0){\unicdcdcdhd}((v10\_vectsp\_1~X1~X0){\unicdcdcdhd}((v11\_vectsp\_1~X1~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v1\_matrlin~X1~X0){\unicdcdcdhd}(l1\_vectsp\_1~X1~X0))))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}(((r1\_xxreal\_0~np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~np\_\_3~\\
(k1\_vectsp\_9~X0~X1))){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_vectsp\_9~X0~X1)~X2){\unicdcdcdid}(\\
(\preoh v2\_struct\_0~(k5\_pencil\_4~X0~X1~X2)){\unicdcdcdhd}((\preoh v3\_pencil\_1~(k5\_pencil\_4~\\
X0~X1~X2)){\unicdcdcdhd}((\preoh v4\_pencil\_1~(k5\_pencil\_4~X0~X1~X2)){\unicdcdcdhd}((v5\_pencil\_1~\\
(k5\_pencil\_4~X0~X1~X2)){\unicdcdcdhd}((v6\_pencil\_1~(k5\_pencil\_4~X0~X1~X2)){\unicdcdcdhd}\\
(l1\_pre\_topc~(k5\_pencil\_4~X0~X1~X2)))))))))))\end{array}$$
\end{theorem}
\end{document}
