\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{t5\_rsspace3 (TMcY2JApHSYm9FcvDL3wNXbpvbHVXScsB7J)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_rsspace3 : {\iota}$ be given.
Let $ k10\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_rsspace : {\iota}$ be given.
Let $ k8\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_rsspace : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_rsspace3 : {\iota}$ be given.
Let $ v13\_algstr\_0 : {{\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 $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_normsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_rlvect\_1~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~(g1\_rlvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v13\_algstr\_0~\\
(g1\_rlvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v2\_rlvect\_1~(g1\_rlvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v3\_rlvect\_1~\\
(g1\_rlvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_rlvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v5\_rlvect\_1~\\
(g1\_rlvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v6\_rlvect\_1~(g1\_rlvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v7\_rlvect\_1~\\
(g1\_rlvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_rlvect\_1~X0))){\unicdcdcdhd}((v8\_rlvect\_1~(g1\_rlvect\_1~(u1\_struct\_0~\\
X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~X0))){\unicdcdcdhd}(l1\_rlvect\_1~\\
(g1\_rlvect\_1~(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~\\
(u1\_rlvect\_1~X0)))))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}(l1\_rlvect\_1~X0)))))))))))\end{array}
\label{hyp:ehbdfdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v13\_algstr\_0~(g1\_rlvect\_1~k1\_rsspace3~\\
(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v2\_rlvect\_1~\\
(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}\\
((v3\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~\\
(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v5\_rlvect\_1~\\
(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}\\
((v6\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v7\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~\\
(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v8\_rlvect\_1~\\
(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}\\
(l1\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3)))))))))))\end{array}
\label{hyp:mgedpfchdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k1\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  {\unicdcdadad} X8 .  {\unicdcdadad} X9 .  (g1\_normsp\_1~\\
X0~X1~X2~X3~X4=g1\_normsp\_1~X5~X6~X7~X8~X9){\unicdbdjdcd}((X0=X5){\unicdcdcdhd}((X1=X6){\unicdcdcdhd}((X2=\\
X7){\unicdcdcdhd}((X3=X8){\unicdcdcdhd}(X4=X9))))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfogpgchngdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((m1\_subset\_1~X1~X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(\\
k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~\\
(k2\_zfmisc\_1~k1\_numbers~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~k1\_numbers))))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(g1\_normsp\_1~\\
X0~X1~X2~X3~X4)){\unicdcdcdhd}(v1\_normsp\_1~(g1\_normsp\_1~X0~X1~X2~X3~X4)))\end{array}
\label{hyp:ggdgedpfchdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v13\_algstr\_0~(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v1\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~\\
(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v2\_rlvect\_1~\\
(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}\\
((v3\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~\\
(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v5\_rlvect\_1~\\
(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}\\
((v6\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}((v7\_rlvect\_1~(g1\_rlvect\_1~k1\_rsspace3~\\
(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))){\unicdcdcdhd}(v8\_rlvect\_1~\\
(g1\_rlvect\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3))))))))))\end{array}
\label{hyp:ggdgddpfchdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v13\_algstr\_0~k7\_rsspace){\unicdcdcdhd}((v2\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}((v3\_rlvect\_1~\\
k7\_rsspace){\unicdcdcdhd}((v4\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}((v5\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}\\
((v6\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}((v7\_rlvect\_1~k7\_rsspace){\unicdcdcdhd}(v8\_rlvect\_1~\\
k7\_rsspace)))))))\end{array}
\label{hyp:ggdgddpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k7\_rsspace}}}})}{\unicdcdcdhd}{({{v1\_rlvect\_1}~{k7\_rsspace}})}}\label{hyp:ggdgcdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_rsspace3}}}}\label{hyp:ggdgbdpfchdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_normsp\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_normsp\_0}~{X0}})}})}}}\label{hyp:egehpfmgbdpfogpgchngdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}\\
((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~\\
X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}\\
(l1\_rlvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v1\_funct\_1~(k9\_rsspace~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k9\_rsspace~\\
X0~X1)~(k2\_zfmisc\_1~k1\_numbers~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k9\_rsspace~\\
X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~X1)~X1)))))\end{array}
\label{hyp:egehpflgjdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}\\
((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~\\
X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}\\
(l1\_rlvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((v1\_funct\_1~(k8\_rsspace~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k8\_rsspace~\\
X0~X1)~(k2\_zfmisc\_1~X1~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k8\_rsspace~X0~X1)~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X1~X1)~X1)))))\end{array}
\label{hyp:egehpflgidpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
{{l1\_rlvect\_1}~{k7\_rsspace}}\label{hyp:egehpflghdpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k2\_rsspace3){\unicdcdcdhd}((v1\_funct\_2~k2\_rsspace3~k1\_rsspace3~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~k2\_rsspace3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_rsspace3~k1\_numbers))))\end{array}
\label{hyp:egehpflgcdpfchdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_rsspace3}}~{({{k1\_zfmisc\_1}~{({{u1\_struct\_0}~{k7\_rsspace}})}})}}\label{hyp:egehpflgbdpfchdhdhahbgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}\\
((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~\\
X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}\\
(l1\_rlvect\_1~X0)))))))))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k10\_rsspace~X0~X1)~X1)\end{array}
\label{hyp:egehpflgbdadpfchdhdhahbgdgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((m1\_subset\_1~\\
X1~X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}(((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k1\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~X0~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~k1\_numbers)))))))){\unicdbdjdcd}\\
((v1\_normsp\_1~(g1\_normsp\_1~X0~X1~X2~X3~X4)){\unicdcdcdhd}(l1\_normsp\_1~(g1\_normsp\_1~\\
X0~X1~X2~X3~X4)))\end{array}
\label{hyp:egehpfhgbdpfogpgchngdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_normsp\_1~X0){\unicdbdjdcd}((v1\_normsp\_1~X0){\unicdbdjdcd}(X0=g1\_normsp\_1~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_rlvect\_1~\\
X0)~(u1\_normsp\_0~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfogpgchngdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfchdhdhahbgdgfgdd}
$$\begin{array}{c}(\preoh v2\_struct\_0~(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~\\
k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~\\
k7\_rsspace~k1\_rsspace3)~k2\_rsspace3)){\unicdcdcdhd}((v13\_algstr\_0~(g1\_normsp\_1~\\
k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~\\
k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
k2\_rsspace3)){\unicdcdcdhd}((v2\_rlvect\_1~(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~\\
k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~k2\_rsspace3)){\unicdcdcdhd}((v3\_rlvect\_1~\\
(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
k2\_rsspace3)){\unicdcdcdhd}((v4\_rlvect\_1~(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~\\
k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~k2\_rsspace3)){\unicdcdcdhd}((v5\_rlvect\_1~\\
(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
k2\_rsspace3)){\unicdcdcdhd}((v6\_rlvect\_1~(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~\\
k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~k2\_rsspace3)){\unicdcdcdhd}((v7\_rlvect\_1~\\
(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
k2\_rsspace3)){\unicdcdcdhd}((v8\_rlvect\_1~(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~\\
k7\_rsspace~k1\_rsspace3)~(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~k2\_rsspace3)){\unicdcdcdhd}(l1\_rlvect\_1~\\
(g1\_normsp\_1~k1\_rsspace3~(k10\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
(k8\_rsspace~k7\_rsspace~k1\_rsspace3)~(k9\_rsspace~k7\_rsspace~k1\_rsspace3)~\\
k2\_rsspace3))))))))))\end{array}$$
\end{theorem}
\end{document}
